[1]Pascal Fua

[1]Computer Vision Laboratory, EPFL, Switzerland 2]Daedalean AG, Zürich,
Switzerland

#  Vision-Based Power Line Cables and Pylons Detection for Low Flying Aircraft

Jakub Gwizdała  Doruk Oner  Soumava Kumar Roy  Mian Akbar Shah  Ad Eberhard
Ivan Egorov  Philipp Krüsi  Grigory Yakushev<EMAIL_ADDRESS><EMAIL_ADDRESS>*  [

###### Abstract

Power lines are dangerous for low-flying aircrafts, especially in low-
visibility conditions. Thus, a vision-based system able to analyze the
aircraft’s surroundings and to provide the pilots with a “second pair of eyes”
can contribute to enhancing their safety. To this end, we develop a deep
learning approach to jointly detect power line cables and pylons from images
captured at distances of several hundred meters by aircraft-mounted cameras.
In doing so, we combine a modern convolutional architecture with transfer
learning and a loss function adapted to curvilinear structure delineation. We
use a single network for both detection tasks and demonstrate its performance
on two benchmarking datasets. We have also integrated it within an onboard
system and run it in flight. We show with our experiments that it outperforms
the prior distant cable detection method [1] on both datasets, while also
successfully detecting pylons, given their annotations are available for the
data.

###### keywords:

Power lines detection, Transmision towers detection, Poles detection,
Delineation, Deep learning

##  1 Introduction

Low-flying aircraft, such as light planes and helicopters, are always at risk
of colliding with ground obstacles. Power lines are especially dangerous
because they are hard to see, even in good weather. In 2010, the Federal
Aviation Administration used 13 years worth of accident data from the National
Transportation Safety Board (NTSB) database to estimate that there are 76
collisions with power line per year on average and that 30% of them resulted
in fatalities [2]. Utility poles and transmission towers, which we will
collectively refer to as pylons, constitute additional dangers and are often
found in the vicinity of power line cables. Many of the accidents stem from
the fact that pilots are expected to simultaneously carry out many
tasks—steering the aircraft, navigating, monitoring the weather, and
performing mission-related tasks—that all require a high level of
concentration. This sometimes causes cognitive overload and loss of
situational awareness [3]. An automated system that would alert the pilots to
an impending collision danger would therefore be extremely valuable.

Systems that rely on a database of known obstacles, such as FLARM [4], are a
good start. However, there always is the possibility of obstacles not being in
the database. Thus, there has long been interest in developing video-based
algorithms to detect power line cables. Most early work relied on image
processing methods designed for line detection, both for detection of cables
[5, 6, 7, 8] and pylons [9]. Feature-based machine learning techniques then
started being used [6, 10, 11] but were superseded by deep-learning based
methods, both for power line cables [12, 13, 14, 15, 16] and transmission
towers [17]. Most of prior research focuses on either the detection of power
line cables or that of pylons [18] and does not treat them jointly. Methods
for power line cables detection are frequently developed in the context of
power line infrastructure inspection, where the cables are likely to be more
clearly visible than at larger distances encountered during regular small
aircraft flights. In this work we tackle this latter challenging scenario with
the aim of developing an aircraft safety system assisting the pilots in
detecting these notorious dangers.

We propose a new deep-learning based approach to jointly detect power line
cables and pylons. We use a pre-trained ConvNeXt [19] as our backbone and
formulate the detection task as one of regressing a map of distances to the
obstacles from the images. To validate our method we compare it with the
approach proposed by Stambler et al. [1] and use the accompanying NE-VBW
dataset – a public high-resolution dataset created for vision-based power line
cables detection in the context of developing aircraft safety system. We
demonstrate that combining transfer learning, a modern backbone, and a
suitable loss function designed for curvilinear structure detection boosts
performance beyond the previously proposed method [1] on their dataset.

There are other datasets that could be used to evaluate cable detection
algorithms [8, 20, 21, 22, 23, 24, 25, 26]. However, they have various
limitations, including: a viewing perspective from the level close to the
ground and mostly in urban settings [8, 26], scaled down higher resolution
images with only image-level labels [20, 21], small dataset size [25] or well
visible power lines [23, 22], including scenarios intended for testing cable
inspection methods with power lines seen from a short distance [24]. We are
facing a very different scenario with broad fields of view, distant barely
visible power lines and high-resolution images. To develop our detection
method we created our more diverse DDLN dataset, recorded with short focals
that provide information about a large area in front of the aircraft. We also
evaluate our approach on it and demonstrate the strong performance of the
proposed method. Finally, we show that, given additional annotations for
pylons, a single network can easily and successfully be trained to detect them
in addition to cables. Furthermore, when only pylon detection is needed and
small detection errors are tolerated, it performs competitively to the state-
of-the-art real-time object detector [27] of similar size.

In the following section 2 we present prior works on vision-based power line
cables and pylons detection. In section 3 we describe our model architecture
and the loss function. Section 4 presents our results, accompanied by the
descriptions of the datasets used for the evaluation, baselines we compare
with and the implementation details. Finally, we summarize our work and
discuss the limitations of the presented method together with the possible
future directions in section 5.

##  2 Related works

###  2.1 Detecting Power Lines

Vision-based detection of power line cables has a long history. Many
approaches, including some relatively recent ones, rely on image processing
techniques, such as edge detection or the Hough and Radon transforms [5, 6, 7,
8, 28, 29, 30, 31, 32, 33, 34].

Such detection methods that rely on manually designed image processing
pipelines have now been outperformed across the whole computer vision field by
learning-based methods, provided that sufficient amount of training data is
available. Thus, the approach to cable detection has changed with the advent
of deep learning techniques. Several works formulated the detection task as
one of classifying image patches according to the presence or absence of power
line cables. In [12], previously extracted image edge maps are used as the
input to the trained model. In [13], Histogram of Gradient (HoG) features are
used instead. The algorithm of [14] performs patch classification and recovers
pixel-wise segmentation indirectly by processing intermediate network
activations. That of [15] follows a hybrid approach with a hierarchical CNN
classifier over a set of different resolution of patches, followed by
traditional techniques based on edge filters and a Hough Transform variant to
precisely localize wires. These classification approaches were by design
weakly-supervised [14] for cables presence and could not benefit from a richer
information about detected objects’ appearance, which can be provided by
binary masks and exploited by segmentation-based approaches.

Another line of research focused on using object, line or key points
detectors. Nguyen et al. [35] proposed LS-Net, a single-shot detector,
combining classification and line endpoints regression tasks, performed over a
set of four overlapping grids of cells. Their method has been evaluated on a
dataset [22] featuring 800 crops extracted from full HD frames, scaled to
$512\times 512$ px patches, with power line cables clearly visible over the
terrain background. Abdelfattah et al. [24] introduced the TTPLA dataset,
featuring high-resolution aerial images captured by a drone flying within a
close distance from power line infrastructure and annotated with cable and
transmission tower masks. They also established an instance segmentation
baseline with the use of YOLACT [36], an extension of single-shot object
detector with a segmentation capability. Recently, Xing et al. [37] designed a
power line detection method for use by inspection drones. They used YOLO [38],
trained solely on synthetic data which additionally classified the inclination
of a power line cable within the detected bounding box. However, as in [24],
their data was restricted to close views of power line cables from the
perspective of a drone hovering above the inspected infrastructure. Finally, a
key point detection scheme was proposed by Dai et al. [39]. They formulate the
detection as a regression of 5 key points evenly distributed across each cable
in the input image. The points regressed by the network are subsequently
clustered and then a curve representing the complete power line cable can be
fitted to their locations. Their method was evaluated on PLDU and PLDM
datasets [23], which contain in total 860 images with $540\times 360$ px
resolution, each of which with several wires to be detected. These datasets
feature again very (PLDU) and relatively (PLDM) close views of cables, often
clearly visible against an urban (PLDU) or a mountainous (PLDM) scenery. This
makes the cable detection task easier than in our challenging setting of
detections at significant distances and over complete high-resolution image.

