Pixel-Wise Gradient Uncertainty for Convolutional Neural Networks
Applied to Out-of-Distribution Segmentation
Kira Maag
∗
and Tobias Riedlinger
∗
Technical University of Berlin, Germany
Keywords:
Deep Learning, Semantic Segmentation, Gradient Uncertainty, Out-of-Distribution Detection.
Abstract:
In recent years, deep neural networks have defined the state-of-the-art in semantic segmentation where their
predictions are constrained to a predefined set of semantic classes. They are to be deployed in applications such
as automated driving, although their categorically confined expressive power runs contrary to such open world
scenarios. Thus, the detection and segmentation of objects from outside their predefined semantic space, i.e.,
out-of-distribution (OoD) objects, is of highest interest. Since uncertainty estimation methods like softmax
entropy or Bayesian models are sensitive to erroneous predictions, these methods are a natural baseline for
OoD detection. Here, we present a method for obtaining uncertainty scores from pixel-wise loss gradients
which can be computed efficiently during inference. Our approach is simple to implement for a large class
of models, does not require any additional training or auxiliary data and can be readily used on pre-trained
segmentation models. Our experiments show the ability of our method to identify wrong pixel classifications
and to estimate prediction quality at negligible computational overhead. In particular, we observe superior
performance in terms of OoD segmentation to comparable baselines on the SegmentMeIfYouCan benchmark,
clearly outperforming other methods.
1 INTRODUCTION
Semantic segmentation decomposes the pixels of an
input image into segments which are assigned to a
fixed and predefined set of semantic classes. In re-
cent years, deep neural networks (DNNs) have per-
formed excellently in this task (Chen et al., 2018;
Wang et al., 2021), providing comprehensive and pre-
cise information about the given scene. However,
in safety-relevant applications like automated driving
where semantic segmentation is used in open world
scenarios, DNNs often fail to function properly on
unseen objects for which the network has not been
trained, see for example the bobby car in Figure 1
(top). These objects from outside the network’s se-
mantic space are called out-of-distribution (OoD) ob-
jects. It is of highest interest that the DNN identi-
fies such objects and abstains from deciding on the
semantic class for those pixels covered by the OoD
object. Another case are OoD objects which might
belong to a known class, however, appearing differ-
ently to substantial significance from other objects of
the same class seen during training. Consequently,
the respective predictions are prone to error. For these
∗
Equal contribution
Figure 1: Top: Semantic segmentation by a deep neural net-
work. Bottom: Gradient uncertainty heatmap obtained by
our method.
objects, as for classical OoD objects, marking them as
OoD is preferable to the likely case of misclassifica-
tion which may happen with high confidence. This
additional classification task should not substantially
degrade the semantic segmentation performance itself
outside the OoD region. The computer vision tasks
112
Maag, K. and Riedlinger, T.
Pixel-Wise Gradient Uncertainty for Convolutional Neural Networks Applied to Out-of-Distribution Segmentation.
DOI: 10.5220/0012353300003660
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2024) - Volume 2: VISAPP, pages
112-122
ISBN: 978-989-758-679-8; ISSN: 2184-4321
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.

of identifying and segmenting those objects is called
OoD segmentation (Chan et al., 2021a; Maag et al.,
2022).
The recent contributions to the emerging field
of OoD segmentation are mostly focused on OoD
training, i.e., the incorporation of additional train-
ing data (not necessarily from the real world), some-
times obtained by large reconstruction models (Bi-
ase et al., 2021; Lis et al., 2019). Another line
of research is the use of uncertainty quantification
methods such as Bayesian models (Mukhoti and Gal,
2018) or maximum softmax probability (Hendrycks
and Gimpel, 2016). Gradient-based uncertainties are
considered for OoD detection in the classification
task (Huang et al., 2021; Lee et al., 2022; Oberdiek
et al., 2018) but up to now, have not been applied to
OoD segmentation. In (Grathwohl et al., 2020), it is
shown that gradient norms perform well in discrimi-
nating between in- and out-of-distribution. Moreover,
gradient-based features are studied for object detec-
tion to estimate the prediction quality in (Riedlinger
et al., 2023). In (Hornauer and Belagiannis, 2022),
loss gradients w.r.t. feature activations in monocular
depth estimation are investigated and show correla-
tions of gradient magnitude with depth estimation ac-
curacy.
In this work, we introduce a new method for
uncertainty quantification in semantic segmentation
based on gradient information. Magnitude features
of gradients can be computed at inference time and
provide information about the uncertainty propagated
in the corresponding forward pass. The features rep-
resent pixel-wise uncertainty scores applicable to pre-
diction quality estimation and OoD segmentation. An
exemplary gradient uncertainty heatmap can be found
in Figure 1 (bottom). Calculating gradient uncer-
tainty scores does not require any re-training of the
DNN or computationally expensive sampling. In-
stead, only one backpropagation step for the gradients
with respect to the final convolutional network layer
is performed per inference to produce gradient scores.
