Towards Reliable Detection of Empty Space: Conditional Marked Point Processes for Object Detection
Authors: Tobias Riedlinger
Kira Maag
Hanno Gottschalk
Venue: ICLR 2026 Poster (2026)
Keywords: Computer Vision
Confidence Calibration
Object Detection
Spatial Point Processes
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: Conditional marked Poisson point processes for object detectors with well-calibrated void confidences.

Abstract: Deep neural networks have set the state-of-the-art in computer vision tasks such as bounding box detection and semantic segmentation. Object detectors and segmentation models assign confidence scores to predictions, reflecting the model’s uncertainty in object detection or pixel-wise classification. However, these confidence estimates are often miscalibrated, as their architectures and loss functions are tailored to task performance rather than probabilistic foundation. Even with well calibrated predictions, object detectors fail to quantify uncertainty outside detected bounding boxes, i.e., the model does not make a probability assessment of whether an area without detected objects is truly free of obstacles. This poses a safety risk in applications such as automated driving, where uncertainty in empty areas remains unexplored. In this work, we propose an object detection model grounded in spatial statistics. Bounding box data matches realizations of a marked point process, commonly used to describe the probabilistic occurrence of spatial point events identified as bounding box centers, where marks are used to describe the spatial extension of bounding boxes and classes. Our statistical framework enables a likelihood-based training and provides well-defined confidence estimates for whether a region is drivable, i.e., free of objects. We demonstrate the effectiveness of our method through calibration assessments and evaluation of performance.

marked point Published as a conference paper at ICLR 2026
TOWARDS RELIABLE DETECTION OF EMPTY SPACE: CONDITIONAL MARKED POINT PROCESSES FOR OBJECT DETECTION
Tobias Riedlinger
Kira Maag kira. maage hhu.de de
Technical University of Berlin riedlingezémathh tu-berlin
Düsseldorf
Hanno Gottschalk
Technical University of Berlin tu- au-berlin.de
ABSTRACT
Deep neural networks have set the state-of-the- in computer vision tasks such bounding box detection and semantic segmentation. Object detectors and seg- mentation models assign confidence scores to predictions, reflecting the model's s uncertainty in object detection pixel-wise classification. However, these confi- dence estimates are often miscalibrated, as their architectures and loss functions are tailored to task performance rather than probabilistic foundation. Even with well calibrated predictions, object detectors fail to quantify uncertainty outside detected bounding boxes, i.e., the model does not make probability assessment of whether an area without detected objects is truly free of obstacles. This poses a safety risk in applications such as automated driving, where uncertainty in empty areas remains unexplored. In this work, we propose an object detection model grounded in spatial statistics. Bounding box data matches realizations process, commonly used to describe the probabilistic occurrence of spatial point events identified as bounding box centers, where marks are used to describe the spatial extension of bounding boxes and classes. Our statistical framework enables a likelihood based training and provides well-defined confidence estimates for whether region is drivable, i.e., free of objects. We demonstrate the effectiveness of our method through calibration assessments and evaluation of performance.
INTRODUCTION
Deep neural networks (DNNs) have demonstrated outstanding performance in computer vision tasks like image classification (Wortsman et al., (2022), object detection (Zong et al., 2023). instance seg- mentation (Yan et al. (222) and semantic segmentation (Xu et al. 2023). Object detection describes the task of identifying and localizing objects of a particular class, for example, by predicting bounding boxes or by labeling each pixel that corresponds to specific instance. Semantic segmentation refers assigning each pixel in an image to one of predefined set of semantic classes. These tasks serve as an indispensable tool for scene understanding, providing precise information about the scenario. Computer vision tasks lend themselves to diverse application areas including safety-critical areas like robotics (Cartucho et al. (021). medical diagnosis (Kang & Gwak 2019) and automated driving (Xu ct al. 2023). Along with high accuracy of the models, prediction reliability in the form of uncertainty assessment (Maag & Riedlinger 2024) and calibrated confidence estimates (Mehrtash et al. 2019 is also highly relevant.
Object detectors provide confidence values ("objectness") about the correctness of each predicted object, while semantic segmentation models output a softmax probability score per pixel indicating the confidence of class affiliation. Both of the former represent notions of probability for correct predictions, which also reflects the prediction uncertainty of the model. For confidence scores to be
"qqual contribution.

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ADAC
ADAC
Figure 1: Left: Semantic segmentation prediction. Center left: Poisson point process intensity. Center right: Conditional marked Poisson point process intensity, Right: Bounding box prediction.
statistically reliable, the assigned confidence should match the observed prediction accuracy, e.g. out of 100 predictions with confidence of 70% each, 70 are correct. If this is approximately the case, we call the confidence assignments "well-calibrated" However, DNN confidences are frequently miscalibrated, with confidence values not matching the observed accuracy (Küppers al.. 2022). This problem can often be tackled by confidence re-calibration methods which regularize the training objective or establish calibration by post-processing (Guo al., 2017). Particularly in the case of object detection, the focus is mainly on correctly calibrating objectness for predicted objects, while false negatives are ignored.
The problem of miscalibration often arises from mis-seecciiiation of the architecture and/or the loss function of the model. The latter are often created based on heuristics and practical considerations, e.g., feature pyramid networks (Lin et al., (017) or anchor box procedures (Redmon et al., (0166), working well empirically but lacking a probabilistie foundation. The logic of condiiional stochastic independence of pixel-wise predictions given the input image, like in semantic segmentation or objectness, are violated in practice. Moreover, the commonly used cross coos-cntropy loss with one-hot targets does not intrinsically give risc to calibration, since its main goal is to optimize classification accuracy (Liu et al.] 2024). The DNN is likely to predict the true class with high probability without calibrating the probabilities of the other classes. Thus, models often predict extremely high low probabilities tending towards overconfidence.
Aside from the calibration of foreground predictions, object detection exhibits the peculiarity that the areas outside detections are (naturally) not annotated and learned as background during training. Object detectors do not provide explicit uncertainty assessment for areas outside their own predictions. That is. the model does not make a probability assessment of whether an area without detected objects truly free of obstacles since such mechanism is not built into the loss function. Such model is then often overconfident in assuming that "no object" means the area is safe. This fact carries significant impact, e.g., in trajectory planning of autonomous cars and robotic agents where it is central to assess whether the planned track actually is collision-free. Conventional object detectors are unsuitable for this purpose because they only provide discrete and potentially erroneous object predictions without having a calibrated, quantitative idea of the collision risk over continuous trajectory, making their predictions unreliable for collision-fre planning. We consider the absence of adequate methods addressing this question be major safety and research gap in the field of safe automated driving. Our approach addresses this flaw and constitutes a step towards safe navigation.
In this work, we propose object detection model based on spatial statistics, regarding bounding box data as realizations of a marked point process (Moller et al. 2003 Sherman [01T). Such models have been used model spatial phenomena, e.g., in astronomy, epidemiology or geostatisties, to describe the probabilistic occurrence of spatial point events. We add marks to center point events describing the spatial extent of objects (width and height) and class affiliation obtaining an object detection model based on the logic of counting processes. When conditioned on the number of events, our model allows for likelihood- based end-to-end training. Out of the box, our model allows to compute well-defined notions of confidence for the event that certain region in space is drivable. We differentiate between two notions of "being drivable" depending on whether we consider to marked or non-marked point process. This gives rise an object detector which defines confidences that an arbitrary test region in space is truly free or objects. This model conceptually provides aleatoric uncertainty, but can be combined with methods for estimating epistemic uncertainty, such as Bayesian approximation. An exemplary prediction of our model is shown in fig. [ We summarize our contribution follows:
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We develop deep learning framework for modeling the intensity function of spatial point processes based on a negative log- ligliikl loss function to obtain probabilistic statements about empty space.