To leverage the precise supervision signal pixel-wise binary masks can
provide, multiple methods formulate power line cable detection as a
segmentation task. Madaan et al. [16] applied a CNN directly to the images
containing wires and treated detection as a semantic segmentation task.
Stambler et al. [1] also performed power line detection relying on
segmentation objective, however trained jointly with a regression of
parameterized line segment proposals. Both of these methods use custom network
architectures, including the use of dilated convolutions and trained from
scratch. An alternative approach involves reusing a CNN model pre-trained on a
large image datasets and fine-tuning for the cable detection task. This was
demonstrated by Zhang et al. [23] with a trimmed VGG16 model [40, 41] pre-
trained on the ImageNet dataset [42], but only on the comparatively easy PLDU
and PLDM datasets [23]. We follow a similar strategy in our own approach.

Other more recent segmentation approaches to power line cables detection
included models based on UNet [43] or UNeXt [44] architectures. Others
leverage generative adversarial networks (GANs) trained to highlight power
lines in the images [45] or added transformer blocks to CNN feature extractors
enabling global attention [46]. Most of these methods [44, 45, 46] were
evaluated on the TTPLA dataset [24], which features high-resolution close
views of cables and pylons, mostly suitable for power line infrastructure
inspection. Jaffari et al. [43] evaluated their model on IVRL [22] and PLDU
[23], both containing well visible cables crossing the images and the former
with low variability of wire appearance. Cheng et al. [44] additionally
measured their performance on the VITL dataset [25] which is rather scarce
with only 400 crops of higher-resolution images, with a size of $256\times
256$ pixels each. In this work, we evaluated the performance of the models on
two datasets – NE-VBW [1] and DDLN dataset collected by us – both of which
comprise complete, high-resolution images captured from the flying aircraft
within significant distances from the detected cables and pylons, a setting
relevant in the development of a system aiming to improve the aircraft safety.

Cable segmentation models have also been used in the field of computational
photography, along with a wire segmentation and in-painting model trained to
improve the image aesthetics by removing cables from the photographs. Chiu et
al. [26] have collected the WireSegHR dataset containing 6000 very high-
resolution images with pixel-wise annotations of wire locations. Judging by
the released test set of 420 images, the dataset contains various kinds of
wires and cables, along with other elongated objects, often with challenging
appearance and poor visibility in a diverse set of urban sceneries and in
cluttered scenes. The images were captured from the ground level as in a
typical photography setting. This makes for a different viewing perspective
than the one encountered by aircraft. In the images from our DDLN dataset and
from the NE-VBW dataset [1], on which we evaluated our method, the wires are
mostly seen by the aircraft-mounted camera during flight.

In our approach to localizing power line cables instead of segmentation we use
distance mask regression, which is a known choice for curvilinear structures
detection [47, 48, 49]. As such, our method is closest to the regression of
line segment proposals in [1]. However, we use a modern convolutional network
architecture [19], leverage transfer learning by starting with a model pre-
trained on the ImageNet dataset [42] and extend the regression loss function
with a component promoting connectivity in the detections, introduced in our
earlier work [50].

###  2.2 Detecting Pylons

The detection of transmission towers and utility poles has also been the focus
of much previous work. Close-range and mid-range detection is usually required
in the contexts of inspection [17, 51, 52, 53], mapping [54], damage
assessment [55, 56] and aircraft safety [57]. In contrast, very long-range
detection in satellite or aerial images is mostly performed in top-down views
[58, 59, 60, 61, 62]. There has been less interest in frontal detection in
aerial views at a distance of hundreds of meters, which is the focus of this
paper.

Like power lines, pylons can be treated either as thin linear objects or as
ones comprised of many line segments, which is especially useful when dealing
with the skeletal structure of larger towers. Therefore, similar image
processing tools have been used in early pylon detection work. Tilawat et al.
[9] used an IIR filter followed by a Hough transform to detect linear segments
in the images. Based on Hough counts in local windows, the probability of
pylon presence can be assessed. Similarly, Araar et al. [63] detect line
segments in the skeleton of towers using a Line Segment Detector (LSD) [64]
and the detections are filtered based on their color characteristics. Other
works rely instead on keypoint detectors. Zhang et al. [65] used SIFT [66] key
points descriptors and matched them with a set of pylon template features,
while Cerón et al. [11] used FAST [67] keypoints and ORB [68] descriptors for
training a SVM for the classification of image regions. Sampedro et al. [10]
obtained the HoG pylon features and used them to train two multi-layer
perceptron (MLP) networks. The former performs binary classification of image
regions for pylon detection, while the latter was used for classification of
pylon structure types.

As with power lines, newer techniques rely on deep learning methods for pylon
detection. Bian et al. [17] designed an unmanned aerial vehicle (UAV)
navigation system for power line inspection. It relies on detecting
transmission towers, for which they used a customized version of Faster R-CNN
[69]. Other works leverage various versions of the YOLO [38] detector [52, 55,
56, 61, 53, 57, 70]. Detections from an urban road-level perspective also tend
to rely on object detectors – Watanabe [51] used SSD [71] and Zhang et al.
[54] used RetinaNet [72].

In our work, we depart from these standard approaches and formulate the task
as distance mask regression, as when detecting cables. We compare distance
mask based pylon detection performance with that of RT-DETR [27], one of the
state-of-the-art real-time object detectors, enhanced with SAHI [73] –
inference and fine-tuning strategies for high-resolution images. We show that
when distinguishing individual pylons as separate objects is not required and
small detection errors are tolerated, our model using similar numbers of
learnable network weights delivers a competitive performance, as measured by
the metrics evaluating detection outputs.

Transmission towers, thanks to their overall greater size and larger thickness
of their components, should be easier to detect than power line cables. Their
presence is naturally related to that of power line cables. Several works have
leveraged this presence as a useful contextual cue to facilitate the
subsequent detection of power lines. A first subgroup of such techniques
relies on hierarchical and algorithmic approaches to infer cable presence
given tower detections. Haroun et al. [59] infers power line locations from
satellite images by simply connecting pairs of closest detected transmission
towers forming a single chain of connections. In a more sophisticated
algorithm, after detecting the pylons from the point cloud data, Flanigen [3]
used the heights, the distances, and the angles formed by a series of detected
towers to infer possible cable connections between the pylons. In another
hierarchical manner, Li and Chen [74] used pylon detections to restrict the
regions of interest for the subsequent detection of cables. In the absence of
pylon detections, either because there are none or because of missed
detections, they proposed a second, cable-only detection pipeline. These
approaches can be understood as using pylon detection as the way of guessing
or restricting the area for cables detection. As observed in Li and Chen [74],
such methods have only limited applicability when pylons can be detected first
[59, 3]. Otherwise, when the support points of the hanging cable are not
visible, there remains a need for handling cable-only detection [74]. In our
work, we show that the joint detections of both cables and pylons is feasible
using a single deep learning model, without any specific supervision relating
both of the detections.

Another group of techniques link cable and pylon detections more tightly.
Combined evidence for cables and pylons presence was used by Zhang et al. [65]
by formulating a Bayesian framework including terms modeling the spatial
correlation between the two object types. This formulation was used to
determine whether a line detected by a line detector should be considered as a
power line cable or not. The method was further developed in [75]. Its
flexibility has been increased by replacing the spatial correlations between
pylons and cables by an unconstrained set of auxiliary regions, automatically
selected in the vicinity of hypothetical power line detections. The results
were evaluated on the BHU dataset [65], which features relatively low
resolution images and power line infrastructure seen from ground level. In our
work, we tackle a different setting, with power lines infrastructure captured
in high-resolution images but further from the camera and seen from the
perspective of an aircraft-mounted camera with cables visible against various
backgrounds, mostly originating from the terrain behind them.