Note, that more than one backpropagation step can be
performed to compute deeper gradients which consid-
ers other parameters of the model architecture. An
overview of our approach is shown in Figure 2.
An application to dense predictions such as se-
mantic segmentation has escaped previous research,
potentially due to the superficial computational over-
head. Single backpropagation steps per pixel on high-
resolution input images quickly become infeasible
given that around 10
6
gradients have to be calculated.
To overcome this issue, we present a new approach
to exactly compute the pixel-wise gradient scores in
a batched and parallel manner applicable to a large
class of segmentation architectures. This is possi-
ble due to a convenient factorization of p-norms for
appropriately factorizing tensors, such as the gradi-
ents for convolutional neural networks. We use the
computed gradient scores to estimate the model un-
certainty on pixel-level and also the prediction qual-
ity on segment-level. Moreover, the gradient uncer-
tainty heatmaps are investigated for OoD segmenta-
tion where high scores indicate possible OoD objects.
We demonstrate the efficiency of our method in ex-
plicit runtime measurements and show that the com-
putational overhead introduced is marginal compared
with the forward pass. This suggests that our method
is applicable in extremely runtime-restricted applica-
tions of semantic segmentation.
For our method, we only assume a pre-trained
semantic segmentation network ending on a con-
volutional layer which is a common case. In our
experiments, we employ a state-of-the-art semantic
segmentation network (Chen et al., 2018) trained
on Cityscapes (Cordts et al., 2016) evaluating in-
distribution uncertainty estimation. We demonstrate
OoD detection performance on four well-known OoD
segmentation datasets, namely LostAndFound (Ping-
gera et al., 2016), Fishyscapes (Blum et al., 2019a),
RoadAnomaly21 and RoadObstacle21 (Chan et al.,
2021a). The source code of our method is made pub-
licly available at https://github.com/tobiasriedlinger/
uncertainty-gradients-seg. We summarize our contri-
butions as follows:
• We introduce a new gradient-based method for
uncertainty quantification in semantic segmenta-
tion. This approach is applicable to a wide range
of common segmentation architectures.
• For the first time, we show an efficient way of
computing gradient norms in semantic segmenta-
tion on the pixel-level in a parallel manner mak-
ing our method far more efficient than sampling-
based methods which is demonstrated in explicit
time measurements.
• We demonstrate the effectiveness of our method
to predictive error detection and OoD segmenta-
tion. For OoD segmentation, we achieve area un-
der precision-recall curve values of up to 69.3%
on the LostAndFound benchmark outperforming
a variety of methods.
2 RELATED WORK
Uncertainty Quantification. Bayesian ap-
proaches (MacKay, 1992) are widely used to
estimate model uncertainty. The well-known ap-
Pixel-Wise Gradient Uncertainty for Convolutional Neural Networks Applied to Out-of-Distribution Segmentation
113

proximation, MC Dropout (Gal and Ghahramani,
2016), has proven to be computationally feasible for
computer vision tasks and has also been applied to
semantic segmentation (Lee et al., 2020). In addition,
this method is considered to filter out predictions
with low reliability (Wickstrøm et al., 2019). In
(Blum et al., 2019a), pixel-wise uncertainty estima-
tion methods are benchmarked based on Bayesian
models or the network’s softmax output. Uncertainty
information is extracted on pixel-level by using the
maximum softmax probability and MC Dropout in
(Hoebel et al., 2020). Prediction quality evaluation
approaches were introduced in (DeVries and Taylor,
2018; Huang et al., 2016) and work on single objects
per image. These methods are based on additional
CNNs acting as post-processing mechanism. The
concepts of meta classification (false positive /
FP detection) and meta regression (performance
estimation) on segment-level were introduced in
(Rottmann et al., 2020). This line of research has
been extended by a temporal component (Maag et al.,
2020) and transferred to object detection (Schubert
et al., 2021; Riedlinger et al., 2023) as well as to
instance segmentation (Maag et al., 2021; Maag,
2021).
While MC Dropout as a sampling approach is still
computationally expensive to create pixel-wise uncer-
tainties, our method computes only the gradients of
the last layer during a single inference run and can
be applied to a wide range of semantic segmentation
networks without architectural changes. Compared
with the work presented in (Rottmann et al., 2020),
our gradient information can extend the features ex-
tracted from the segmentation network’s softmax out-
put to enhance the segment-wise quality estimation.
OoD Segmentation. Uncertainty quantification
methods demonstrate high uncertainty for erroneous
predictions, so they are often applied to OoD de-
tection. For instance, this can be accomplished
via maximum softmax (probability) (Hendrycks
and Gimpel, 2016), MC Dropout (Mukhoti and
Gal, 2018) or deep ensembles (Lakshminarayanan
et al., 2017) the latter of which also capture model
uncertainty by averaging predictions over multiple
sets of parameters in a Bayesian manner. Another
line of research is OoD detection training, relying
on the exploitation of additional training data, not
necessarily from the real world, but disjoint from
the original training data (Blum et al., 2019b; Chan
et al., 2021b; Grcic et al., 2022; Grcic et al., 2023;
Liu et al., 2023; Nayal et al., 2023; Rai et al., 2023;
Tian et al., 2022). In this regard, an external recon-
struction model followed by a discrepancy network is
considered in (Biase et al., 2021; Lis et al., 2019; Lis
et al., 2020; Vojir et al., 2021; Voj
´
ı
ˇ
r and Matas, 2023)
and normalizing flows are leveraged in (Blum et al.,
2019b; Grcic et al., 2021; Gudovskiy et al., 2023).