We propose a mathematically principled model for object detection based on the theory of marked Poisson point processes allowing for end-to-end training. Contrasted with existing object detectors, we have zero training and only a single inference hyperparameter.
We propose an evaluation protocol for testing calibration of empty space confidences and evaluate our method on street scene data, indoor robotics data as well as on drone data as practical use cases.
The proposed model is shown to be well-calibrated on image regions while having compara- ble performance to standard object detection architectures.
To our knowledge, this is the first time, a spatial statistics approach has been used for deep object recognition in computer vision. Our derivation of the loss function is principled and mathematically underpinned approach to deep object detection highlighting parallels and differences with typical design choices in object detection. The source code of our method is publicly available at https 7/g1 thub. com/ CMP PP CV/pppppce///eeetttt cmpppnet
2 RELATED WORK
Drivable area prediction. Drivable area free space detection refers to task related to au- tonomous driving that does not focus on objects, but on the classification between drivable and background (everything else). This can be done based on different sensoric data such as LiDAR, radar, camera and aerial imaging (Hortelano et al.] (023) where we focus on camera data. The basis for the drivable area prediction is often semantic segmentation architecture, since pixel level predictions are desired (Chen et al., 2025 Qiao & Zulkernine, [002)) ). Different network design choices have been pursued to solve drivable area prediction including fully convolutional models (Yu it al. 2023 Chan et al. 2019). incorporation of LSTM layers (Lyu et al. 2019) or boundary attention units (Sun al.] 2019) to overcome task task -peciiicc difficulties. Another approach improve drivable area detection involves multi-task architectures, e.g., for different segmentation tasks (Lee) (021)) detection of lane lines (Wang et al. 2024) or instance segmentation (Luo et al. 2024). In Qian et al.) (2020), unified neural network is constructed to detect drivable areas, lane lines and traffic objects using sub-task decoders to share designate influence among tasks. In addition to combining tasks, dif- ferent types of sensor data can also help, such as combining RGB images with depth information (Fan ctt al. 2020: Jain et al. 2023). An uncertainty-awe aware symmetric network is presented in Chang et al. (2022) to achieve favorable speed-accurace trade-off by fully fusing RGB and depth data.
In contrast to our methodology, drivable area prediction and free space detection are based on design choices and practical considerations and do not exhibit well-defined notions of void confidence. In direct contrast to our approach, which assigns occupation confidences to arbitrary test regions, the aim of drivable area prediction is to concretely localize regions that do not contain obstacles.
Object detection models. In computer vision, space occupation by objects is classically treated in the form of object detection. Object detectors typically model the existence of foreground objects by assigning objectness score super pixels (Farhadi & Redmon| 2018 Ren al. 2015 Liu et al. 2016) which is trained via binary cross entropy. Super pixels with sufficient objectness then contribute a bounding box prediction the final set of detections which is subsequently pruned by non-maxiimmm-suppees
to filter double predictions that indicate the same object. Our proposed intensity model shares similarities with objectness in single stage detectors like the YOLO models (Redmon et al., 2016 Redmon & Farbadi, 2017 Farhadi & Redmon] 2018). SSD (Liu et al., 2016). FCOS (Tian et al., (019)) or also CenterNet (Duan et al.] (2019) in that spatial feature map is computed which indicates the existence of foreground objects. The same mechanism is used in region proposal modules of two-stage architectures like the R-CNN family (Girshick et al. 2014 probabilistic two-stage extensions
Ren et al.) 2015 Girshick] 2015 Cai & Vasconcelos 2018) like CenterNetv2 (Zhou et al. 2021). However, there is a central difference in the meaning of the feature maps. Objectness is interpreted
the basis of superpixels and in binary fashion (foregroundd/backgroond) where different pixels are stochastically independent as prescribed by the loss function. Intensity on the other hand is built cumulative logic via integration over image
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regions and, hence, modeled densely on the same resolution the input image. Spatial dependence between pixels is incorporated by free spatial point process loss function presented in section [3 and leads to statistically reliable confidence estimation for space occupation. Due to its focus modeling center points, anchor-free models like CenterNet (Duan et al.] 2019) and FCOS (Tian et al. 2019) share similarities with our model in terms of inference logic. We emphasize, however, that the "centerness" score of CenterNet is conceptually more closely related with objectness than intensity due the built-in superpixel independence rendering both models misspecified for calibration of space occupation. Additionally, we do not claim that our model is capable of outperforming the abooe-mentioned object detectors in terms of detection accuracy as our model has not gone through several generations of architectural optimization. Rather, we present the firsi ever approach to object detection which is fully probabilistically founded. Our model is capable of assigning calibrated void/occupation probubilities to urbitrary regions in space, central research gap for autonomous driving and robotic perception. An important evaluation protocol for object detectors in terms of the PDQ score (Hall et al., 2020) has been introduced viewing object detection in light of the underlying probabilistic modeling assumptions for bounding box regression. Bounding box localization is modeled by Gaussian distributions, however, irrespective of the chosen optimization objective. In contrast, we rigorously derive the correct correspondence between regression loss and probabilistic model for bounding box uncertainty.
3 METHOD DESCRIPTION
In this section, we propose our object detection model architecture and inference logic. To this end, we derive the optimization functional from the theory of spatial point processes and propose an implementation modeling point process intensity coupled with bounding box properties as marks.
3.1 MARKED POINT PROCESS MODELS
Bounding box data as marked point configurations. We briefly introduce marked point processes as way of representing object detection. A statistical model has reflect the structure of the data. Intuitively, in object detection each foreground object corresponds to (center- jpoint equipped with mark describing size and class. The data describing an instance is viewed tuples
(E, m), where & = <E Sy) [0. 1|2 encodes the location of the instance's 's center while m = (h, k) E IR? C proves height and width of the bounding box as well as the label x from a discrete set of classes We call { "(center) point" location and m the "mark" attached to &.
The object detection ground truth data for a given image consists of set {21,..., =n) of marked points, where n E No varies between images. The corresponding point configuration (E...... { lives in the space of n-point configurations E,, over [0, 1]2, where we allow for zero points, i.e.. 5 {0}. containing only the "empty configuration". The center points then specified by an element of r = ① Dngk, E,, the space of finite point patterns. Let (9, A, IP) be probability space, then a random variable X Ω + I is said to be distributed according (spatial) point process over [0, 1]2 (A) = [X n A| is the associated counting process counting the number of points X ((w) (E: (w), ... (w)) inside the measurable set A _ [0, 1J2. N(W))
generic image are
N N[O, (Ww) gives the total count of points for the given random parameter w Ω. Likewise, marked point process XM : Ω + I'M takes values in I'M- = + neeo (En x M where the mark
space M for object detection is given by M = IR2 x C. The projection {21,..., 2n} + {EI...... } associates a mooomm) point process X with XM and XM can be considered as a point process over the extended space [0, 112 x M.
We are interested in statistical models that are eligible to model the distribution of a marked point process XMs Here we use the Poisson point process (PPP) as the simplest model and "workhorse" of spatial statistics. It is based on an intensity measure = A(x) dz, where dz is the Lebesgue measure on (0, 1]2 R22 x C where on C we chose the cardinality measure. For Am C [0, 1]2 x M specify the statisties of (AM(A) by the Poisson distribution with intensity A(AM = SAM A ((=) dz, i.e., the
probability of finding n E No marked point instances in AM is given by
PP (Nar (AMr =n) = A(As)) exp -A(A A((As))
(1)
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Choosing AM = A M, A S [0, 1J2 measurable, also the associated point process of center points (AA is a Poisson point process with intensity on [0, 1]2 given by
X(E) = Sas A m) dm.