Most recently, deep learning methods were tried for joint power line cables
and pylon detection [76, 77, 18, 78]. Two of these methods [18, 78] are
instance segmentation approaches that yield detailed segmentation masks for
high resolution inputs. Both of them were evaluated on datasets gathered by
UAVs. They comprise close views of the power line infrastructure seen from the
top. Zhu et al. [18] evaluated their method additionally on the TTPLA dataset
[24], which is mostly suitable for power line inspection related tasks. Feng
et al. [76] and Zhencang et al. [77] opted for modified YOLOv3 [79] object
detectors. The former used the detection and clustering of auxiliary targets,
such as transmission towers, to determine power distribution corridors area
and filter out power line detections outside of this zone, a method
reminiscent of the algorithmic approaches discussed above [59, 74]. The method
was evaluated on a dataset of low-voltage power lines in urban setting, in
close, inspection views of the power line infrastructure. Finally, Zhencang et
al. [77] added to an object detector’s architecture a relational suggestion
network with an attention mechanism designed to establish relationships
between power lines and pylons. While their dataset features more distant
views of power lines than others, the images are captured in relatively low
resolution of $640\times 480$ pixels, by an infrared camera and from a low
altitude of at most $60\text{\,}\mathrm{m}$ above ground. These are therefore
quite different from the ones we use.

##  3 Method

To jointly detect cables—power and telephone lines—and pylons—utility poles
and transmission towers—we train a single CNN based on a modern backbone.
Taking our inspiration from the delineation work of [50], we train it to
produce distance maps, one from the detected cables and other from the
detected pylons. This effectively turns the detection problem into a
regression one in which we treat a zero distance as a detection. Our network
can be used for cable- or pylon-only detection by simply removing one of its
heads.

For cable detection, we differ from the approach of Stambler et al. [1] by
predicting only the undirected distance to the closest wire, as opposed to
distance, direction, and a binary value indicating the presence or absence of
a cable. The superior performance of our model, which we demonstrate in the
result section, is achieved by combining transfer learning, a modern
convolutional backbone, and a loss function that favors cable-like topologies.

###  3.1 Network Architecture

Fig. 1 depicts the architecture of our model. It comprises two main parts, a
pre-trained convolutional feature extractor and two small output heads that
regress distances maps from the features.

Figure 1: Architecture of the joint power line cables and pylons detection
model. Output heads regress cables and pylons distance masks directly from the
common feature map $F{}$ generated by the fine-tuned truncated ConvNeXt-Tiny
feature extractor.

Feature Encoder. As our backbone, we use ConvNeXt-Tiny [19] pre-trained on the
ImageNet [42] dataset. We discard its classification head and only use the
feature extractor. We can reduce the original model’s size by adapting the
number of blocks $B$, as defined in [19], in the feature extractor by removing
the final ones. In this way, we generated the following variants of our model:

  * •

DDLN-S (small) with $B=(3,3,1)$,

  * •

DDLN-M (medium) with $B=(3,3,5)$,

  * •

DDLN-L (large) with $B=(3,3,9)$,

  * •

DDLN-H (huge) with $B=(3,3,9,1)$.

We do not use the layer normalization and strided convolution following the
third stage in the complete ConvNeXt-Tiny model. Therefore our models output a
$384\times(H/16)\times(W/16)$ feature map $F$, where $(H,W)$ is the resolution
of the input image. For DDLN-H the feature map is
$768\times(H/32)\times(W/32)$ and the model requires an additional spatial
downsampling level.

Output Heads. They are implemented using pixel-wise regression layers coded as
$1\times 1$ convolutions. They are applied directly to the feature map $F$
computed by the feature extractor. Distance predictions are obtained using a
clamped-ReLU activation, restricting the outputs to the $[0,1]$ range. Zero
denotes the detected object, either a cable or a pylon depending on the model
head. One corresponds to a set maximal distance value $d_{\rm max}$ that
denotes an area sufficiently far away from the objects of interest. In our
experiments, we take $d_{\rm max}$ to be 128 pixels at the original input
image resolution.

###  3.2 Loss Function

Given an image ${\bf I}$, our network outputs two distance maps
$\hat{\mathbf{x}}^{c}$ and $\hat{\mathbf{x}}^{p}$, one from the cables and the
other from the pylons. Let us assume we are given ground-truth versions
$\mathbf{x}^{c}$ and $\mathbf{x}^{p}$ of these distance maps thresholded at
the $d_{\rm max}$ distance introduced above and linearly scaled to the range
$[0,1]$. Our goal is to train the network so that predictions and ground-truth
are as similar as possible to each other, while enforcing good connectivity in
the cable reconstruction. To this end, we define a composite loss function
that is a weighted sum of a data term and a connectivity term, which we
describe below.

Data Loss Term $\mathcal{L}_{\rm dat}{}$. The simplest way to write a data
loss term would be in terms of the Mean Square Difference (MSD) between
$\hat{\mathbf{x}}^{c}$ and $\mathbf{x}^{c}$ on one hand, and
$\hat{\mathbf{x}}^{p}$ and $\mathbf{x}^{p}$ on the other. However, this would
not account for the imbalance between the number of pixels that belong to
target structures and the much larger one of those that do not. To do so, let
us consider the frequency function $f^{k}$ that associates to each pixel
$\mathbf{x}^{k}_{i}$ its distance value occurrence frequency in
$\mathbf{x}^{k}$, where $k$ can be either $c$ for cable of $p$ for pylon. In
other words, we write

$f^{k}(\mathbf{x}^{k}_{i})=\frac{1}{N}\sum_{1\leq j\leq
N}\mathbbm{1}{}(\mathbf{x}^{k}_{j}=\mathbf{x}^{k}_{i})\;,$ (1)

where $N$ is the total number of pixels in $\mathbf{x}^{k}$ and the
$\mathbf{x}^{k}$ distance masks are discretized to integer values. We use $f$
to write the weighted version of MSD

$\displaystyle\mathcal{L}_{\rm dat}(\hat{\mathbf{x}}^{k},\mathbf{x}^{k})$
$\displaystyle=\sum_{1\leq i\leq
N}w(\mathbf{x}^{k}_{i})\|\hat{\mathbf{x}}^{k}_{i}-\mathbf{x}^{k}_{i}\|^{2}\;,$
(2) $\displaystyle~w(\mathbf{x}^{k}_{i})$
$\displaystyle=\left(\log(1+\epsilon+f^{k}(\mathbf{x}^{k}_{i}))\right)^{-1}\;,$

where $\epsilon$, which we set to 0.02, has the purpose of preventing division
by values close to 0 and therefore caps the weights at values lower than
$\left(\log(1+\epsilon)\right)^{-1}$. This scheme gives more weight to the
sparse features of interest (cables and pylons) and less to the more extensive
background regions, mitigating the imbalance in their occurrence frequency. At
the same time, it gives greater weights to areas in the $(0,1)$ range than to
the 0-valued areas at the precise location of the detected objects. However,
thanks to the logarithmic scaling, the difference in weights remains smaller
by an order of magnitude than what it would be using inverse frequency weights
and avoids excessive penalization of the most frequent distance values – 0 and
1, corresponding to target objects and distant background, respectively.

Connectivity Loss Terms $\mathcal{L}_{\texttt{MALIS}}$. The loss function
$\mathcal{L}_{\rm dat}{}$ as described above is a pixel-wise loss. When the
annotations do not perfectly coincide with the imaged structures, which is
often the case, networks trained using such per-pixel losses produce binary
masks plagued by topological errors, such as interruptions and missed
junctions. In earlier work [50], we introduced a loss function
$\mathcal{L}_{\texttt{MALIS}}{}$ whose minimization forces to produce distance
maps with the same topology as that of the ground truth, even if the actual
location of the detection is somewhat imprecise. The difficulty in writing
such a loss is to express this requirement in the form of a differentiable
loss function that can be used to train a deep network. The central idea of
this earlier approach is to forgo enforcing connectivity of the pixels
annotated as belonging to linear structures and whose location may be
inaccurate. Instead, we express the connectivity of the annotated structures
in terms of the disconnections that they create between regions annotated as
background. More precisely, we require that two regions separated by a line in
the ground truth, are also separated in the prediction. This effectively
enforces continuity of the predicted cables. By requiring that connected
components of pixels annotated as background remain connected in the
prediction, we prevent predicting false positives. To capture dead-ending
segments, we compute our loss in small image windows, which are likely to be
subdivided even by short cable sections. In other words, we re-purpose the
differentiable machinery proposed in the MALIS segmentation algorithm [80, 81]
to enforce the dis-connectivity of image regions separated by cables, which we
illustrate in the figure 2. For more details, we refer the interested reader
to our earlier publication.

