Original: Impact of realistic properties of the point spread function on classification tasks to reveal a possible distribution shift
Revised: Impact of realistic properties of the point spread function on classification tasks to reveal a possible distribution shift

Original: Anonymous Author(s)

Original: AffiliationAddress email

Original: Abstract
Revised: Abstract

Original: Image classification is a long-standing task in computer vision with deep neuralnetworks (DNN) producing excellent results on various challenges.
Revised: Image classification is a long-standing task in computer vision with deep neural networks (DNN) producing excellent results on various challenges.

Original: However, theyare required not only to perform highly accurate on benchmarks such as ImageNet,but also to robustly handle images in adverse conditions, such as modified lighting, sharpness, weather conditions and image compression.
Revised: However, they are required not only to perform highly accurate on benchmarks such as ImageNet, but also to robustly handle images in adverse conditions, such as modified lighting, sharpness, weather conditions and image compression.

Original: Various benchmarksaimed to measure robustness show that neural networks perform differently wellunder distribution shifts.
Revised: Various benchmarks aimed to measure robustness show that neural networks perform differently well under distribution shifts.

Original: While datasets such as ImageNet-C model for examplecommon corruptions such as blur and adverse weather conditions, we argue thatthe properties of the optical system and the potentially resulting complex lens blurare insufficiently well studied in the literature.
Revised: While datasets such as ImageNet-C model for example common corruptions such as blur and adverse weather conditions, we argue that the properties of the optical system and the potentially resulting complex lens blur are insufficiently well studied in the literature.

Original: This study evaluates the impact ofrealistic optical corruptions on the ImageNet classification.
Revised: This study evaluates the impact of realistic optical corruptions on the ImageNet classification.

Original: The proposed complexcorruption kernels are direction and wavelength dependent and include chromaticaberration, which are all to be expected in realistic scenarios such as autonomousdriving applications.
Revised: The proposed complex corruption kernels are direction and wavelength dependent and include chromatic aberration, which are all to be expected in realistic scenarios such as autonomous driving applications.

Original: Our experiments on twelve different DNN models show significant differences of more than 5% in the top1 classification error, when comparedto the model performances on matched ImageNet-C blur kernels.
Revised: Our experiments on twelve different DNN models show significant differences of more than 5% in the top1 classification error, when compared to the model performances on matched ImageNet-C blur kernels.

Original:  Introduction
Revised:  Introduction

Original: Neural networks for computer vision tasks are used in a wide range of applications and are expectedto be reliable in safety-critical situations such as in autonomous driving [1, 2, 3].
Revised: Neural networks for computer vision tasks are used in a wide range of applications and are expected to be reliable in safety-critical situations such as in autonomous driving [1, 2, 3].

Original: Therefore, it iscrucial that neural networks are able to generalize from the training distribution to unknown imagesand slight domain shifts.
Revised: Therefore, it is crucial that neural networks are able to generalize from the training distribution to unknown images and slight domain shifts.

Original: In order to test such behavior, various benchmarks have been proposedthat introduce targeted corruptions [4, 5, 6, 7] or mimic common corruptions and adverse weatherconditions [8, 9].
Revised: In order to test such behavior, various benchmarks have been proposed that introduce targeted corruptions [4, 5, 6, 7] or mimic common corruptions and adverse weather conditions [8, 9].

Original: The simulation of effects such as lighting conditions, noise or image sharpnesshave been addressed for examples by Hendrycks et al.
Revised: The simulation of effects such as lighting conditions, noise or image sharpness have been addressed for examples by Hendrycks et al.

Original: In [9], Kar et al.
Revised: In [9], Kar et al.

Original: aim for more realisticmodeling by proposing additional 3D corruptions such as change of field of view, camera roll or farfocus.
Revised: aim for more realistic modeling by proposing additional 3D corruptions such as change of field of view, camera roll or far focus.

Original: While these papers cover a wide range of corruptions, they introduce necessary simplifications foreach of them.
Revised: While these papers cover a wide range of corruptions, they introduce necessary simplifications for each of them.

Original: As a result, they do not consider complex corruptions as they can result from the opticalrecording system.
Revised: As a result, they do not consider complex corruptions as they can result from the optical recording system.

Original: In this paper, we argue that the modeling of such realistic optical blur kernels thatinclude chromatic aberrations and astigmatism should be considered, since they are very likely toeventually occur in practice.
Revised: In this paper, we argue that the modeling of such realistic optical blur kernels that include chromatic aberrations and astigmatism should be considered, since they are very likely to eventually occur in practice.

Original: Thus, we examine the effects of two complex kernel types on ImageNet and evaluate on the resultingcorruptions the behavior of existing, robust and non-robust classification models, using ImageNet-C[ as a baseline.
Revised: Thus, we examine the effects of two complex kernel types on ImageNet and evaluate on the resulting corruptions the behavior of existing, robust and non-robust classification models, using ImageNet-C [8] as a baseline.