(2)
Object detection via conditional marked Poisson point processes. Equation 1 defines prob- abilistic model for bounding box data {zI.-. En on a fixed image 1. A predictive model can be derived by conditioning the intensity A(z) = A[=[T) on the input [o, 1] x IR represented by three values for RGB channels. We call such a model a conditional marked Poisson point process (CMPPP) model. The input resolution of the pixelized image Ia determines the discretization of the Lebesgue measure over [0, 1J² and, therefore, the area/mass of each pixel. We denote by II the set of pixel locations in [0, 1|2 associated with Ta-
Let us now consider suitable models for object detection from CMPPP. We take a factorizing model
A( = A(g.m = X(E|I) p(m|,, I),
(3)
where A(z(1)= 2 0 and p(m|g. I) is a Markov kernel that models the probability density of the mark
m (h, w. x) given that there is a bounding box centered in &. Since JM p(m [ I) dm 1 for any & E [0, 1J3. X(E) = X(E) follows from eq. (2) and eq. (3). It remains to model the conditional intensity and the conditional probability on mark space as follows
Ta = exp (Lgg(a)),
p(mlç. Ia) A (Be(Ta) Ph (Ce())
for a continuous distribution Pw, for the bounding box width and height and some categorical distribution Px for the object class. Note, that both, Pw. and Pu, are technically conditional on la. which is omitted in the notation for readability. The functions L, B and C are realized as dense (pixel-wise, i.e,, indexed by pixel& {) output of a neural network which is fitted based on data (Ia, .1...., 2n), where 2 (E:; W/, h4, K2) for = 1....., in maximum-likelihood approach. In our implementation, Pu., is realized as a bivariate (independent) Laplace distribution with location parameter (ue, h) and isotropic scale parameter which is discussed further in the next section. We model Px by a softmax distribution with logits Cę(Ta). independently of Be (Ta)-
3.2 LIKELIHOOD TRAINING APPROACH AND INFERENCE FOR CMPPP MODELS
CMPPP loss function. Commonly, one chooses the negative log density function with respect to the Lebesgue measure dx as loss function for parametric model density pa, i.e., f(x, 0)
-log (o))) where ~ 140 = (x) dæ a hypothesis on the distribution of the data represented by (independent copies of) the random variable X Ω - Rd. This is no longer feasible in the setting of point processes Ω + I as no Lebesgue measure exists on the infinite dimensional space and therefore the notion of a density w.r.t. dx is ill-defined. The notion of likelihood can, however, be adapted to reference measures other than dr. Let, in the finite dimensional setting, μ be another (probability) measure Rd with density Px (x) such that Pp = 0 implies (2 O. We obtain
Exx, 0) - log (x) = - log [=( (m)
log (r) = log dise (z)) - (x)).
(5)
(RN) derivative of μ4 with respect to the reference measure μ.. As the gradients (r, 0) of eq. 5 do not depend on Pμ. training with the negative
dis Here dise ((ee(x) (z) pa(w) is the Radon-Nikodie
(x)
log likelihood loss is equivalent to training with the negative log-RN derivative. Furthermore, the
gradients also do not depend on the particular choice of μ. provided the RN derivative exists.
The training of stochastic models with an infinite dimensional state space is based on the insight that RN derivatives with respect to adequately chosen reference measures l still exist, as long as dpg- = Pe du holds, where the relative density po po(x) due (x) again is the Radon-Nikodym derivative at x E T. As the reference measure, we choose the distribution μ of the homogeneous PPP over [0, 1 with intensity function Ay. (the normalized Lebesgue measure). The RN derivative of
du
the distribution μo of a process with intensity Ao(E) w.r.t. μ then is
duaa (x) exp (- (-Ja.1y (No(EE) 1) ds) IT Xo(E)). x dy
(6)
This identity is a standard exercise in textbooks on spatial statistics, see, e.g., (Daley & Vere Jones 2006). For the convenience of the reader provide proof in appendix A.1 Equation (6)
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immediately generalizes to marked CMPPP if we replace a I with (,) E Tas, Ao(Es) with A0(2; [. & with 2, [o, 1]2 with [o, 1]² x M and de with dz.
Inserting eq. (3) and eq. 4 into the updated version of eq. (6) and taking the negative logarithm, obtain the CMPPP loss function for (L", ,B, C
[(x, 8) f0.13 (L dg Ei=I (Ta) -E- Iog(P (Ta)) + log(p (Ta)]: (7)
Here, = = (zi,..., zn} E T M is the bounding box configuration observed in the image I. Minimiz- ing the loss function now enables a strictly iikeihhoddbbsee training.
is now easy to interpret the first two terms of eq. 7 as the loss for the center point intensity Ag = exp(L") and hence a loss for "distributed objectness score". Assuming Laplace distribution, the Pw, yields the standard -'-loss for bounding box regression and the px-term the cross entropy classification loss. The integral in the first term is discretized over [0, 1]2 according to the image resolution H W as
fa.j exp (L)( de ~ Eçen exp (Le(t)) HW
(8)
with each pixel obtaining area प ZW. We note that we choose to not fit the scale vari- able a of the Laplace distribution by the model. This makes the training of B is independent of the value of a > 0 such that training with the L'-loss can be conducted first resulting in the approximately optimal weights 0. Thereafter, the maximum likelihood equations for yield - B (Ia) i.e., the mean average deviation of the bounding box regression allowing for object detection training with zero hyperparameters.
G -= - we (
Probabilistic predictions of empty space. On the basis of a trained model with parameters (0, we now derive probabilistic conditional prediction that a measurable test region A S [0, 1) is "free of objects". We interpret this statement in two different ways.
On the one hand, it may mean "A is free of object centers". The random variable X models object centers and N 5x the associated counting (Dirac-) measure. Then, the event that "A free" amounts to X ( A 0 or N (A) O. Using the Poisson statistic I for the associated center point
process, i.e., Ag( Ta) = exp(L.,) instead of A()). we obtain
(A) 0 = exp (- SA A = exp (-EW ECEAnD exp (LL(T)))
(9)
On the other hand, an interpretation is the event that "A does not intersect any of the bounding boxes" "r (Ez - 2 Ee + [] x (5, h
2 =: b(2) for any 2 = (Ex, Ey: W. h x:) E XM-- To this end, consider the critical set (E) S [0, 2 x M for a point & E A, that is, the set of all bounding boxes z' E [0, 1|2 x M such that E is contained in the corresponding bounding box b(z'). It is easily seen that (E) = {=' = (g', w', hh,,",,'' k²) ) E [o, 1j2 x M : Kr. E S w/2 and key - Eg < h/2). The critical set for the entire region then is given by (A) = USEA (E) and the probability that no bounding box in a given image I intersects A is
2 Ey + h
(A) 0 exp (-SDrca) Ap(z1I)
(10)
where A(z(Z) is evaluated using eq. (3) and eq. 44. Let us shortly consider the evaluation of the integral the right hand side of eq. (10.. By our modeling ansatz, the integral over Ag separates to
Jo. (( [[meMMi((..mmmaa) p(mls, dm dg.
(11)
For the special case that the test region A a rectangle with center point (E.² Ed) ) E 112, width wnd and height h A intersects b(E, w, h, k) if both, I5-1 Exl I 2 [w + w) and hold. The inner integral then factorizes and the integral in eq. (TO) becomes
( Egl I 2 (h + h)
EeEr, cL2(1a), [ - 25
- -ww (4a) Saig,- 1
1 In B (4)) dh (12)
which can easily be expressed by the cumulative distribution function of Pw, The evaluation of the void confidence generalizes e.g., to modeling with normal distributions and can easily be algorithmically implemented. While the inner integral over {m E M b(g, m) n A A 0} may in general be computed by logical querying of pixels and CDFs, more general shapes may also be treated via the inclusion-exclusion principle.