In (Lee et al., 2018; Liang et al., 2018), adversarial
perturbations are performed on the input images to
improve the separation of in- and out-of-distribution
samples.
Specialized training approaches for OoD detec-
tion are based on different kinds of re-training with
additional data and often require generative models.
Meanwhile, our method does not require OoD data,
re-training or complex auxiliary models. Moreover,
we do not run a full backward pass which is, how-
ever, required for the computation of adversarial sam-
ples. In fact we found that it is often sufficient to
only compute the gradients of the last convolutional
layer. Our method is more related to classical uncer-
tainty quantification approaches like maximum soft-
max, MC Dropout and ensembles. Note that the latter
two are based on sampling and thus, much more com-
putationally expensive compared to single inference.
3 METHOD DESCRIPTION
In the following, we consider a neural network
with parameters θ yielding classification probabil-
ities
ˆ
π(x,θ) = (
ˆ
π
1
,... ,
ˆ
π
C
) over C semantic cate-
gories when presented with an input x. During
training on paired data (x, y), where y ∈ {1, .. .,C}
is the semantic label given to x, such a model is
commonly trained by minimizing some kind of loss
function L between y and the predicted probabil-
ity distribution
ˆ
π(x,θ) using gradient descent on
θ. The gradient step ∇
θ
L (
ˆ
π(x,θ)∥y) then indicates
the direction and strength of training feedback ob-
tained by (x,y). Asymptotically (in the amount
of data and training steps taken), the expectation
E
(X,Y )∼P
[∇
θ
L (
ˆ
π(X,θ)∥Y )] of the gradient w.r.t. the
data generating distribution P will vanish since θ sits
at a local minimum of L . We assume, that strong
models which achieve high test accuracy can be seen
as an approximation of such a parameter configura-
tion θ. Such a model has small gradients on in-
distribution data which is close to samples (x,y) in the
training data. Samples that differ from training data
may receive larger feedback. Like-wise, it is plausible
to obtain large training gradients from OoD samples
that are far away from the effective support of P.
In order to quantify uncertainty about the predic-
tion
ˆ
π(x,θ), we replace the label y from above by
some fixed auxiliary label for which we make two
concrete choices in our method. On the one hand,
VISAPP 2024 - 19th International Conference on Computer Vision Theory and Applications
114

we replace y by the class prediction one-hot vector
y
oh
k
= δ
k ˆc
with ˆc = argmax
k=1,...,C
ˆ
π
k
and the Kro-
necker symbol δ
i j
. This quantity correlates strongly
with training labels y on in-distribution data. On the
other hand, we regard a constant uniform, all-warm
label y
uni
k
= 1/C for k = 1, .. .,C as a replacement for
y. To motivate the latter choice, we consider that clas-
sification models are oftentimes trained on the cate-
gorical cross entropy loss
L (
ˆ
π∥y) = −
C
∑
k=1
y
k
log(
ˆ
π
k
). (1)
Since the gradient of this loss function is linear in the
label y, a uniform choice y
uni
will return the average
gradient per class which is expected to be large on
OoD data where all possible labels are similarly un-
likely. The magnitude of ∇
θ
L (
ˆ
π∥y) serves as uncer-
tainty / OoD score. In the following, we explain how
to compute such scores for pixel-wise classification
models.
3.1 Efficient Computation in Semantic
Segmentation
We regard a generic segmentation architecture utiliz-
ing a final convolution as the pixel-wise classification
mechanism. In the following, we also assume that the
segmentation model is trained via the commonly-used
pixel-wise cross entropy loss L
ab
(φ(θ)|y) (cf. eq. (1))
over each pixel (a,b) with feature map activations
φ(θ). However, similarly compact formulas hold for
arbitrary loss functions. Pixel-wise probabilities are
obtained by applying the softmax function Σ to each
output pixel, i.e.,
ˆ
π
ab,k
= Σ
k
(φ
ab
(θ)). With eq. (1), we
find for the loss gradient
∇
θ
L
ab
(Σ(φ(θ))∥y) =
C
∑
k=1
Σ
k
(φ
ab
)(1 − y
k
) · ∇
θ
φ
k
ab
(θ).
(2)
Here, θ is any set of parameters within the neural
network. Here, φ is the convolution result of a pre-
convolution feature map ψ (see Figure 2) against a fil-
ter bank K which assumes the role of θ. K has param-
eters (K
h
e
)
f g
where e and h indicate in- and out-going
channels respectively and f and g index the spatial fil-
ter position. The features φ are linear in both, K and
ψ, and explicitly depend on bias parameters β in the
form
φ
d
ab
= (K ∗ ψ)
d
ab
+ β
d
=
∑
κ
j=1
∑
s
p,q=−s
(K
d
j
)
pq
ψ
j
a+p,b+q
+ β
d
.