Original: Practically, the image of an object plane produced by a lens can be described using linear systemstheory: If an idealized point light source is propagated through a camera’s objective lens, the pointfunction is spread to some degree on the image side.
Revised: Practically, the image of an object plane produced by a lens can be described using linear systems theory: If an idealized point light source is propagated through a camera’s objective lens, the point function is spread to some degree on the image side.

Original: This observed intensity function is thereforecalled the intensity point spread function (PSF).
Revised: This observed intensity function is therefore called the intensity point spread function (PSF).

Original: In the best case, the PSF is diffraction-limited andtherefore small and rotationally-symmetric.
Revised: In the best case, the PSF is diffraction-limited and therefore small and rotationally-symmetric.

Original: As a rule, however, the optical system is not perfectlybalanced and aberrations arise.
Revised: As a rule, however, the optical system is not perfectly balanced and aberrations arise.

Original: These aberrations directly affect the observed PSF.
Revised: These aberrations directly affect the observed PSF.

Original: Thus, nonrotationally symmetric shapes that differ in wavelength can often occur and show the effects ofe.g. Astigmatism and chromatic aberration.
Revised: Thus, nonrotationally symmetric shapes that differ in wavelength can often occur and show the effects of e.g. Astigmatism and chromatic aberration.

Original: PSF examples are given in the appendix A.
Revised: PSF examples are given in the appendix A.

Original: In general,the PSF varies over the image field.
Revised: In general, the PSF varies over the image field.

Original: The superposition of all these point responses weighted with thescene’s intensity yields the observed image.[10, 11] By means of simulation, such PSFs applied to animage can mimic the capture with the virtual lens model.
Revised: The superposition of all these point responses weighted with the scene’s intensity yields the observed image.[10, 11] By means of simulation, such PSFs applied to an image can mimic the capture with the virtual lens model.

Original: For simplicity, we assume isoplanarity suchthat a single PSF represents a virtual lens, but with a focus on directional and wavelength dependencein contrast to approximate rotational symmetric blur kernels such as assumed in ImageNet-C[8]. 
Revised: For simplicity, we assume isoplanarity such that a single PSF represents a virtual lens, but with a focus on directional and wavelength dependence in contrast to approximate rotational symmetric blur kernels such as assumed in ImageNet-C[8]. In other words, here, the lens effect is mimiced by convolution of an image with a single PSF kernel representing the whole lens which assumes independence of the incident angle of light. This post-process filter is applied to an already projected scene excluding distortion and we do not model vignetting or effects like ghosts or scattering. Further, convolution assumes a large depth of field resulting in a PSF, which does not depend on depth.

Revised: Also, camera sensor simulation is not covered in this study, excluding e.g. noise and color filter array effects.

Revised: We focus on the shape of realistic PSFs compared to disk-like blur kernels.

Original:  Analysis of the impact of realistic PSF properties to classification
Revised:  Analysis of the impact of realistic PSF properties to classification

Original: This article investigates the impact of directional and wavelength dependent PSFs at differentseverities.
Revised: This article investigates the impact of directional and wavelength dependent PSFs at different severities.

Original: The optically motivated kernels will be called optical kernels here in contrast to thecorruption kernels from ImageNet-C .
Revised: The optically motivated kernels will be called optical kernels here in contrast to the corruption kernels from ImageNet-C [8].

Original: We take the defocus blur kernels from ImageNet-C and compare to them in size approximate matchedoptical kernels.
Revised: We take the defocus blur kernels from ImageNet-C and compare to them in size approximate matched optical kernels.

Original: Subsequently the image datasets (defocus blur from ImageNet-C and the proposedoptical kernels) are classified by different pretrained neural networks.
Revised: Subsequently the image datasets (degraded with defocus blur from ImageNet-C and the proposed optical kernels) are classified by different pretrained neural networks.

Original: We compare the results for allseverities of classification and image degradation.
Revised: We compare the results for all severities for classification and image degradation.

Original: All operations are done in python and pytorch.
Revised: All operations are done in python and pytorch.

Original: Google Colab GPUs are used to perform the inference for the image datasets and to perform thedifferent image dataset comparisons.
Revised: Google Colab GPUs are used to perform the inference for the image datasets and to perform the different image dataset comparisons.

Original: 2.1 Metrics
Revised: 2.1 Metrics

Original: To compare the data, different metrics are used following the dataflow from a set of PSFs toimages (IMG) and classification (CLS).
Revised: To compare the data, different metrics are used following the dataflow from a set of PSFs to images (IMG) and classification (CLS).

Original: First, PSFs are generated, see Figure 1(left).
Revised: First, PSFs are generated, see Figure 1(left).

Original: From this,the modulation transfer function (MTF) can be generated, which is an established optical qualitymetric.[12, 13] The two-dimensional function is given in pairs of orthogonal slices in a particulardirection, e.g. in direction of the coordinate axes or in diagonal direction.
Revised: From this, the modulation transfer function (MTF) can be generated, which is an established optical quality metric.[12, 13] The two-dimensional function is given in pairs of orthogonal slices in a particular direction, e.g. in direction of the coordinate axes or in diagonal direction.