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Prediction of foreground objects. For bounding box prediction, instead of the standard non- maximum suppression algorithm, we exploit the counting statistics of the spatial point process and determine the expected number of center points in [0, 1]2 by [[N]
Jo.11= A s HW Eeen >z(S((a). Afterwards, we extract this number of peaks (see fig. 2 from the intensity function to find the predicted center points. As the intensity function is sharply peaked but still somewhat spread-out, we crop square patches of 32 x 32 pixels around determined maxima before searching for the next peak. An ablation study on crop square size, our only hyperparameter, is provided in appendix [A.2] We observe robust behavior over large range of settings. Marks are determined by evaluation of (La) and (Ia) feature maps at the respective locations.
4 EXPERIMENTS
4.1 MODEL DESIGN AND EXPERIMENTAL SETTING
Network architecture. In order model the functions B and C' in eq. (4). we choose deep neural networks that are capable to compute pixel-wise outputs, in particular we utilize architectures used in semantic segmentation with 1 1+ 2 |C] output channels modeling the tuple (L", B CO). Given ground truth data (Ia, 21. ..... 2n this allows for computing the full CMPPP loss (eq. 7 and training end-to-end. In appendix A..5 we present additional experiments with a two-stage architecture and additional experiments where we model the residuals as normal distributions instead of I Laplace distributions. We implement our CMPPP model in the MMDetection environment (Chen et al. 2019), importing segmentation architectures from MMSegmennatiin.. Our investigations involve a DeepLaby3+ (Chen et al., 2018) model with ResNet-50 backbone, an FCN model with HRNet (Wang et al. (021)) backbone, well as SegFormer-BS (Xie et al. 2021) model. Training ran Nvidia A100 GPU with 80GBs of memory and standard (pre-set) parameter settings for training on the various datasets.
Datasets, In our experiments, we use three datasets: Cityscapes and TiROD, street and indoor robotics datasets where empty spaces are relevant for safe and collision-free navigation as well, as VisDrone, an acrial drone dataset where the detection of free landing sites is of interest. The Cityscapes dataset (Cordts et al. 2016) depicts dense urban traffic scenarios various German cities. This dataset consists of 2,975 training images and 500 validation images of size 1,024 x 2,048 from 18 and 3 different cities, respectively, with labels for semantic and instance segmentation of road users (different vehicles and humans). From the instance labels, we obtain the center points and bounding box ground truth of the objects. The VisDrone-DETT dataset (Zhu et al. 2022) shows aerial images of urban scenarios in different Chinese cities. The dataset consists of 6,471 training and 548 validation images of varying resolutions and bounding box annotations for 10 different road-related semantic classes. The Tiny Robotics Object Detection (TiROD) dataset (Pasti al. 2025) contains frog perspective scenes recorded in indoor lab/office settings and outdoor garden settings with two different illumination conditions in 5,336 training and 666 validation images. The 640 480 pixel images contain 13 different semantic classes of foreground instances.
4.2 NUMERICAL RESULTS
PPP intensity calibration. In this section, we compare our intensity prediction of the (non-marked) PPP with an analogous semantic segmentation prediction regarding the respective calibration of predicting empty spaces. We aim at answering the question whether a test region A is drivable. Given an input image Ia and learned weights, a semantic segmentation model computes a probability distribution p(- Ta)e E j0. 1] over C. for each pixel & E II specifying the probability p(k[TT)) (T(Ta) E [0 for each class k E C. The probability that a region is drivable is given by (A is drivable) Iggennn p( "raad"")aa) as the pixel predictions are assumed to be independent when conditioned on fixed image T. We consider a region to be drivable if it contains no classes other than "road". For the PPP model, the probability that the region is free is derived from the case n = 0 in eq. ( under the discretization (8
IP p (A is drivable) = exp (- X(E) dE) ~ exp + A(6))
(13)
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Table 1: Calibration values of semantic segmentation model (ECEs and our PPP method (ECEp for the Cityscapes dataset and different box sizes s.
250
500
750
1,000
1,500
2,500
5,000
10,000
Deep-
0.1102
0.1741
0.2033
0.2245
0.2521
0.2667
0.2417
0.1948
Labv3+
ECEp
0.0012
0.0017
0.0029
0.0029
0.0046
0.0062
0.0109
0.0164
HRNet
ECE₃ 0.0413
0.0859
0.1142
0.1443
0.1785
0.2206
0.2295
0,1939
ECEp
0.0008
0.0012
0.0014
0.0019
0.0022
0.0041
0.0053
0.0071
SegFormer
ECE,
0.0621
0.0585
0.0609
0.0593
0.0588
0.0582
0.0626
0.0713
ECEP
0.0006
0.0008
0.0014
0.0018
0.0027
0.0046
0.0053
0.0082
1.0
0.8
accuracy
0.6
0.4
0.2
ECE, 0.2245 ECE, 0.0029
0.0
0.0
0.1
0.2
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 confidence
Figure 2: Intensity landscape over an input im- age from the Cityscapes val dataset. Peaks are mostly sharply localized and indicate foreground detections.
Figure 3: Confidence calibration plots for seman- tic segmentation (blue) and PPP (orange) with corresponding ECE for the Cityscapes dataset and the Lae33abby3++ detector and 1,000.
We consider a region to be drivable if it contains no center point. To determine the calibration of the methods, sample random boxes (test regions) of fixed area (height and width chosen randomly), where the number of boxes per image is fixed (here 50). For each box, we determine whether it is drivable and determine the respective probability. Based these quantities, calculate the expected calibration error (ECE) (Nacini et al. 2015) to evaluate calibration.
The results for the Cityscapes dataset are shown in Table depending on the box size. We observe that calibration for smaller boxes also achieves smaller ECE errors. Furthermore, we find that HRNet more accurately calibrated than DeepLabv3+ for semantic segmentation. The reason for this could be the difference in model capacity and that HRNet does not use significant downsampling or pyramid architecture, instead relying on high-resolution representations through whole process. However, both convolutional networks are less well calibrated than the SegFormer. These differences between the models become significantly smaller with our PPP method; only slight trends can still be identified. It is quite evident that PPP method is significantly better calibrated than the semantic segmentation prediction. corresponding confidence calibration plot shown in fig. 3 The semantic segmentation model is consistently underconfident. If any pixel indicates that the test area may not be drivable, the confidence vanishes as expected from the probability factorization. In comparison, our method fluctuates close optimal calibration (gray diagonal in the plot). We also observe good calibration on the TiROD dataset and the more complex VisDrone dataset, as shown in table 2 (top row, respectively). Moreover, we provide calibration results for re-calibrated (e.g. temperature scaled) semantic segmentation models in appendix A.3] which still remain at least an order of magnitude worse calibrated than our model. Re-calibration methods are incapable of rectifying void confidences of models which treat pixels as independent, even when fixing the test box sizes.
Bounding box detection. Using our CMPPP model, instead of the center point of an object, we receive bounding box prediction with the corresponding class and score value. The latter reflects the probability (12) that region is drivable, whereby we use the Laplace distribution function as in eq. (12) due to training with the loss. An example of CMPPP confidence and the bounding
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Table Calibration values of our DeepLabv3+ PPP model (ECEp U) and CMPPP object detector (ECEBB 4) for the VisDrone as well as the TiROD dataset for different box sizes s.
250
500
750
1,000
1,500
2,500
5,000
VisDrone
ECEp
0.0025
0.0063
0.0081
0.0090
0.0163
0.0210
0.1114
ECEн#
0.2344
0.2018
0.1763
0.1532
0.1199
0.0823
0.1246
TiROD
ECEp 0.0015
0,0046
0.0062
0.0087
0.0122
0.0198
0.0383
pCEpp
0.09-12
0.1051
0.1120
0.1197
0.1339
0.1571
0.1783
Table 3:
Calibration values of our CMPPP object detection models (ECE 4) for the Cityscapes dataset and different box sizes
250
500
750
1,000
1,500
2,500
5,000
10,000
DoepLabv3+
0.1011
0.0925
0.0869
0.0842
0.0803
0.0697
0.0692
0.0762
HRNet
0.1223
0.1133
0.1089
0.1050
0.0954
0.0781
0.0665
0.0641
SegFormer
0.0905
0.0813
0.0760
0.0737
0.0627
0.0538
0.0176
0.0600
We observe the differences in intensity between the objects more clearly than with the PPP because box height and width contribute the confidence level.
box prediction is shown in fig. (see appendix A.6 for further visualizations) D.