Figure 2: A selection of two outputs for two loss function variants
illustrating the application of $\mathcal{L}_{\texttt{MALIS}}$ connectivity
loss term. The rows contain from left to right: an input image patch, a
ground-truth cables segmentation mask, prediction of a model trained with MSD
loss alone and prediction of a model trained with MSD loss combined with
$\mathcal{L}_{\texttt{MALIS}}$ connectivity term. The two last images in each
row contain distance masks in which $[0,1]$ values range was mapped to a
grayscale range from white to black. $\mathcal{L}_{\texttt{MALIS}}$ is applied
to distance mask predictions within the marked square windows. Points A and B
belong to two disjoint background regions, which should be separated by the
cable detection in between. In the exemplary distance masks predicted for the
cables with independent MSD loss supervision these points can be joined with a
path traversing through not sufficiently small distance values. This can
result in a broken cable detection in the final segmentation, i.e. in a
thresholded distance mask. Such segmentation means having an unwanted merger
of the background regions which $\mathcal{L}_{\texttt{MALIS}}$ aims to
prevent.

Composite Loss Term $\mathcal{L}_{\rm dat}{}$. Given the $\mathcal{L}_{\rm
dat}{}$ and $\mathcal{L}_{\texttt{MALIS}}{}$ loss terms defined above, we
optimize the composite loss function

$\displaystyle\mathcal{L}((\hat{\mathbf{x}}^{c},\hat{\mathbf{x}}^{p}),(\mathbf{x}^{c},\mathbf{x}^{p}))$
$\displaystyle=\mathcal{L}_{\rm
dat}^{c}(\hat{\mathbf{x}}^{c},\mathbf{x}^{c})+$ (3)
$\displaystyle\mathcal{L}_{\rm dat}^{p}(\hat{\mathbf{x}}^{p},$
$\displaystyle\mathbf{x}^{p})+\lambda\mathcal{L}_{\texttt{MALIS}}{}(\hat{\mathbf{x}}^{c},\mathbf{x}^{c})$

where upper indices $c$ and $p$ differentiate between cables and pylons and
$\lambda$ is a weighting factor for the MALIS loss component, which we set to
0.2.

###  3.3 System Deployment

We deployed DDLN-S, our smallest model variant for joint cables and pylons
detection, to Eval Kit, Daedalean’s hardware flight assistant system and set
it up on a Robinson R44 Raven II helicopter. In order to achieve that, the
PyTorch representation of the model and its trained weights were first
converted into the ONNX format and then optimized using TensorRT API for the
target system and an NVidia GeForce 3060 GPU card. To increase the inference
speed, we additionally used half-precision floating point format for the
network.

We also developed a pre- and post-processing pipelines, applied to the model’s
inputs and to its predictions, respectively. The $4096\times 3000$ px raw
images captured by the camera are debayered, padded and split into $1024\times
1024$ px non-overlapping patches. The patches are processed by the GPU in
batches of size 4 and then stitched into a $128\times 93$ px output
representing detections over the complete camera frame. In parallel, dense
inverse search optical flow [82, 83] is applied to the two subsequent
downsampled camera frames to estimate the movement in the image. Once both
results are available, the previous model prediction for the complete frame is
warped according to the optical flow output and then it is combined with the
prediction for the current frame by computing the average of the two. This
averaging operation aims to make the result less susceptible to both false
positive and false negative noise. In the following step, we threshold the
averaged distance masks turning cable and pylon detections into segmentation
masks. Finally, these binary masks are upscaled to the original image size,
overlapped with the input image and the result is forwarded to the system’s
user interface.

##  4 Results

###  4.1 Datasets

There are many publicly available annotated datasets that can be used to
validate power line detection algorithms. They include USF [8], IVRL [20, 21,
22], PLDU and PLDM [23], TTPLA [24], VITL [25] and WireSegHR [26]. As
previously discussed in section 1, these have their shortcomings, including:
viewing perspective and setting different from the one encountered in manned
aircraft flights [8, 26], small size of the dataset with crops of larger
images [25], containing scaled down larger images, with low resolution and
image-level labels [20, 21] or featuring clearly visible power lines [22, 23,
24], oftenly seen from a short distance. The latter are more suitable to test
algorithms designed to guarantee the safety of UAVs operating in the proximity
of the power line infrastructure, mostly for inspection purposes. However, in
this work, we want to perform the detection at longer ranges for collision-
avoidance purposes. Furthermore, we are doing it in images captured by
aircraft-mounted cameras with short focal lengths to cover the large area in
front of the aircraft required to ensure safety.

Figure 3: Examples of the images from the NE-VBW dataset [1] (left) and from
our DDLN dataset (right).

To start developing an aircraft safety system for cable and pylon obstacles
avoidance, we created and labeled our own dataset, which we will refer to as
the DDLN dataset. The NE-VBW dataset [1] is the publicly available dataset
that most resembles ours and was created with the same purpose in mind. We
tested our algorithm on both datasets and we provide additional details below.

NE-VBW Dataset [1]. It is a public dataset containing 109 images of size up to
$6576\times 4384$ px. They were extracted from recordings captured by
aircraft-mounted, forward facing cameras with a large focal length. The high
resolution and the large focal length of the cameras allowed for the capture
of power line cables at long ranges within a narrow field of view – 25°
horizontally and 18° vertically. The images were labeled using pixel-wise
masks of power line cables. All data originates from flights conducted around
Pittsburgh, PA in the USA.

DDLN Dataset. We built it ourselves from videos acquired during flights over
Switzerland, the UK, Brazil, and the USA. It contains 865 images of size
$4096\times 3000$ px each. They were recorded by aircraft-mounted, forward
facing cameras with a wide field of view – up to 81° horizontally and 64°
vertically. It is significantly wider than the one in the images from the NE-
VBW dataset. This makes the detection task more challenging but provides more
context by covering a larger area in front of the aircraft. The videos were
recorded at the rate of 6 frames per second, but the annotated frames were
extracted with sufficient time intervals between them to provide for a
diversified scene content. Polyline approximations of individual power line
cables were generated by hand and bounding boxes were used to denote the
pylons. Additionally, exclusion areas, that is, regions containing thin
objects not associated with cables—flagpoles, cranes, communication
towers—were marked by bounding boxes. We did not use them to create training
data and excluded them from the pylon detection performance evaluation.

###  4.2 Baselines

We compare the performance of our models against three baselines: DeepWireCNN
[1], PIDNet-S [84] and RT-DETR [27]. We chose the first as the only method
which has been so far evaluated for the detection of far-away cables on the
NE-VBW dataset. We chose the other two as modern representatives of semantic
segmentation and object detection network architectures, respectively, and
because they were designed with issues of inference speed in mind. This is an
important consideration for the deployment of deep networks that must run in
real-time on hardware that can be installed in an aircraft.

We compare cable detection performance obtained by our models against that of
DeepWireCNN on both datasets, while the remaining comparisons are done on the
DDLN dataset alone.

We present each of the baselines in more detail below.

DeepWireCNN [1] – cable detection. It is a cable detection model introduced
jointly with the NE-VBW dataset. We reimplemented the CNN as described in the
publication. However, we did not reimplement the post-processing steps
involving clustering of the regressed line segments and a refinement with
moving least squares which ultimately led to the generation of segmentation
masks at input image resolution. This makes it simple to compare the
performance of DeepWireCNN against ours using the coarse resolution
predictions of both models. They are 16 times spatially downsampled with
respect to the input image size.

PIDNet-S [84] – cable detection. This is a member of a family of models
designed for semantic segmentation. We train it without boundary-aware loss
components, thus also without D branch supervision. We did this because these
components are mostly useful for multi-class semantic segmentation with
multiple, potentially confusing, object boundaries in the image. These issues
do not arise for power line cables. We start from the ImageNet-pretrained
checkpoint of the PIDNet-S model and add at the end of it a single $2\times 2$
strided convolution layer to match the downsampling factor of our models. We
also replaced the SGD optimizer with Adam [85] and did not use the poly
learning rate strategy.