(3)
We denote by κ the total number of in-going channels
and s is the spatial extent to either side of the filter
K
d
j
which has total size (2s + 1) × (2s + 1). We make
different indices in the convolution explicit in order
to compute the exact gradients w.r.t. the filter weights
(K
h
e
)
f g
, where we find for the last layer gradients
∂φ
d
ab
∂(K
h
e
)
f g
= δ
dh
ψ
e
a+ f ,b+g
. (4)
Together with eq. (2), we obtain the closed form for
computing the correct backpropagation gradients of
the loss on pixel-level for our choices of auxiliary la-
bels which we state in the following paragraph. The
computation of the loss gradient can be traced in Fig-
ure 2.
If we take the predicted class ˆc as a one-hot label
per pixel as auxiliary labels, i.e., y
oh
, we obtain for the
last layer gradients
∂L
ab
(Σ(φ)∥y
oh
)
∂K
h
e
= Σ
h
(φ
ab
) · (1 − δ
h ˆc
) · ψ
e
ab
(5)
which depends on quantities that are easily accessi-
ble during a forward pass through the network. Note,
that the filter bank K for the special case of (1 × 1)-
convolutions does not require spatial indices which is
a common situation in segmentation networks, albeit,
not necessary for our method to be applied. Similarly,
we find for the uniform label y
uni
j
= 1/C
∂L
ab
(Σ(φ)∥y
uni
)
∂K
h
e
=
C − 1
C
Σ
h
(φ
ab
)ψ
e
ab
. (6)
These formulas reveal a practical factorization of the
gradient which we will exploit computationally in the
next section. Therefore, pixel-wise gradient norms
are simple to implement and particularly efficient to
compute for the last layer of the segmentation model.
3.2 Uncertainty Scores
We obtain pixel-wise scores, i.e., still depending on a
and b, by computing the partial norm ∥∇
K
L
ab
∥
p
of
this tensor over the indices e and h for some fixed
value of p. This can again be done in a memory ef-
ficient way by the natural decomposition ∂L /∂K
h
e
=
S
h
·ψ
e
. In addition to their use in error detection, these
scores can be used in order to detect OoD objects
in the input, i.e., instances of categories not present
in the training distribution of the segmentation net-
work. We identify OoD regions with pixels that have
a gradient score higher than some threshold and find
connected components like the one shown in Figure 1
(bottom). We also consider values 0 < p < 1 in addi-
tion to positive integer values. Note, that such choices
do not strictly define the geometry of a vector space
norm, however, ∥ · ∥
p
may still serve as a notion of
magnitude and generates a partial ordering. The ten-
sorized multiplications required in eqs. (5) and (6)
Pixel-Wise Gradient Uncertainty for Convolutional Neural Networks Applied to Out-of-Distribution Segmentation
115

Segmentation Network
ψ
K
conv layer
ϕ
Σ
softmax probs
aux. label y
L(Σ(ϕ)|y)
gradient heatmap ∥∇
K
L∥
eqs. (5),(6)
Figure 2: Schematic illustration of the computation of pixel-wise gradient norms for a semantic segmentation network with a
final convolution layer. Auxiliary labels may be derived from the softmax prediction or supplied in any other way (e.g., as a
uniform all-warm label). We circumvent direct back propagation per pixel by utilizing eqs. (5), (6).
are far less computationally expensive than a forward
pass through the DNN. This means that computation-
ally, this method is preferable over prediction sam-
pling like MC Dropout or ensembles. We abbreviate
our method using the pixel-wise gradient norms ob-
tained from eqs. (5) and (6) by PGN
oh
and PGN
uni
, re-
spectively. The particular value of p is denoted by su-
perscript, e.g., PGN
p=0.3
oh
for the (p = 0.3)-seminorm
of gradients obtained from y
oh
.
4 EXPERIMENTS
In this section, we present the experimental setting
first and then evaluate the uncertainty estimation qual-
ity of our method on pixel and segment level. We ap-
ply our gradient-based method to OoD segmentation,
show some visual results and explicitly measure the
runtime of our method.
4.1 Experimental Setting
Datasets. We perform our tests on the
Cityscapes (Cordts et al., 2016) dataset for se-
mantic segmentation in street scenes and on four
OoD segmentation datasets
1
. The Cityscapes dataset
consists of 2,975 training and 500 validation images
of dense urban traffic in 18 and 3 different German
towns, respectively. The LostAndFound (LAF)
dataset (Pinggera et al., 2016) contains 1,203 vali-
dation images with annotations for the road surface
and the OoD objects, i.e., small obstacles on German
roads in front of the ego-car. A filtered version (LAF
test-NoKnown) is provided in (Chan et al., 2021a).