In this object detection application, we consider a test regions to be drivable if the test box and the ground truth bounding box do not overlap. In the same way as before, we sample 50 random test boxes of a fixed size s per image to evaluate the calibration. The results depending on s for Cityscapes are given table and and for VisDrone and TiROD in @ While the PPP only predicts the center points of objects, CMPPP adds the prediction of the height and width of the bounding box, which is more challenging for confidence calibration. We achieve slightly worse values compared to the PPP predictions, although the calibration errors still small. The Segformer model consistently exhibits better calibration than its convolutional counterparts. However, per architecture we do not identify clear trend between eтror and box size indicating robustness across test region scales.
row in each case).
Object detection is usually evaluated using mean average precision (mAP), which assesses detection capability and accuracy. On the two classes, persons and vehicles, the DeepLabv3++ CMPPP model achieves mAP of 49. 49.43%, HRNet 55.49% and SegFormer 51.04% on the Cityscapes images. In comparison, Faster R-CNN and CenterNet, well-known object detection networks, obtain mAP value of 59.32% and 57.00 .8%, respectively. We do not claim that our model is capable of outperforming these models in terms of object detection performance as our model has not gone through several generations of architectural optimization. Rather, our model is capable of assigning well-call callibaaat occupation probabilities to arbitrary regions in space. Treating superpixel objectness similarly to softmax confidences, Faster R-CNN and CenterNet both compute highly ill-calibrated void confidences, obtaining ECE values of 0.9915 (for 1,000), as expected.
Runtime and scalability. Our models essentially have the complexity of modern semantic seg- mentation architectures with minimal additional post-processing. Our Deepl model (43.6M params, 16.2 FPS) is slightly slower than a comparable Faster R-CNN (41. .4M params, 29.4 FPS) while our HRNet model (65.9M params, 15.4FPS) is on par with a Faster R-CNN with Re55eS150 backbone (65.8M params, 16. 16.4FPS). Overall, we conclude that our model scales well along with existing architectures even without specific tuning for efficiency.
5 LIMITATIONS
In fig. we observe residual miscalibration of the model for center bins which we hypothesize is due to the fact that the model invested significant amounts of capacity to also calibrate P(N((A) = T)
Public demo http://ww..p/////......ooooooo/. jNSN-

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for other Our model assigns square patch intensity to any found peak during inference which often conflicts with large foreground objects whose intensity is spread over larger areas. This suggests using depth-dependent patch sizes to differentiate between objects from different size scales. Finally, road participants and obstacles occupy physical space while we model "free" /non-interacting point configurations in our model, not incorporating repelling potentials between events.
6 CONCLUSION
In this work, we have introduced a novel object detection architecture and learning objective guided by the question "With what probability is some particular region of the input image devoid of objects, i.e., drivable?". Following a principled approach based on the theory of spatial point processes, we have derived an object detection model which may be trained by a notion negative log-likelihood to model the object intensity function over the input image. Modeling the point configuration with shape and class distribution markings constitutes an object detection model capable of assigning meaningful confidence to the event of test region intersecting any predicted object in the image. We investigate three instances of our model on three application-driver dataset and show in numerical experiments that it is capable of solid object detection performance and is well-calibrated on emptiness. Compared to semantic segmentation and conventional object detectors, we obtain significantly better confidence calibration, and particularly, the first object detection models providing reliable information about object-free areas.
ACKNOWLEDGMENT
Funding by the Federal Ministry for Economic Affairs and Energy (BMWE) through the Safe AI Engineering consortium grant no. 19A24000U is gratefully acknowledged.
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A APPENDIX / SUPPLEMENTAL MATERIAL
A.1 COMPUTATION OF THE RADON NIKODYM DERIVATIVE AND NEGATIVE LOG-LIKELIHOOD
In this appendix we provide the computations which lead to eqs. (6) and 7 for the convenience of the reader. For the ease of notation, we perform this computation for the non-marked point process and omit conditioning on the image
Derivation of eq. (6). Let thus j be the standard (homogeneous) PPP on I with intensity Ahom = 1
with counting measure Nhom (A) Poi (Apom (A)) for moruu-measurable A E [([0, 113). Further, let He be a PPP on I' with intensity function Äs : [0, 1]2 - [0, oo] and denote by Aa(A) = Sa (E dç.
Analogous to eq. (T) the counting measure No of μo follows the Poisson statistics
P(No(() n) AA)" exp(-AA(AA).
We now derive that the expression given in eq. (6) is indeed the correct (conditional) Radon-Nikodym derivative of [40 with respect to jr. Note, that the given expression holds when explicitly evaluated at E1 ..,,........ eq. to hold when conditioned on Ng (A)
I which is an element of the n-point sector in We can, therefore, only expect
(respectively, Nhom = =n).
To prove eq. (6) by Bochner's theorem it is enough to check the characteristic function Epo (c))). We obtain for E R
(A) dryp du
Ey No duu du
En
Nhom (10, 112) m]
n!
n=0
10.10m II
(o(E)) Eis la(E) ...dg.
x
n!
x Ao(E)
(0 do(E)elrlaa
foo1j
Σ n= nd
de
=
=exp (oAUP (dizLa69 - Xe(E) de = exp (L, >o(E) de (d'r ( 1))
which is the characteristic function of the Poisson distribution with intensity parameter Ag( (A), exactly as the Poisson distribution in eq. (T).
Derivation of eq. 77. Let us now consider the computation leading to the expression of the negative log likelihood. We start with the relative conditional density given in eq. (6) and compute the negative logarithm. This amounts to
J JO.PP (E 11 Σ log (Ao(E:)),
replacing (E) by (22(1a)) and canceling the exponential function with the logarithm. This recovers the first two terms in eq. (7). Note that the constant term -1 is irrelevant for the optimization objective, however, it leads to non-negative loss function which is sometimes desirable for tracking purposes.
Like in the product in eq. 66, for a marked point configuration the product in the density eq. (6) for the marked PPP by eq. (3) includes additional factors p(mil,; I). Note that the pre-factor ( (A) remains unchanged when replacing À by A as JM p(m= Et, Ia)dm; = 1. To evaluate the negative log- ligelloooooo of the additional product factors, we have to insert the second equation in eq. (4h to evaluate p(m) Es, Ta). This provides
((Ei, (E.. m.))..
log [I 1)
Σ
log
1
Be, (D]l, soffmax (Ce, (T))
20
1=1
and following the computation rues for the logarithm, we arrive at eq. | Note that here we also use (enssoftmax(eee Ev and thus log tttatmm)))))))) (C)x)) = C. (oggEwee cld).
that coftmax(( tma Cn
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Table Ablation on the box size for peak detection for the Cityscapes dataset on the DeepLabv3+ based network indicating the number of false positives (FPs 4) and mean average precision (mAPf).
30
32
34
36
38
40
42
100
FPs.
2,305
1.695
1,682
1,669
1,663
1,664
1,648
1,634
1,632
1,642
1,662
1,676
2,374
mAP
43.46
48.97
49.06
49.23
49.27
49.33
49.43
49.52
49.57
49.54
49.40
49.16
41.89
A.2 ABLATION STUDY
Our only hyperparameter is the box size for peak detection during inference. We performed a robustness check/ablation on the box size for the Cityscapes dataset on the DeepLabv3+ based network and indicate the number of false positives and the mAP in each case (see table 4 The default size of the results from the main paper was 32 x 32. We observe robust behavior over large range of settings.