RT-DETR [27] – pylon detection. This object detector uses the ResNet18
backbone [86]. As PIDNet-S, it has been designed with real-time applications
in mind. It builds on top of transformer-based object detectors. We
additionally combine it with SAHI [73], training and inference strategy for
object detection in high-resolution images. We evaluate two variants of
patched input scales. In both cases, we run the object detector over full-
resolution image and its split into $1024\times 1024$ overlapping patches,
appropriately resizing the inputs for the detector and combining all of its
outputs. In the second variant we additionally use similarly generated sets of
$512\times 512$ and $256\times 256$ patches and add their detection results to
the output. For evaluation, we rescale the final predicted bounding boxes to
the downsampled output resolution of our model, use them to generate binary
segmentation masks and convert them into distance masks. Also, for this model
we initialize it with the pretrained weights provided with the official model
implementation, obtained from training on the Objects365 [87] dataset and
subsequent fine-tuning on the COCO [88] dataset.

PIDNet-S [84] – joint cables and pylons detection. We added additional
segmentation heads to three branches of the PIDNet-S model to enable joint
prediction of cables and pylons segmentation masks, as in our own model. In
the loss function, we duplicate the cross-entropy term for the newly added
pylon branch and add a weighting hyper parameter by which the added pylon
segmentation loss components are multiplied. As before, we do not use
boundary-aware loss components, start from the pre-trained model and use the
Adam optimizer without learning rate scheduler. To match the downsampling
factor of our models the final segmentation outputs for cables and pylons are
bilinearly downsampled before being passed to the loss function.

###  4.3 Evaluation Metrics

To compare the different models, we computed pixel-wise precision, recall and
F1 score for the generated cable and pylon segmentation masks. To obtain these
masks for our models from the predicted distance masks we simply threshold
them at a selected distance value.

We also report correctness, completeness and quality (CCQ) metrics [89]. These
metrics were originally applied to road extraction task and defined in terms
of _lengths_ of the extracted and ground-truth road segments. We implement
them with respect to the _areas_ of foreground objects, measured in the output
resolution on the binary segmentations obtained from thresholded distance
masks. Correctness and completeness operate as standard precision and recall,
respectively, but include a controllable tolerance for small detection errors
within the defined error margin. Those inaccuracies can stem from, for
instance, imprecisions in localizing the object by the detection network or
the $\mathcal{L}_{\texttt{MALIS}}$ loss component in cable detections, which
can cause them by forcing mergers in predictions of disconnected cable line
segments. In our experiments we set the tolerated error distance to a value
corresponding to the closest 8-pixel neighborhood of the ground-truth
segmentation foreground. In other words, the correctness and completeness
should be considered as relaxed precision and recall, respectively. This
relaxation can be implemented with dilation by 1 pixel of ground truth area
for considering true positive detections, decreasing accordingly the area in
which the detections are treated as false positives and counting as a false
negative any exact ground-truth pixel which is not covered by 1-pixel-dilated
exact prediction. Effectively, these metrics are insensitive to the spurious
or lacking detections in the predicted segmentation masks if those are found
within the tolerated error distance from the exact ground-truth.

We did not use a held out test set for either of the datasets. Instead, in the
development of our model we mostly relied on a fixed train/validation split of
the DDLN dataset, as well as on a 5-fold cross validation split. For the
performance comparisons presented below, we report the validation performance
obtained from running a single 5-fold cross validation for each model. Since
both datasets contain temporally dependent image sequences, we partitioned the
data into folds by splitting on the recordings level. Additionally, for the
5-fold cross validation we grouped the recordings so as to minimize the
overlap of the same geographical locations within single folds.

The reported metrics are for the model states at epochs at which the mean
validation quality of the target object segmentation was the highest during
each respective 5-fold cross validation run. The target objects are cables or
pylons, depending on the specific performance comparison presented in the
tables below. For models performing joint cables and pylons segmentation, the
cables are selected as target objects and pylon detection metrics are reported
as achieved at the respective epochs. We report the means and standard
deviations of each metric computed across all validation folds.

###  4.4 Performance Evaluation

Table 1: Comparison of power line cables detection performance between our
method and DeepWireCNN (DWCNN) [1] on the NE-VBW and DDLN datasets. Results
for the two size variants of our models are shown – DDLN-S and DDLN-L. DDLN-S
has 2.7 million trainable parameters, about the same amount as the DeepWireCNN
model.

Method | Object | FPS | Precision | Recall |  F1 | Correctness | Completeness | Quality
---|---|---|---|---|---|---|---|---
|  |  | NE-VBW
DWCNN | cables | $9.2$ | $0.71\pm 0.07$ | $0.63\pm 0.06$ | $0.66\pm 0.06$ | $0.73\pm 0.07$ | $0.72\pm 0.07$ | $0.57\pm 0.08$
DDLN-S | cables | $12.8$ | $0.74\pm 0.09$ | $0.70\pm 0.08$ | $0.71\pm 0.04$ | $0.79\pm 0.06$ | $0.79\pm 0.07$ | $0.65\pm 0.05$
DDLN-L | cables | $9.1$ | $0.73\pm 0.07$ | $0.83\pm 0.06$ | $0.78\pm 0.06$ | $0.79\pm 0.07$ | $0.90\pm 0.05$ | $0.72\pm 0.07$
|  |  | DDLN
DWCNN | cables | $9.2$ | $0.52\pm 0.09$ | $0.42\pm 0.06$ | $0.47\pm 0.07$ | $0.54\pm 0.09$ | $0.49\pm 0.06$ | $0.35\pm 0.07$
DDLN-S | cables | $12.8$ | $0.56\pm 0.12$ | $0.64\pm 0.04$ | $0.59\pm 0.09$ | $0.65\pm 0.14$ | $0.74\pm 0.03$ | $0.53\pm 0.10$
DDLN-L | cables | $9.1$ | $0.71\pm 0.06$ | $0.73\pm 0.05$ | $0.72\pm 0.05$ | $0.83\pm 0.05$ | $0.80\pm 0.04$ | $0.69\pm 0.06$
DDLN-S | cables | 12.8 | $0.59\pm 0.08$ | $0.60\pm 0.05$ | $0.59\pm 0.06$ | $0.67\pm 0.08$ | $0.70\pm 0.05$ | $0.52\pm 0.07$
(joint) | pylons | $0.41\pm 0.08$ | $0.40\pm 0.07$ | $0.39\pm 0.04$ | $0.68\pm 0.07$ | $0.56\pm 0.10$ | $0.43\pm 0.06$
DDLN-L | cables | 9.1 | $0.71\pm 0.05$ | $0.75\pm 0.05$ | $0.73\pm 0.04$ | $0.83\pm 0.04$ | $0.82\pm 0.04$ | $0.70\pm 0.04$
(joint) | pylons | $0.41\pm 0.10$ | $0.61\pm 0.04$ | $0.48\pm 0.08$ | $0.71\pm 0.11$ | $0.76\pm 0.03$ | $0.58\pm 0.07$

Bolded results highlight the best mean metric value within each group of the
given dataset and the detected object type.

Figure 4: Exemplary predictions of the three models trained on the NE-VBW
dataset [1]: DeepWireCNN [1], DDLN-S and DDLN-L. The inputs are $1536\times
1536$ px crops from full-resolution images from the validation set.
Predictions were generated by models initialized from checkpoints at epochs
with highest validation cable segmentation quality metric.

Cable Only Detection.