The Fishyscapes LAF dataset (Blum et al., 2019a)
1
Benchmark: http://segmentmeifyoucan.com/
includes 100 validation images (and 275 non-public
test images) and refines the pixel-wise annotations
of the LAF dataset distinguishing between OoD
object, background (Cityscapes classes) and void
(anything else). The RoadObstacle21 dataset (Chan
et al., 2021a) (412 test images) is comparable to the
LAF dataset as all obstacles appear on the road, but
it contains more diversity in the OoD objects as well
as in the situations. In the RoadAnomaly21 dataset
(Chan et al., 2021a) (100 test images), a variety of
unique objects (anomalies) appear anywhere on the
image which makes it comparable to the Fishyscapes
LAF dataset.
Segmentation Networks. We consider a state-of-
the-art DeepLabv3+ network (Chen et al., 2018) with
two different backbones, WideResNet38 (Wu et al.,
2016) and SEResNeXt50 (Hu et al., 2018). The net-
work with each respective backbone is trained on
Cityscapes achieving a mean IoU value of 90.58%
for the WideResNet38 backbone and 80.76% for the
SEResNeXt50 on the Cityscapes validation set. We
use one and the same model trained exclusively on
the Cityscapes dataset for both tasks, the uncertainty
estimation and the OoD segmentation, as our method
does not require additional training. Therefore, our
method leaves the entire segmentation performance of
the base model completely intact.
4.2 Numerical Results
We provide results for both, error detection and OoD
segmentation in the following.
Pixel-Wise Uncertainty Evaluation. In order to
assess the correlation of uncertainty and prediction er-
rors on the pixel level, we resort to the commonly
VISAPP 2024 - 19th International Conference on Computer Vision Theory and Applications
116

Table 1: Pixel-wise uncertainty evaluation results for both
backbone architectures and the Cityscapes dataset in terms
of ECE and AuSE.
WideResNet SEResNeXt
ECE ↓ AuSE ↓ ECE ↓ AuSE ↓
Ensemble 0.0173 0.4543 0.0279 0.0482
MC Dropout 0.0444 0.7056 0.0091 0.5867
Maximum Softmax 0.0017 0.0277 0.0032 0.0327
Entropy 0.0063 0.0642 0.0066 0.0623
PGN
p=2
oh
(ours) 0.0019 0.0268 0.0039 0.0365
used sparsification graphs (Ilg et al., 2018). Spar-
sification graphs normalized w.r.t. the optimal ora-
cle (sparsification error) can be compared in terms of
the so-called area under the sparsification error curve
(AuSE). The closer the uncertainty estimation is to
the oracle in terms of Brier score evaluation, i.e., the
smaller the AuSE, the better the uncertainty elimi-
nates false predictions by the model. The AuSE met-
ric is capable of grading the uncertainty ranking, how-
ever, does not address the statistics in terms of given
confidence. Therefore, we resort to an evaluation
of calibration in terms of expected calibration error
(ECE, (Guo et al., 2017)) to assess the statistical reli-
ability of the uncertainty measure.
As baseline methods we consider the typically
used uncertainty estimation measures, i.e., mutual in-
formation computed via samples from deep ensem-
bles and MC dropout as well as the uncertainty rank-
ing provided by the maximum softmax probabili-
ties native to the segmentation model and the soft-
max entropy. An evaluation of calibration errors re-
quires normalized scores, so we normalize our gradi-
ent scores according to the highest value obtained on
the test data for the computation of ECE.
The resulting metrics are compiled in Table 1 for
both architectures evaluated on the Cityscapes val
split. We see that the calibration of our method is
roughly on par with the stronger maximum softmax
baseline (which was trained to exactly that aim via
the negative log-likelihood loss) and outperforms the
other three baselines. In particular, we achieve supe-
rior values to MC Dropout which represents the typi-
cal uncertainty measure for semantic segmentation.
Segment-wise Prediction Quality Estimation. To
reduce the number of FP predictions and to esti-
mate the prediction quality, we use meta classification
and meta regression introduced by (Rottmann et al.,
2020). As input for the post-processing models, the
authors use information from the network’s softmax
output which characterize uncertainty and geometry
of a given segment like the segment size. The de-
gree of randomness in semantic segmentation predic-
Figure 3: Segment-wise uncertainty evaluation results for
both backbone architectures and the Cityscapes dataset in
terms of classification AuROC and regression R
2
values.
From left to right: ensemble, MC Dropout, maximum soft-
max, mean entropy, MetaSeg (MS) approach, gradient fea-
tures obtained by predictive one-hot and uniform labels
(PGN), MetaSeg in combination with PGN.
tion is quantified by pixel-wise quantities, like en-
tropy and probability margin. Segment-wise features
are generated from these quantities via average pool-
ing. These MetaSeg features used in (Rottmann et al.,
2020) serve as a baseline in our tests.