A.3 COMPARISON WITH RE- RE-CALIBRATION METHODS
To measure the miscalibration, the expected calibration error (ECH) error is frequently used (Guo itt al. 2017) where all samples of dataset are binned based on their predicted confidence information to measure the accuracy in each bin, which is an approximation to the definition of calibration. On
the one hand, binning techniques were developed, for example histogram binning (Zadrozny & Elkan 2001), isotonic regression (Zadrozny Elkan 2002) and Bayesian binning (Naeini et al. | [2015]. which group all samples by their predicted confidence and assign the observed bin accuracy calibrated confidence to the grouped samples. On the other hand, scaling methods were considered, e.g. Platt scaling (Plati) 1999), temperature scaling (Guo et al. 2017), beta calibration (Kull et al., 2017) and Dirichlet calibration (Kull et al. 2019). which rescale the logits before sigmoid or softmax operation to obtain calibrated confidence estimates, but differ in their assumptions about the input data and the resulting recalibration scheme. Scaling methods achieve good calibration performance given only small amount of samples compared to binning methods, but are limited by the underlying parametric assumptions. For this reason, combinations of both approaches have been developed (Ji et al. 2019; Kumar et al., 2019). Another line of work addresses calibration inference time by explicitly estimating prediction quality by uncertainty features and using them to recalibrate object detection and instance segmentation outputs (Maag et al.) 2021] Riedlinger et al.] 2023). Another strategy for confidence calibration is to adjust the optimization objective during model training (Pereyra et al. 2017 Kumar et al., 2018, Mukhoti et al. 2020 Fernando & Tsokos 2022).
Our motivation for applying spatial point process models is that void confidences from pixel classifiers such as semantic segmentation or objectness cannot be rectified by re-calibration techniques. We provide intuitive conceptual explanation of this phenomenon by the following thought experiment. For test region A, semantic segmentation or objectness model predicts some void confidence P(A) as a product of confiddncces/objecteee paper. We show that, and argue why, these values are vast under-esting estimaestimt of the measured void frequencies. Increasing the area by a factor of 2 to an area A' will also increase the number of factors in the confidence multiplication by 2, so we expect a behavior of ((A') ~ [T))] i.e., we have exponential scaling with respect to the increasing factor of the area. One the one hand, this means that it is impossible to re-calibrate well across significantly differing test region sizes. On the other hand, even for fixed areas of test regions A, the confidences obtained from a pixel classifier by multiplying per per-pixel confidences cannot even be re- re-calibrated to a satisfactory degree. This is because the model not designed to yield meaningful confidences across image neighborhoods.
values over (super-) )ixels within A described in our
For empirical validation of this claim, we provide results for semantic segmentation and objectness post-hoe calibration which show that satisfactory re-calibration of the obtained confidences is not possible, even when the area of test regions is fixed. In table[5] the calibration values for semantic segmentation with temperature and Platt scaling are shown. We fit a temperature/Platt scaling to 20% of the Cityscapes validation data and evaluate s. we fit and evaluate on test boxes of that size exclusively as this is a best case scenario for the re-calibration of pixel classifiers. No generalization to other (significantly larger or smaller) test box sizes is required. Realistically, calibration would be performed at the pixel level and then tested on other sizes, which yields poorer results than scaling for the respective test box size shown in the
the complementary set. For each value of
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Published as a conference paper at ICLR 2026
Table 5: Calibration values of semantic segmentation model without (ECEs 4) and with scaling (temperature or Platt) and our PPP method (ECEp 4) for the Cityscapes dataset and different box sizes s.
250
500
750
1,000
1,500
2,500
5,000
10,000
Deep- Labv3+
BCEs RCFs is
0.0591
0,1102
0.1741
0.2033
0.2245
0.2521
0.2667
0.2417
0.1948
0.0511
0.1286
0.1411
0.1525
0.1618
0.1653
0.1797
0.17
0.0922
ECEs platt
0.0176
0.0230
0.0335
0.0492
0.0544
0.0705
0,05488
0.0521
0.0507
ECEp
0.0196
0.0012
0.0017
0.0029
0.0029
0.0046
0.0062
0.0109
0.0164
HRNet
RCEs
0.0682
0.0413
0.0859
0.1142
0.1443
0.1785
0.2206
0.2295
0. 0.1939
ECEs is
0.0606
0.0378
0.0596
0. 0.1245
0.1329
0.1397
0.1520
0.1597
0.1641
ECEs plat
0.0203
0.0097
0.0096
0.0166
0.0212
0.0298
0.0444
0.0799
0.0988
BCEP
0.0195
0.0008
0.0012
0.0014
0.0019
0.0022
0. 0.0041
0.0053
0.0071
Seg-
ECEs
0.0755
0.0621
0.0585
0.0609
0.0593
0.0588
0.0582
0.0626
0.0713
Former
ECEs ts
0.0858
0.0434
0.0378
0.0379
0.0338
0.0344
0.0333
0.0364
0.0481
RCFs plat
0.0142
0.0096
0.0113
0.0150
0.0159
0.0095
0.0133
0.0193
0.0303
ECEP
0.0196
0.0006
0.0008
0.0014
0.0018
0.0027
0.0046
0.0053
0.0082
table. Although this re-scaling slightly improved void calibration of the baseline models, they remain at least an order of magnitude worse calibrated than our model.
We perform the same re-calibration scheme for our object detection baselines (Faster R-CNN and CenterNet). The ECE value for both models tested for sample box size of 1,000 improves from 0.9915 when uncalibrated to 0.5435 with temperature scaling and 0.0023 with Platt scaling. While calibrating test boxes on fixed size yields improved results, this gain stems from size-specific calibration effects. Once the calibration model is trained at one scale and evaluated on different test box sizes, performance degrades to levels comparable to the uncalibrated baseline. The problem with calibration for object detection models comes from the fact that uncertainty relates to question and a prediction. As object detectors offers no prediction for the probability that a region is not occupied, it cannot be scaled or re-calibrated. Taking the confidence scores surrogate for the pixel-wise prediction, we end up in the same problem we found for semantic segmentation. On the pixel level (s = 1), these models are calibrated. But the more pixels region contains, the less calibrated are pixel-based predictions. Consider a thought experiment and let the resolution of the image tend to infinity. In this limit, the only calibrated pixel-based models would be the perfect models that never err. All other perception networks that are calibrated on the pixel level will predict zero probability for empty space for any region.
A.4 ENSEMBLING AND RANDOM SEEDS
Repeated training of the DeepLabv3+ CMPPP model on Cityscapes on 5 different random seeds reveals that model performance is reasonably robust with respect to initial seeds. We evaluate the object detection performance in section 4.2 and obtain an mAP statistics of 51.46 + 0.82 across the 5 models showing standard multi-seed variation. Additionally, we evaluate the models as a small (n 5) ensemble and evaluate both, object detection performance and calibration of the ensemble. To this end, we average the computed intensity functions and the mark feature maps and perform the same prediction algorithm as for the individual CMPPP model and obtain significantly improved mAP of 54.29 while the ECE for test box size s = 1,000 remains similar to the values reported in table with 0.10. Therefore, we observe improved object detection performance under preserved calibration properties. Figure shows visualizations of the intensity standard deviation of the deep ensemble. While generally, the variance is highly correlated with the mean value itself, we can see the high uncertainty mainly in areas around the centers of foreground objects. Instances that appear small in the input image due to their distance to the ego car have strongly concentrated variances while large appearing instances have intensity variance spread out over a respectively large area.