Table 1 shows the main performance comparison between the two variants of our
model and the DeepWireCNN [1], both on the NE-VBW dataset and our DDLN
dataset. We also measured inference speed as a number of processed $1\times
3\times 4096\times 3000$ random input tensors per second (i.e. frames per
second, FPS) on a NVidia V100 GPU, using automatic mixed-precision arithmetic.
Additionally, Figure 4 depicts qualitative results. After tuning the
hyperparameters of the DeepWireCNN model we achieved 0.70$\pm$0.09 AP for the
segmentation of cables at coarse resolution and the values for the remaining
metrics as reported in the first row of the Table 1. The results on NE-VBW
dataset demonstrate that both the small and the large variant of our model
outperform DeepWireCNN on all cable detection metrics. Additionally, they do
so without increasing the inference time. We also observed that our models
achieve high performance scores earlier in the learning process than the
DeepWireCNN. We attribute this to the initialization of the networks with the
pretrained weights. Focusing only on our models, it is also clear that the
larger variant achieves better or equivalent performance to its smaller
counterpart across all cable detection metrics.

Figure 5: Exemplary predictions of the two size variants of our model trained jointly for cable and pylon detection on the DDLN dataset. The inputs are $1024\times 1024$ px crops from full-resolution images from the validation set. Predictions were generated by models initialized from checkpoints at epochs with highest validation cable segmentation quality metric. Table 2: Comparison of cable detection performance on DDLN dataset between our models and PIDNet-S [84], a modern semantic segmentation network for real-time applications. PIDNet-S was trained for cable detection only, while our models were trained jointly for cables and poles detection. Method | Size | FPS | Precision | Recall |  F1 | Corr. | Compl. | Quality
---|---|---|---|---|---|---|---|---
PIDNet-S | $7.6$ | $22.2$ | $0.74\pm 0.07$ | $0.69\pm 0.05$ | $0.71\pm 0.06$ | $0.81\pm 0.07$ | $0.76\pm 0.04$ | $0.65\pm 0.07$
DDLN-M | $7.5$ | $10.7$ | $0.71\pm 0.07$ | $0.71\pm 0.05$ | $0.71\pm 0.06$ | $0.83\pm 0.06$ | $0.80\pm 0.04$ | $0.68\pm 0.06$

In Table 2 we compare the cable detection performance of our DDLN-M model
against that of PIDNet-S [84]. As the latter is designed for real-time
performance, we also report the model size and inference speeds for the
networks. The size is given as the number of millions of trainable parameters
in the respective model. Regarding detection performance, our DDLN-M model,
which has the same size as PIDNet-S, yields slightly better cable detection
quality and a similar F1 score. Given this result, we conducted additional
experiments with PIDNet-S trained to simultaneously detect cables and pylons,
as previously described in section 4.2, and compared its performance on both
tasks with our joint detection model, which we detail below.

Table 3: Comparison of joint cables and pylons detection performance on DDLN dataset between DDLN-M and PIDNet-S [84]. PIDNet-S was trained for cable and pylon detection jointly as described in section 4.2. The reported metrics are measured at the epochs with the highest validation cable detection quality. Method | Object | Precision | Recall |  F1 | Corr. | Compl. | Quality
---|---|---|---|---|---|---|---
PIDNet-S | cables | $0.70\pm 0.05$ | $0.68\pm 0.04$ | $0.69\pm 0.04$ | $0.81\pm 0.03$ | $0.76\pm 0.04$ | $0.65\pm 0.05$
pylons | $0.55\pm 0.04$ | $0.59\pm 0.02$ | $0.57\pm 0.03$ | $0.71\pm 0.04$ | $0.68\pm 0.02$ | $0.53\pm 0.03$
DDLN-M | cables | $0.73\pm 0.06$ | $0.70\pm 0.06$ | $0.71\pm 0.05$ | $0.86\pm 0.06$ | $0.78\pm 0.05$ | $0.69\pm 0.07$
pylons | $0.52\pm 0.11$ | $0.56\pm 0.04$ | $0.53\pm 0.06$ | $0.74\pm 0.10$ | $0.66\pm 0.04$ | $0.54\pm 0.05$

Joint Cable and Pylon Detection.

To continue the comparison of our method with the PIDNet-S [84] baseline, we
added to the latter a second segmentation output head to enable it to also
perform pylon detection. We report our results in Table 3 and shown in Figure
6 the evolution of the validation score during training. Our DDLN-M model
still outperforms PIDNet-S on the cable detection quality, as well as on the
previously equal F1 score. It also delivers minimally higher pylon detection
quality, while it records a slightly lower F1 score than PIDNet-S. Identical
observations can be made by looking at the Figure 6 where validation
performance curves of our DDLN-M model are consistently, and across all
validated epochs, above those of PIDNet-S for cable detection quality and F1
score. As in the metrics reported in Table 3, pylon detection quality of
DDLN-M is also minimally above that of PIDNet-S, while pylon detection F1
score is slightly below the one of the segmentation baseline. Furthermore,
recall from Table 1 that DDLN-L performs even better.

Regarding the network inference speeds, PIDNet-S is the faster one with 22.2
FPS compared to our 10.7. However, this high speed provided by PIDNet-S may
not be absolutely necessary for a possible deployment of our method. We have
successfully integrated DDLN-S, the less performant but faster smaller
alternative of our model, in the hardware system operating in real-time
onboard of a helicopter, as described in section 3.3. We run the system in
flight and reached average inference speed of 5 FPS. This is already a good
running speed for the application purpose of an aircraft safety system.

Additional results for our models trained jointly for cables and pylons
detection on the DDLN dataset are shown at the bottom of Table 1. Qualitative
results are shown in Figure 5. The cable detection performance metric is not
significantly affected by adding joint detection of pylons. It can be
hypothesized that the model trained for cable detection alone has already
implicitly learned to rely on pylon presence contextual cues. Alternatively,
the models trained for the joint prediction leverage the supervision for the
pylon detection task to adapt their cable detection outputs, but affecting the
detection of power lines both positively and negatively, with both
contributions equalizing in the final scores. However, as for independent
cable detection, pylon detection performance also improves with increased
model size.

In other words, relying on pylon detections for cable detection, which the
network may learn to do in joint prediction setting, can be a double-edged
sword. Power line cable presence does not have to be accompanied by a visible
presence of pylon structures. Multiple occlusion scenarios can occur when the
pylons exist but are hidden behind terrain, buildings etc. or are outside of
the current field of view. Furthermore, for cables close to the camera, the
associated pylons, even if contained within the camera frustum, may fall out
of the receptive field of the network for the given cable section. Moreover,
the power line cables can also be attached to other structures, e.g. mounted
on the rooftops of the buildings. Finally, the cables or other wiry objects
which also pose the danger to the low-altitude aircraft do not have to be
transmission lines per se. As such they are not related to the presence of
transmission towers. Therefore, in some scenarios pylon detection may be
helpful in finding poorly visible cables by inferring their presence from the
better visible pylons to which these cables are most likely attached. In other
situations, the model could rely too heavily on pylon detections to determine
whether the power line cable exists at a certain location and fail to detect
it independently.

Figure 6: Evolution of validation metrics – quality and F1 for cable and pylon
detection – in 5-fold cross validation runs reported in table 3 for DDLN-M and
PIDNet-S [84], both trained for joint detection task. The solid lines are
means of respective metrics, while the shaded areas correspond to standard
deviations.

Pylon Only Detection.

Finally, we compare our models against RT-DETR [27] in table 4 focusing on the
pylon detection alone. In the presented results we adapt two kinds of
thresholds used to turn RT-DETR predictions into distance masks: a cutoff
confidence threshold filtering out the least certain bounding box predictions
and a distance mask threshold used to convert a distance mask, derived from
predicted bounding boxes, into a segmentation mask. The choice of these
hyperparameters is different depending on whether we optimize for best quality
or F1 score, therefore we report both, underlining the metric with respect to
which we optimized the thresholds.

Firstly, looking at the two variants of inference done with the RT-DETR object
detector we find that using either multiple scales of overlapping input image
patches (with sizes of $256\times 256$ px, $512\times 512$ px and $1024\times
1024$ px) or just a single scale ($1024\times 1024$ px patches) does not
change the obtained final performance much, with single scale providing with
slightly higher performance. Using multiple scales affects greatly the
inference speed of the model, as each level of smaller patch size adds roughly
four times more input images to process per frame than found on the previous
patch size level.