Similarly, we construct segment-wise features
from our pixel-wise gradient p-norms for p ∈
{0.1,0.3,0.5,1,2}. We compute the mean and the
variance of these pixel-wise values over a given seg-
ment. These features per segment are considered
also for the inner and the boundary since the gradient
scores may be higher on the boundary of a segment,
see Figure 1 (bottom). The inner of the segment con-
sists of all pixels whose eight neighboring pixels are
also elements of the same segment. Furthermore, we
define some relative mean and variance features over
the inner and boundary which characterizes the de-
gree of fractality. These hand-crafted quantities form
a structured dataset where the columns correspond to
features and the rows to predicted segments which
serve as input to the post-processing models.
We determine the prediction accuracy of seman-
tic segmentation networks with respect to the ground
Pixel-Wise Gradient Uncertainty for Convolutional Neural Networks Applied to Out-of-Distribution Segmentation
117

Figure 4: Semantic segmentation prediction and PGN
p=0.5
uni
heatmap for the Cityscapes dataset (left) and the RoadAnomaly21
dataset (right) for the WideResNet backbone.
Table 2: OoD segmentation benchmark results for the LostAndFound and the RoadObstacle21 dataset.
OoD data
OoD arch
adversarial
LostAndFound test-NoKnown RoadObstacle21
AuPRC ↑ FPR
95
↓ sIoU ↑ PPV ↑ F
1
↑ AuPRC ↑ FPR
95
↓ sIoU ↑ PPV ↑ F
1
↑
Void Classifier ✓ 4.8 47.0 1.8 35.1 1.9 10.4 41.5 6.3 20.3 5.4
Maximized Entropy ✓ (✓) 77.9 9.7 45.9 63.1 49.9 85.1 0.8 47.9 62.6 48.5
SynBoost ✓ ✓ 81.7 4.6 36.8 72.3 48.7 71.3 3.2 44.3 41.8 37.6
Image Resynthesis ✓ 57.1 8.8 27.2 30.7 19.2 37.7 4.7 16.6 20.5 8.4
Embedding Density ✓ 61.7 10.4 37.8 35.2 27.6 0.8 46.4 35.6 2.9 2.3
ODIN ✓ 52.9 30.0 39.8 49.3 34.5 22.1 15.3 21.6 18.5 9.4
Mahalanobis ✓ 55.0 12.9 33.8 31.7 22.1 20.9 13.1 13.5 21.8 4.7
Ensemble (✓) 2.9 82.0 6.7 7.6 2.7 1.1 77.2 8.6 4.7 1.3
MC Dropout (✓) 36.8 35.6 17.4 34.7 13.0 4.9 50.3 5.5 5.8 1.1
Maximum Softmax 30.1 33.2 14.2 62.2 10.3 15.7 16.6 19.7 15.9 6.3
Entropy 52.0 30.0 40.4 53.8 42.4 20.6 16.3 21.4 19.5 10.4
PGN
p=0.5
uni
(ours) 69.3 9.8 50.0 44.8 45.4 16.5 19.7 19.5 14.8 7.4
truth via the segment-wise intersection over union
(IoU, (Jaccard, 1912)). On the one hand, we per-
form the direct prediction of the IoU (meta regres-
sion) which serves as prediction quality estimate. On
the other hand, we discriminate between IoU = 0 (FP)
and IoU > 0 (true positive) (meta classification). We
use linear classification and regression models.
For the evaluation, we use AuROC (area under
the receiver operating characteristic) for meta clas-
sification and determination coefficient R
2
for meta
regression. As baselines, we employ an ensemble,
MC Dropout, maximum softmax probability, entropy
and the MetaSeg framework. A comparison of these
methods and our approach for the Cityscapes dataset
is given in Figure 3. We outperform all baselines
with the only exception of meta classification for
the SEResNeXt backbone where MetaSeg achieves
a marginal 0.41 pp higher AuROC value than ours.
Such a post-processing model captures all the infor-
mation which is contained in the network’s output.
Therefore, matching the MetaSeg performance by a
gradient heatmap is a substantial achievement for a
predictive uncertainty method. Moreover, we enhance
the MetaSeg performance for both networks and both
tasks combining the MetaSeg features with PGN by
up to 1.02 pp for meta classification and up to 3.98 pp
for meta regression. This indicates that gradient fea-
tures contain information which is partially orthogo-
nal to the information contained in the softmax out-
put. Especially, the highest AuROC value of 93.31%
achieved for the WideResNet backbone, shows the
capability of our approach to estimate the prediction
quality and filter out FP predictions on the segment-
level for in-distribution data.
OoD Segmentation. Figure 4 shows segmentation
predictions of the pre-trained DeepLabv3+ network
with the WideResNet38 backbone together with its
corresponding PGN
p=0.5
uni
-heatmap. The two pan-
els on the left show an in-distribution prediction on
Cityscapes where uncertainty is mainly concentrated
around segmentation boundaries which are always
subject to high prediction uncertainty. Moreover, we
see some false predictions in the far distance around
the street crossing which can be found as a region of
high gradient norm in the heatmap. In the two pan-
els to the right, we see an OoD prediction from the
RoadAnomaly21 dataset of a sloth crossing the street
which is classified as part vegetation, terrain and per-
son. The outline of the segmented sloth can be seen
brightly in the gradient norm heatmap to the right in-
dicating clear separation.