A.5 NUMERICAL RESULTS FOR DIFFERENT MODEL DESIGN CHOICES
Two-stage Architecture. In addition to the proposed "one-stage" model, it may seem natural to design two-stage architecture with first stage 0z modeling region proposal in the shape of
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Figure 4: Visualization of ensemble intensity variance on two Cityscapes street scenes. We observe similar behavior as for individual models, where intensity for objects in the distance are sharply peaked, just as the standard deviations computed here. The top image shows how objects close to the ego car have medium variances spread out over a larger area.
detection heads
A8y (-12)
FCNN model
UNet
Bo (::
1
fc
Cae ( I)
Figure 5: Alternative two-stage object detection architecture based on first-stage FCNN model for the intensity function. The second stage consists of a UNet encoder-decoder model with two heads, one predicting the spatial extension of bounding boxes and the other one classification. The second stage model is trained separately from first stage on original input images and intensity predictions.
dense intensity function Ao, and a second stage (0s, 0c) modeling bounding box marks on top of the intensity function.
The training protocol guided by the interdependency of the parameters 0z, Ag and fc of the three neural networks L, B and C. If parameters, e.g., in the model's backbone, are shared, all parameters in can be trained jointly in a one shot manner. However, one can also choose to disentangle the training of fz, B, fc in stages, if not all parameters are shared. In this work we, follow the latter protocol depicted in Figure The hierarchical model we introduce builds on semantic segmentation model with one output channel modeling the intensity function by 0r. As in the first stage, the regression and classification heads are frozen, the loss function for 0r involves only the first line in eq. (7) with object center points as point configuration. We utilize an exponential activation for the intensity function. For the second stage training. we now freeze 0, The RGB input image concatenated with λo and fed through UNet (Ronneberger al. 2015) architecture (5 stages
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Table 6: Calibration values of our PPP method (ECEp 4) and object detector (ECEgB 4) for the Cityscapes dataset and different box sizes s.
250
500
750
1,000
1,500
2,500
5,000
10,000
DeepLabv3+
ECEp
0.0012
0.0021
0.0029
0.0030
0.0051
0.0086
0.0120
0.0184
HRNet
ECEp
0.0014
0.0019
0.0027
0.0032
0.0049
0.0085
0.0121
0.0177
DeepLabv3+
ECEрв ECEpp
0.0775
0.0698
0.0625
0.0574
0.0578
0.0567
0.0569
0.0683
HRNet
0.0825
0.0750
0.0709
0.0641
0.0641
0.0631
0.0621
0.0750
Table Calibration values of our object detector (ECE BB J) trained with Lo-loss for the Cityscapes dataset and different box sizes
250
500
750
1,000
1,500
2,500
5,000
10,000
DeepLabv3+ 0.0795
0.0724
0.0642
0.0587
0.0578
0.0550
0.0541
0.0668
with a base channel number 16) for secondary feature extraction after which the features are interpolated back to input shape and concatenated. Two-layer detection heads predict width and height (fg) and the class affiliation (fc), respectively. The feature maps B and C are evaluated at the point configuration and trained with the second and third line of eq. (7) with available ground truth information. While B and C' are computed from the shared parameters in the UNet model, they disentangled and conditioned on the intensity XOE
The PPP (top) as well as the CMPPP model (bottom) intensity calibration results for the two-stage architecture depending on the test box size are shown in Table For PPP, we observe that calibration for smaller boxes also achieves smaller ECE errors. For CMPPP, we achieve smaller errors, i.e., improved calibrations, compared to semantic segmentation and slightly worse values compared to PPP predictions. While the PPP only predicts the center points of objects, CMPPP adds the prediction of the height and width of the bounding box, which is more challenging for confidence calibration. We observe a similar calibration of the DeepLabv34 and the HRNet based models. With respect to the bounding box prediction, the DeepLabv3+ based model achieves mAP of 51.19% and HRNet 54.28 54.28%.
Gaussian Residuals. In Section 3, we discussed a CMPPP model with suplace-distrbutted residuals which leads to training based on the L' regression loss. While this is a widely spread approach to bounding box regression,
may analogously model the residuals normal distributions by adjusting 2 in eq. (4). In eq. (12), we then require the cumulative distribution function the normal distribution with the same mean parameters and variance o² determined analogously to the Laplace distribution the mean squared error.
The calibration values are very similar to those in Table 6 We see small deviations, with training using the -o's yielding better values for smaller sampled boxes and slightly worse values for larger ones.
Resulting calibration errors are displayed in Table 7
A.6 VISUAL RESULTS
In Figure 6 we show more qualitative examples, i.e., PPP and CMPPP intensity heatmaps as well as the corresponding bounding box prediction. In Figure visualizations for the VisDrone dataset are given.
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Figure 6: Left: Semantic segmentation prediction. Center left: Poisson point process intensity. Center right: Conditional marked Poisson point process intensity. Right: Bounding box prediction.
TH THE FL
THE 7C
FRAL
Figure 7: Left: Poisson point process intensity. Right: Bounding box prediction.
20


Reviews:
[{"review_id": "xJPzRKROi9", "reviewer": "Reviewer_PjVJ", "summary": "In this paper, the authors tackles the problem that modern object detectors provide confidence only for detected objects but not for empty regions. The authors propose a probabilistic approach based on Conditional Marked Poisson Point Processes (CMPPP) that are able to model both detections and confidently predict empty spaces. By treating object centers as spatial points with marks for size and classes, the model can estimate the probability that any region is truly object-free. Trained with corresponding likelihood loss, the authors demonstrate that their approach results in well-calibrated aleatoric uncertainty and achieves competitive detection accuracy.", "questions": "* Have you evaluated how well the method generalizes beyond Cityscapes, for instance on KITTI or BDD100K, or considered extending it to 3D datasets like nuScenes or Waymo?\n\n* How would your approach compare to standard post-hoc calibration methods such as temperature scaling or pixel-wise calibration applied to CenterNet-style detectors?\n\n* How could the proposed emptiness calibration be integrated into downstream tasks like motion planning or trajectory evaluation to demonstrate its practical value?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* The paper contributes to the important study of uncertainty-based object detection, which is highly relevant for autonomous driving and robotics applications.\n\n* It is clearly written and easy to follow; the main idea of the proposed method is intuitive, and the limitations of prior approaches are well described.\n\n* The proposed probabilistic framework is principled and mathematically grounded, providing a coherent way to quantify uncertainty for both detected objects and empty regions.", "weaknesses": "* The experimental evaluation is relatively narrow, focusing mainly on the Cityscapes dataset; testing on additional datasets (e.g., KITTI, BDD100K) would better demonstrate generalization to diverse environments and scene layouts. The same experimental protocol could also be extended to 3D object detection tasks using datasets such as nuScenes or Waymo, which would show whether the proposed probabilistic modeling scales to spatially richer domains.\n\n* The claimed improvement in calibration would be more convincing with comparisons to strong post-hoc calibration baselines (e.g., temperature scaling) applied to existing detectors with center-prediction segmentation heads (CenterNet-style), where re-calibration could be performed pixel-wise. While such methods may require a separate calibration set, this limitation can often be mitigated in practice. To strengthen the claim, the paper could include an analysis of how much calibration data would actually be needed to achieve comparable performance with standard post-hoc approaches.\n\n* While the method enables probabilistic estimation of empty-space confidence, its practical relevance remains unclear. The paper does not demonstrate how this “emptiness calibration” translates to downstream tasks such as planning, risk estimation, or control. To make the contribution more impactful, the authors could connect the calibrated emptiness probabilities to decision-making metrics — for instance, by integrating them into a planner or trajectory evaluation module. Extending the framework to 3D object detection and testing on datasets like nuScenes or Waymo would also allow assessing how such uncertainty information might affects predicted vehicle trajectories and safety-related metrics.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "rtwLxeFHGQ", "reviewer": "Reviewer_hbUL", "summary": "The paper proposes a Conditional Marked Poisson Point Process (CMPPP) model for object detection. The core motivation is to provide a probabilistically sound framework that can accurately estimate the confidence of \"empty space\" (drivable areas), addressing the lack of such uncertainty measures in standard object detectors. The method is derived from spatial statistics, using a negative log-likelihood loss for end-to-end training. Experiments on Cityscapes and VisDrone compare the proposed method's calibration against semantic segmentation and older object detection baselines.", "questions": "- Why did you not include temperature scaling (or other standard post-hoc calibration methods) for the baseline models? Comparing against uncalibrated raw logits is a weak baseline.