Comparing RT-DETR with our approach, we note that if we grow the size of our
model to nearly match the size of this object detector, our network
outperforms it on correctness, completeness, quality and recall metrics and
falls short on segmentation precision and F1 score. Focusing on the precision,
we can observe though that its relaxed version—correctness—is much larger than
its exact version for our models. That indicates that a large part of the
pylon pixels predicted by our DDLN-H model and treated as false positives is
actually away from the pylon segmentation ground-truth only by the distance
smaller or equal to the error margin, as previously described in section 4.3.

One reason for our superior performance on the CCQ metrics is due to the fact
that those give, by design, more favourable evaluation to the method
inherently using distance mask regression than to the one in which the
distance masks are only derived from a different representation – precisely
regressed bounding boxes, as done for RT-DETR. The distance mask regression
objective imposes a distance-dependent structure on the outputs regressed by
our networks. This structure is also maintained when a segmentation mask is
obtained through distance mask thresholding. Finally, the CCQ metrics, which
relax standard precision and recall, also have a distance-dependent component
in their use of error tolerance margin, which interplays favourably with the
imposed distance-dependent structure of our targets. Meanwhile, the distance
masks generated for RT-DETR are only derived with exact Euclidean distance
transform from originally predicted bounding boxes. Therefore, they do not
naturally inherit the distance-dependent structure in the resulting distance
mask representation of the object detector’s original output.

We hypothesize that another reason for the favourable CCQ evaluation of the
distance mask approach can be found in the cases concerning distant pylons
clustered into groups. Those are not individually distiguishable on the
predicted distance masks and an inaccurate or incomplete segmentation of
partially detected pylon groups may not affect the metrics negatively. For
example, if spurious foreground detections happen to fall into the region
corresponding to the less clearly detected neighboring pylon, this will not
have a negative impact on the CCQ metrics.

Nonetheless, our model performs well in comparison to RT-DETR, while it is
simultaneously successfully detecting cable presence, using the same distance
regression based method. The joint detection of power line cables is something
that an object detector like RT-DETR is not well suited to do. The cables are
extremely elongated and thin objects, found in various orientations. Detecting
them with an object detector method would mean that the ground truth bounding
boxes would have highly variable size, be frequently largely overlapping with
each other or would need to encompass cable groups as single objects and that
they would contain mostly background objects and texture within their bounds.

Table 4: Comparison of pylon detection on DDLN dataset between our distance
mask regression method and RT-DETR [27] combined with SAHI [73]. Our models
were trained jointly for cables and pylons detection. The metrics for our
models are reported for epochs with the best mean validation pylon detection
quality. For RT-DETR runs, the reported epochs were selected as ones with
maximal mean validation value of the underlined metric – quality or F1. The
outputs of the models are evaluated with distance masks of 32 times smaller
resolution than the input image size, corresponding to the size of the output
of the DDLN-H model.

Method | Size | FPS | Precision | Recall |  F1 | Corr. | Compl. | Quality
---|---|---|---|---|---|---|---|---
RT-DETR | $20.1$ | $0.9$ | $0.62\pm 0.12$ | $0.50\pm 0.09$ | $0.55\pm 0.09$ | $0.71\pm 0.14$ | $0.58\pm 0.12$ | $0.47\pm 0.12$
$0.25\pm 0.05$ | $0.50\pm 0.09$ | $0.33\pm 0.07$ | $0.74\pm 0.10$ | $0.75\pm 0.05$ | $0.60\pm 0.05$
RT-DETRs | $20.1$ | $16.5$ | $0.64\pm 0.06$ | $0.50\pm 0.09$ | $0.56\pm 0.08$ | $0.74\pm 0.09$ | $0.58\pm 0.06$ | $0.49\pm 0.06$
$0.26\pm 0.05$ | $0.52\pm 0.08$ | $0.34\pm 0.06$ | $0.75\pm 0.07$ | $0.76\pm 0.05$ | $0.61\pm 0.05$
DDLN-H | $18.3$ | $8.8$ | $0.45\pm 0.07$ | $0.61\pm 0.03$ | $0.51\pm 0.05$ | $0.83\pm 0.04$ | $0.79\pm 0.04$ | $0.68\pm 0.03$

s – single scale of input image patches (1024 $\times$ 1024).

###  4.5 Implementation Details

Distance and segmentation masks. To generate learning targets for our models,
we converted the annotations into distance masks by computing unsigned
Euclidean distance transform to the detected objects (cables and pylons). For
the DDLN, we treat as object areas 5-pixel-thick regions around annotation
polylines and the insides of the pylons’ bounding boxes. The target distance
regression masks are first computed in pixel distance units, then clamped to
the maximum distance value of 128 and finally normalized to the $[0,1]$ range.
The distance masks are downsampled through $16\times 16$ min-pooling operation
to provide the targets for learning at the coarse resolution.

To generate segmentation masks used by our baselines – DeepWireCNN [1] and
PIDNet-S [84], we binarized full resolution distance masks with a distance
value threshold of 32. Then we downsampled the labels to match the output
resolution. To perform the $n$ times downsampling of the segmentation masks we
look at the center 4 pixels of $n\times n$ patches and if they contain a
foreground object we label the pixel in the downsampled output as foreground
as well, and as background otherwise.

Patch sampling. For the experiments run on NE-VBW dataset and also for those
using DeepWireCNN, we followed the patch sampling procedure proposed by
Stambler et al. [1]. For all other experiments, we use our own sampling
method. We select patch center locations dynamically during training from the
high-resolution images, based on the data annotations. Patches are sampled as
centered on some part of the target detected object or within its vicinity,
with a set maximal allowed distance to the closest object and ensuring that
the entire patch remains within the image boundaries. This effectively
implements sampling position with random horizontal and vertical jitter. When
training our cable detection and joint cable and pylon detection models we do
not sample purely background patches. We did so only when training the
baselines models, where this setting was one of the hyperparameters. In most
experiments we centered the sampled patches on power line cables. This
procedure was different when training pylon-only detection model – RT-DETR
[27] – where we analogously centered the sampled patches on pylons instead of
cables. It was also different when training PIDNet-S [84] and DDLN-M models
for comparing the joint detection performance in table 3. In those experiments
we centered patches within the union of close-to-cables and close-to-pylons
areas.

Data augmentations. For the models trained on the NE-VBW dataset, we used the
set of augmentations proposed in [1]. For all our models trained on the DDLN
dataset, as well as for PIDNet-S [84], we use color jittering and random
horizontal flipping. Since the weights of these models were initialized with
those obtained by pretraining on the ImageNet [42] dataset, we normalize the
input with the standard ImageNet mean and variance statistics. The RT-DETR was
trained with a larger set of augmentations, including color jittering, random
zoom-out, IoU crop and horizontal flipping; we refer the interested reader to
the work of Zhao et al. [27] and the official implementation of this object
detector where this data augmentations set can be found. All the models were
trained with large image patches of $1024\times 1024$ px size.

Hyperparameters. For all models we compare against, we tuned selected sets of
their hyperparameters on one of the splits of the NE-VBW dataset or on our
train/validation development split of DDLN. For this procedure we used SMAC3
[90], a framework implementing Bayesian optimization and Hyperband (BOHB) [91]
for hyperparameter optimization. To obtain the reported performance metrics
values we run the 5-fold cross validation with the model and data
augmentations configured according to the found best performing
hyperparameters configurations. Finally, when thresholding on the
probabilities predicted by DeepWireCNN [1] and PIDNet-S [84] models, as well
as on confidence scores and on distance masks derived from RT-DETR [27]
predictions, we also choose threshold values which maximize the validation
metrics of the obtained target object segmentation. We choose these threshold
values for each data fold separately, maximizing their respective validation
performance, therefore the reported mean metrics represent the best achievable
performance, providing very strong baseline results for our models to compare
with.

For our cable detection models, we selected the hyper parameters firstly
mostly manually, throughout the method development process, and then by trying
out several configurations and running with them the complete 5-fold cross
validation experiments. Finally, we selected the configurations achieving the
best maximal mean validation cable or pylon segmentation quality. We also
selected thresholds, same for all folds in a single 5-fold cross validation
run, for converting predicted distance masks into segmentations so as to
maximize the detection validation quality metric, both for cables and pylons.
We resorted to some automated tuning with SMAC3 [90] for our comparison with
PIDNet-S [84] for joint cables and pylons detection.