Our results in OoD segmentation are based on
the evaluation protocol of the official SegmentMeIfY-
ouCan benchmark (Chan et al., 2021a). Evaluation
on the pixel-level involves the threshold-independent
area under precision-recall curve (AuPRC) and the
false positive rate at the point of 0.95 true positive rate
(FPR
95
). The latter constitutes an interpretable choice
of operating point for each method where a minimum
VISAPP 2024 - 19th International Conference on Computer Vision Theory and Applications
118

Table 3: OoD segmentation benchmark results for the Fishyscapes LostAndFound and the RoadAnomaly21 dataset.
OoD data
OoD arch
adversarial
Fishyscapes LostAndFound RoadAnomaly21
AuPRC ↑ FPR
95
↓ sIoU ↑ PPV ↑ F
1
↑ AuPRC ↑ FPR
95
↓ sIoU ↑ PPV ↑ F
1
↑
Void Classifier ✓ 11.7 15.3 9.2 39.1 14.9 36.6 63.5 21.1 22.1 6.5
Maximized Entropy ✓ (✓) 44.3 37.7 21.1 48.6 30.0 85.5 15.0 49.2 39.5 28.7
SynBoost ✓ ✓ 64.9 30.9 27.9 48.6 38.0 56.4 61.9 34.7 17.8 10.0
Image Resynthesis ✓ 5.1 29.8 5.1 12.6 4.1 52.3 25.9 39.7 11.0 12.5
Embedding Density ✓ 8.9 42.2 5.9 10.8 4.9 37.5 70.8 33.9 20.5 7.9
ODIN ✓ 15.5 38.4 9.9 21.9 9.7 33.1 71.7 19.5 17.9 5.2
Mahalanobis ✓ 32.9 8.7 19.6 29.4 19.2 20.0 87.0 14.8 10.2 2.7
Ensemble (✓) 0.3 90.4 3.1 1.1 0.4 17.7 91.1 16.4 20.8 3.4
MC Dropout (✓) 14.4 47.8 4.8 18.1 4.3 28.9 69.5 20.5 17.3 4.3
Maximum Softmax 5.6 40.5 3.5 9.5 1.8 28.0 72.1 15.5 15.3 5.4
Entropy 14.0 39.3 8.0 17.5 7.7 31.6 71.9 15.7 18.4 4.2
PGN
p=0.5
uni
(ours) 26.9 36.6 14.8 29.6 16.5 42.8 56.4 25.8 21.8 9.7
Table 4: Runtime measurements in seconds per frame for
each method; standard deviations taken over samples in the
Cityscapes validation dataset.
sec. per frame ↓ WideResNet SEResNeXt
Softmax 3.02 ± 0.18 1.08 ± 0.04
MC Dropout 7.52 ± 0.35 2.31 ± 0.10
PGN
oh
+ PGN
uni
(ours) 3.05 ± 0.16 1.09 ± 0.05
true positive fraction is dictated. On segment-level, an
adjusted version of the mean intersection over union
(sIoU) representing the accuracy of the segmentation
obtained by thresholding at a particular point, positive
predictive value (PPV or precision) playing the role of
binary instance-wise accuracy and the F
1
-score. The
latter segment-wise metrics are averaged over thresh-
olds between 0.25 and 0.75 with a step size of 0.05
leading to the quantities sIoU, PPV and F
1
.
Here, we compare the gradient scores of PGN
uni
as an OoD score against all other methods from the
benchmark which provide evaluation results on all
given datasets. We restrict ourselves to PGN
uni
since
we suspect it performs especially well in OoD seg-
mentation as explained in Section 3. The results
are based on evaluation files submitted to the public
benchmark and are, therefore, deterministic. As base-
lines, we also include the same methods as for error
detection before since these constitute a fitting com-
parison. Note, that the standard entropy baseline is
not featured in the official leaderboard, so we report
our own results obtained by the softmax entropy with
the WideResNet backbone which performed better.
The results verified by the official benchmark are
compiled in Table 2 and Table 3. We separate both ta-
bles into two halves. The bottom half contains meth-
ods with similar requirements as our method while
the top half contains the stronger OoD segmentation
methods which may have heavy additional require-
ments such as auxiliary data, architectural changes,
retraining or the computation of adversarial examples.
Note, the best performance value of both halves of
the table is marked. In the lower part, a comparison
with methods which have similarly low additional re-
quirements is shown. We mark deep ensembles and
MC dropout as requiring architectural changes since
they technically require re-training in order to serve
as numerical approximations of a Bayesian neural
network. PGN performs among the strongest meth-
ods, showing superior performance on LostAndFound
test-NoKnown, Fishyscapes and the RoadAnomaly
dataset. While not clearly superior to the Entropy
baseline on RoadObstacles, PGN still yields stronger
performance than the deep ensemble and MC dropout
baselines. Especially in Table 3, the methods in the
lower part are significantly weaker w.r.t. most of the
computed metrics.