\n\n- Why did you not train the semantic segmentation baselines on the binary \"road vs. non-road\" task for a fairer comparison of empty space calibration?\n\n- Can you provide results comparing your method to modern detection architectures like DETR?\n\n- Given that calibration is not a substitute for accuracy, how does the downstream planner benefit from a well-calibrated but less accurate detector?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- Theoretical Novelty: The derivation of the object detection task from the theory of marked point processes is mathematically grounded and offers a different perspective compared to standard heuristic-based loss functions.\n\n- Addressing an Overlooked Problem: attempting to quantify the uncertainty of regions without detections is a relevant topic for safety-critical applications.", "weaknesses": "- Questionable Problem Formulation: The paper heavily prioritizes calibration over standard accuracy metrics. However, calibration does not mean high accuracy. The premise that drivable area requires such a complex probabilistic setup is not entirely convincing; in many standard applications, drivable area is effectively treated as a discrete distribution for decision-making. The experimental setting for calibration appears somewhat contrived to highlight the proposed method's strengths while ignoring standard operational requirements (high mAP).\n\n- Missing Standard Calibration Techniques in Baselines: The paper compares its intrinsically calibrated method against standard DNNs (like DeepLabv3+) that are known to be miscalibrated out-of-the-box. A fair comparison requires these standard models to be evaluated with common post-hoc calibration techniques applied, most notably temperature scaling. It is possible that a standard detector with simple temperature scaling achieves comparable empty-space calibration to the proposed complex CMPPP method, which would significantly diminish the core contribution.\n\n- Unfair Baselines (Segmentation Task): The comparison with semantic segmentation models regarding \"drivable area\" calibration is unfair. The baselines were trained in a multi-class setting. For a fair comparison, the semantic segmentation baselines should be trained specifically in a binary classification setting (road vs. non-road).\n\n- Outdated Baselines (Detection Architectures): The chosen object detection baselines (Faster R-CNN, CenterNet) are outdated for ICLR 2026. The field has moved to transformer-based architectures. The authors should compare against DETR or its more recent variants to demonstrate if the proposed CMPPP really offers advantages over modern state-of-the-art detectors.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "r8kQ7W0W0V", "reviewer": "Reviewer_EoWf", "summary": "The paper formulates object detection as a conditional marked Poisson point process (CMPPP): box centers are points; widths/heights/classes are marks; an image-conditioned intensity λ and mark distribution p(m|ξ,I) yield a likelihood-based loss and, crucially, closed-form probabilities that arbitrary regions are empty (“drivable”). The loss emerges from the Radon–Nikodym derivative of the (marked) PPP relative to a homogeneous PPP reference, giving a principled alternative to heuristic detection losses. Implementations use segmentation backbones (DeepLabv3+, HRNet, SegFormer) to predict dense maps for intensity, size, and class. Experiments report calibration of void probabilities on Cityscapes and VisDrone and compare mAP to baseline detectors (lower mAP, better void calibration).", "questions": "N/A", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "Principled probabilistic formulation. \n- Clear derivation of a likelihood (negative log-RN) for (marked) point processes → a coherent objective for detection and void confidence, instead of ad-hoc objectness + CE/L1. The derivation and discretization details are explicit.\n\nOperational “empty-space” probability. \n- Two definitions (no centers in A; no boxes intersecting A) lead to computable expressions, incl. a practical Laplace-based integral for box intersection (Eq. 10–12). This directly targets a safety-critical question standard detectors don’t answer.\n\nCalibration protocol & results. \n- Expected Calibration Error (ECE) for randomly sampled boxes across scales; PPP/CMPPP show orders-of-magnitude lower ECE than segmentation-product or standard detectors. Plots and tables are convincing for the posed metric.\n\nHonest positioning. \n- Authors explicitly do not claim SOTA mAP and frame the contribution as a probabilistic foundation enabling calibrated emptiness estimates.\n\nFor me, this paper look like an \"old dish but with a completely new taste.\" I personally think we need more paper like this.", "weaknesses": "Modeling assumptions (independence / PPP). \n- A PPP ignores interactions (e.g., repulsion/occlusion between objects). Authors note this in limitations; nonetheless, it undercuts realism and may bias void probabilities in crowded scenes. Extending to Gibbs/repulsive processes or Cox processes would strengthen claims. \n\n\nEmpirical scope is narrow. \n- Only two datasets (Cityscapes, VisDrone), limited classes; no distribution-shift tests, no multi-seed variance, and little analysis of sensitivity to discretization (H×W) or the single inference hyperparameter (crop size) beyond an appendix note. Also, more experiments on more standard detection datasets will be helpful, e.g., COCO.\n\nmAP lags standard detectors. \n- Reported CMPPP mAP is worse than common baselines like Faster R-CNN/CenterNet; the paper argues calibration is the goal, but many venues expect Pareto curves (mAP vs calibration vs speed) to contextualize trade-offs. \n\nCalibration baseline for segmentation may be weak. \n- Their segmentation “void” probability multiplies per-pixel “road” probabilities (independence assumption). Modern segmentation calibration (temperature scaling, Dirichlet, focal-calibration) could shrink the reported gap—this isn’t explored. \n\n\nEvaluation choices. \n- Random box sampling is simple but may not reflect planner-relevant regions (e.g., near obstacles/curbs). Lack of PDQ reporting (they cite PDQ) misses a natural probabilistic detection metric to compare against probabilistic baselines. \n\nUncertainty taxonomy. \n- The method yields aleatoric void probabilities; epistemic uncertainty (e.g., via ensembles/MC-Dropout) is mentioned as combinable but not evaluated. For “reliable” navigation, both matter. \n\nTODOs:\n- Trying to extend the model with more advanced architectures, e.g., DINO (the detection one) or latest YOLO. \n- Add more experiments on COCO or other larger datasets that covers more diverse objects.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4O84jSA9nQ", "reviewer": "Reviewer_dzBf", "summary": "This paper proposes a novel object detection framework based on spatial statistics, specifically conditional marked point processes, to address the critical problem of quantifying uncertainty in empty space regions. Unlike traditional object detectors that only provide confidence scores for detected objects, this approach can assess the probability that a given region is truly free of obstacles - a crucial capability for safety-critical applications like autonomous driving. The method models bounding box data as realizations of marked point processes and derives a likelihood-based training objective that enables well-calibrated confidence estimates for empty space regions.", "questions": "1)How realistic is the Poisson assumption for object distributions in real scenes with clustering or mutual exclusion?\n2)Have you considered hybrid approaches combining high-performance detectors with your calibration framework?\n3)How does computational overhead compare to standard detectors?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1) Novel Problem Formulation and Theoretical Foundation: The paper addresses a fundamental gap in object detection by providing uncertainty quantification for empty space regions, which is crucial for safety-critical applications. The approach is mathematically rigorous, grounded in spatial point process theory, and represents the first application of such methods to deep object detection.\n2)Clear Presentation and Methodology: The paper is well-written with clear mathematical exposition, good visualization of results, and comprehensive experimental evaluation across multiple network architectures.", "weaknesses": "1) The paper lacks comparison with other uncertainty quantification methods in object detection (Bayesian approaches, ensemble methods, Monte Carlo dropout) and existing calibration techniques. Evaluation is restricted to only two datasets, and there's insufficient analysis of baseline comparisons beyond semantic segmentation models.\n2) The Poisson assumption may not hold for real object distributions which often exhibit clustering or repulsion. The factorization in Eq. (3) assumes independence between spatial location and object properties, which may be unrealistic. The method also has scale issues, assigning square patches to detected peaks that conflict with objects of varying sizes.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)