We note that selection of these hyperparameters is important for the final
performance. In the process we found that with improperly selected values, the
DDLN-S model achieved on the NE-VBW dataset the performance equivalent to that
of DeepWireCNN model.

###  4.6 Ablations

To demonstrate the impact of the components used in the proposed method on the
performance of power line cable detection, we run ablation experiments with
the DDLN-S model trained on the NE-VBW dataset for independent cable
detection. Their results are presented in the table 5.

Table 5: Ablation study demonstrating the impact of the components in our proposed method on cable detection performance. The ablation experiments have been conducted with the DDLN-S model on the NE-VBW [1] dataset. “Pretr.” indicates the initializing the model parameters with the weights of ConvNeXt-Tiny pretrained on the ImageNet [42] dataset. “LIF” refers to logarithmically scaled inverse frequency weights in $\mathcal{L}_{\rm dat}$. $\mathcal{L}_{\texttt{MALIS}}$ [50] referes to the loss term promoting connectivity in cable detections. Pretr. |  LIF |  $\mathcal{L}_{\texttt{MALIS}}$ | Precision | Recall |  F1 | Correctness | Completeness | Quality
---|---|---|---|---|---|---|---|---
✓ |  $-$ |  $-$ | $0.85\pm 0.08$ | $0.49\pm 0.17$ | $0.60\pm 0.14$ | $0.88\pm 0.06$ | $0.56\pm 0.19$ | $0.51\pm 0.16$
✓ |  ✓ |  $-$ | $0.75\pm 0.11$ | $0.67\pm 0.08$ | $0.70\pm 0.04$ | $0.78\pm 0.09$ | $0.75\pm 0.09$ | $0.61\pm 0.05$
✓ |  $-$ |  ✓ | $0.67\pm 0.15$ | $0.71\pm 0.09$ | $0.67\pm 0.07$ | $0.74\pm 0.13$ | $0.81\pm 0.09$ | $0.62\pm 0.08$
✓ |  ✓ |  ✓ | $0.74\pm 0.09$ | $0.70\pm 0.08$ | $0.71\pm 0.04$ | $0.79\pm 0.06$ | $0.79\pm 0.07$ | $0.65\pm 0.05$

Initializing the model with pretrained weights and training it with simple MSD
loss provides a highly precise model – with high precision and correctness
scores. However, the same model has low recall and completeness, missing a lot
of cable detections, which in turn negatively affects the quality metric. We
note however, that the initialization of our ConvNeXt-Tiny backbone with pre-
trained weights is indispensable to allow for successful training of our model
– we did not succeed in training this model in the same manner but from
scratch.

The results are similarly improved by either adding the inverse frequency
based weight terms, as in $\mathcal{L}_{\rm dat}$ from equation 2, or by
adding just $\mathcal{L}_{\texttt{MALIS}}$, the loss term promoting cable
detections connectivity, to the plain MSD loss. Thanks to these additions the
recall and the completeness increase significantly compared to the model
trained only with the simple MSD loss.

For our complete setup we used both the $\mathcal{L}_{\rm dat}$ and
$\mathcal{L}_{\texttt{MALIS}}$, which is the configuration for the model
presented in all result tables apart from table 5. However, comparing the
evolution of the validation cable segmentation quality metric during training
for the complete setup and for those using either of the loss function
components in isolation, it is apparent that these configurations are actually
leading to equal performance for cable-only detection. We also note that the
final scores depend here on the value of the used binarization threshold with
which we convert distance masks into segmentation masks. In our experiments we
observed that with a lower threshold value, using solely
$\mathcal{L}_{\texttt{MALIS}}$ component gives better cable segmentation
quality than $\mathcal{L}_{\rm dat}$ alone or both loss components jointly.
However, overall the performance was lower than in the ablation experiments
presented here in which we used a larger binarization threshold. Ultimately,
for all the runs of our models reported in the previously described result
tables we used both loss components and the larger binarization threshold
value.

##  5 Conclusion

We have proposed a vision-based approach to joint detection of power line
cables and transmission towers as seen by low-flying aircraft. To this end, we
have combined a modern convolutional architecture with transfer learning and a
loss function adapted to curvilinear structure delineation [50]. We have used
a single network for both detection tasks and have demonstrated its
performance on two benchmarking datasets.

As all methods, ours suffer from some limitations, some inherent to the
general vision-based detection methodology and others that can be remedied by
further work. Firstly, our method yields localized detections of power line
cables and pylons in the form of segmentation masks. For training, we rely on
bounding box annotations of the pylons, which are not particularly accurate
representations for the not distant ones. More precise segmentation masks
could be used instead in situations where the pylons’ structure and background
can be easily separated. Another avenue worth pursuing is to study how much
the model relies on pylon predictions for cable detections, and vice versa, as
discussed in section 4.4. This aspect is important when deploying our approach
in unusual scenarios that may not exhibit the same correlations as our
training set. Also vertical obstacles that can be confused for pylons should
be studied separately. Finally, the appearance of power line cables and pylons
naturally varies under weather and lighting conditions, and also between
different geographical locations with differing power lines infrastructure.
Any vision-based deep learning method, such as ours, relies on a model trained
on an ultimately limited dataset and therefore with a limited set of
appearances for the obstacles that it is capable of handling.

Increasing the inference speed of our model should also constitute a direction
for future work. To achieve it, modifications in architectural components of
the model backbone should be considered, a single example of which can be
found in InceptionNeXt [92] regarding depth-wise convolutions. Incorporating
attentional components into the model architecture, as can be found in PIDNet
[84], also presents a viable research direction, with the aim of increasing
the receptive field and the expressivity of the network.

## Declarations

### Funding

This work was supported under an Innosuisse Grant number 57140.1 IP-ICT
funding the collaboration between Daedalean AG and EPFL.

### Competing Interests

Employment and financial interests Ad Eberhard, Ivan Egorov, Philipp Krüsi and
Grigory Yakushev declare that this work was done as part of their employment
with Daedalean AG. Jakub Gwizdała, Doruk Oner, Soumava Kumar Roy, Mian Akbar
Shah and Pascal Fua declare they have no financial interests.

Non-financial interests None.

### Dual-use

The authors declare that the solutions and results of this work are intended
for and were developed for commercial/industrial civilian aircraft operations.
They shall not be used in any context in which any harm done to human lives,
property and/or infrustructure as well as to natural habitats and ecosystems
is a direct or an indirect consequence of their use.

### Data

This work used publicly available Near Earth Autonomy Vision Based Wire
Detection (NE-VBW) dataset which is described at
https://sites.google.com/nearearth.aero/ne-vbwd and can be downloaded from
https://drive.google.com/drive/folders/1A4hViJWaf9mwSISBAG629CGg_VnVHRtb. Used
5-fold cross validation split of this dataset content can be accessed at
https://drive.google.com/file/d/1eodtX6bU-6lBSz1-rlIL5ptocu8kqV3t/view?usp=sharing.
The collected DDLN dataset remains proprietary to Daedalean AG and is not
publicly available.

### Authors’ Contribution Statements

Conceptualization: Grigory Yakushev, Pascal Fua; Funding acquisition: Pascal
Fua; Data preparation: Ad Eberhard, Grigory Yakushev; Methodology: Doruk Oner,
Pascal Fua, Grigory Yakushev; Investigation: Jakub Gwizdała, Mian Akbar Shah,
Soumava Kumar Roy; Project administration: Pascal Fua, Ad Eberhard, Grigory
Yakushev; Software: Jakub Gwizdała, Ivan Egorov, Mian Akbar Shah, Doruk Oner;
Supervision: Grigory Yakushev, Pascal Fua, Doruk Oner; Writing – original
drafts: Jakub Gwizdała, Ivan Egorov, Pascal Fua; Writing – review & editing:
Pascal Fua, Doruk Oner, Ivan Egorov, Philipp Krüsi, Soumava Kumar Roy.

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