The upper part of the table provides results for
other OoD segmentation methods utilizing adversar-
ial samples (ODIN (Liang et al., 2018) and Maha-
lanobis (Lee et al., 2018)), OoD data (Void Classi-
fier (Blum et al., 2019b), Maximized Entropy (Chan
et al., 2021b) and SynBoost (Biase et al., 2021)) or
auxiliary models (SynBoost, Image Resynthesis (Lis
et al., 2019) and Embedding Density (Blum et al.,
2019b)). Note, that the Maximized Entropy method
does not modify the network architecture, but uses
another loss function requiring retraining. In several
cases, we find that our method is competitive with
some of the stronger methods. We outperform the two
adversarial-based methods for the LostAndFound as
well as the RoadAnomaly21 dataset. In detail, we ob-
tain AuPRC values up to 22.8 pp higher on segment-
level and F
1
values values up to 24.8 pp higher on
pixel-level. For the other two datasets we achieve
similar results. Furthermore, we beat the Void Clas-
sifier method, that uses OoD data during training, in
most cases. We improve the AuPRC metric by up to
64.5 pp and the sIoU metric by up to 48.2 pp, both for
the LostAndFound dataset. In addition, our gradient
Pixel-Wise Gradient Uncertainty for Convolutional Neural Networks Applied to Out-of-Distribution Segmentation
119

norm outperforms in many cases the Image Resyn-
thesis as well as the Embedding Density approach
which are based on an external reconstruction model
followed by a discrepancy network and normalizing
flows, respectively. Summing up, we have shown su-
perior OoD segmentation performance in comparison
to the other uncertainty based methods and outper-
form some of the more complex approaches (using
OoD data, adversarial samples or generative models).
Computational Runtime. Lastly, we demonstrate
the computational efficiency of our method and show
runtime measurements for the network forward pass
(“Softmax”), MC dropout (25 samples) and comput-
ing both, PGN
oh
and PGN
uni
, in Table 4. While sam-
pling MC dropout requires over twice the time per
frame for both backbone networks, the computation
of PGN
oh
+ PGN
uni
only leads to a marginal com-
putational overhead of around 1% due to consisting
only of tensor multiplications. Note, that the entropy
baseline requires roughly the same compute as Soft-
max and deep ensembles tend to be slower than MC
dropout due to partial parallel computation. The mea-
surements were each made on a single Nvidia Quadro
P6000 GPU.
Limitations. We declare that our method is merely
on-par with other uncertainty quantification methods
for pixel-level considerations but outperforming well-
known methods such as MC Dropout. For segment-
wise error detection, our approach showed improved
results. Moreover, there have been some submis-
sions to the SegmentMeIfYouCan benchmark (requir-
ing OoD data, re-training or complex auxiliary mod-
els) which outperform our method. However, a direct
application of the methods is barely possible if suit-
able OoD data have to pass into the training or aux-
iliary models are used in combination with the seg-
mentation network, which also increases the runtime
during application, in comparison to our simple and
flexible method. Note, our approach has one light ar-
chitectural restrictions, i.e., the final layer has to be
a convolution, but this is in general common for seg-
mentation models.
5 CONCLUSION
In this work, we presented an efficient method of
computing gradient uncertainty scores for a wide
class of deep semantic segmentation models. More-
over, we appreciate a low computational cost associ-
ated with them. Our experiments show that large gra-
dient norms obtained by our method statistically cor-
respond to erroneous predictions already on the pixel-
level and can be normalized such that they yield simi-
larly calibrated confidence measures as the maximum
softmax score of the model. On a segment-level our
method shows considerable improvement in terms of
error detection. Gradient scores can be utilized to seg-
ment out-of-distribution objects significantly better
than sampling- or any other output-based method on
the SegmentMeIfYouCan benchmark and has com-
petitive results with a variety of methods, in several
cases clearly outperforming all of them while coming
at negligible computational overhead. We hope that
our contributions in this work and the insights into
the computation of pixel-wise gradient feedback for
segmentation models will inspire future work in un-
certainty quantification and pixel-wise loss analysis.
ACKNOWLEDGEMENTS
We thank Hanno Gottschalk and Matthias Rottmann
for discussion and useful advice. This work is sup-
ported by the Ministry of Culture and Science of the
German state of North Rhine-Westphalia as part of the
KI-Starter research funding program. The research
leading to these results is funded by the German Fed-
eral Ministry for Economic Affairs and Climate Ac-
tion within the project “KI Delta Learning“ (grant
no. 19A19013Q). The authors would like to thank
the consortium for the successful cooperation. The
authors gratefully acknowledge the Gauss Centre for
Supercomputing e.V. www.gauss-centre.eu for fund-
ing this project by providing computing time through
the John von Neumann Institute for Computing (NIC)
on the GCS Supercomputer JUWELS at J
¨
ulich Super-
computing Centre (JSC).
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