Original: There exist differentfunctionals derived from the MTF curve such as MTF50, which denotes the frequency value wherethe MTF falls to 50 % , and area under the curve (AUC), which is the integral of the MTF.
Revised: There exist different functionals derived from the MTF curve such as MTF50, which denotes the frequency value where the MTF falls to 50 % , and area under the curve (AUC), which is the integral of the MTF.

Original: The metricsare meaningful, if curves of similar shape are compared to ensure for example for AUC, that theintensity is concentrated in similar frequency regions.
Revised: The metrics are meaningful, if curves of similar shape are compared to ensure for example for AUC, that the intensity is concentrated in similar frequency regions.

Original: These curves are used to match the corruptionkernels and optical kernels.
Revised: These curves are used to match the corruption kernels and optical kernels.

Original: The application of each PSF kernel to ImageNet yields a modified image dataset for each severity,which is compared to the unmodified ImageNet validation dataset.
Revised: The application of each PSF kernel to ImageNet yields a modified image dataset for each severity, which is compared to the unmodified ImageNet validation dataset.

Original: Every image of a modified datasetis compared to the unmodified original.
Revised: Every image of a modified dataset is compared to the unmodified original.

Original: These comparisons are evaluated with mean squared error(MSE) and the structural similarity index (SSIM).[14] To obtain a manageable overview, the meansof these metrics are taken and are denoted as mMSE and mSSIMrespectively.
Revised: These comparisons are evaluated with mean squared error (MSE) and the structural similarity index (SSIM).[14] To obtain a manageable overview, the means of these metrics are taken and are denoted as mMSE and mSSIM

Original: These images are then fed to the different classifiers.
Revised: These images are then fed to the different classifiers.

Original: The classifiers are assessed with the top1-error,which takes the mean of all falsely classified images.
Revised: The classifiers are assessed with the top1Accuracy, which takes the mean of all falsely classified images subtracted from 1 to have a similarity measure.

Original: These values are then compared for the differentmodels and for each severity.
Revised: These values are then compared for the different models and for each severity.

Original: 2.2 Blur models
Revised: 2.2 Blur models

Original: The corruption kernels represent the reproduced "defocus blur" corruption kernels from ImageNet-Cfor five severities.
Revised: The corruption kernels represent the reproduced "defocus blur" corruption kernels from ImageNet-C for five severities.

Original: The generation of these kernels is a two step process: First, a disk shape is created,which is then blurred with Gaussian blur.[8]
Revised: The generation of these kernels is a two step process: First, a disk shape is created, which is then blurred with Gaussian blur.[8]

Original: This yields approximate rotationally symmetric blurkernels, which do not depend on the color channel and model  defocus.
Revised: This yields approximate rotationally symmetric blur kernels, which do not depend on the color channel and model constant defocus.

Original: To compare such kernels with more realistic optical kernels, we use the color-dependent average PSFof aspace-variant Cooke-Triplet lens model [15] as base PSF:
Revised: To compare such kernels with more realistic optical kernels, we parameterize the color-dependent central PSF of a Cooke-Triplet lens model [15]. The below Eq. 1 models the optical system as a black box, where Eq.

Revised: 1 propagates the wave containing the effect of the lens from the exit pupil to the imager position at focus z i .

Revised: At this distance an intensity PSF h can be observed, representing imaging with diffraction and aberration [11]:

Original: [Equation]
Revised: [Equation]

Original: where h denominates the intensity PSF acquired from a complex pupil description consisting ofthe pupil shape P and its phase with thereal wavefront aberration W λ .[11] 
Revised: The complex argument of the Fourier Transform F contains the information about the lens consisting of the pupil shape P and its phase with the wavefront aberration W λ .[11] The model assumes scalar diffraction theory and therefore no polarization.

Revised: Since we use a l 1 -normed discrete PSF to preserve energy in the final image, any scalar weights are suppressed.

Revised: In this article, we further restrict the model to represent the lens with a single PSF and no dependence on the object distance and angle and no magnification to concentrate on the kernel’s shape.

Revised: We observe the PSF h in a region u, v ∈ [0 , 24) pixels.

Original: For the average PSF awavefront aberration description W λ is available from [15] in terms of Zernike Polynomials Z mn [10]:
Revised: To get the specific PSF, the wavefront aberration description W λ representing the lens as available from [15] in terms of Zernike Polynomials Z mn [10] is parameterized:

Original: [Equation]
Revised: [Equation]

Original: Each coefficient A mn in multiples of the wavelengths λ i ∈ { 0 . 4861 µ m , 0 .
Revised: Each coefficient A mn in multiples of the wavelengths λ i ∈ { 0 . 4861 µ m , 0 .

Original: µ m and 0 .
Revised: µ m and 0 .

Original: 6563 µ m }represents the contribution of a particular type of aberration.
Revised: 6563 µ m } represents the contribution of a particular type of aberration.

Original: This allows to parameterize differentaspects such as the amount of coma, astigmatism or defocus.
Revised: This allows to parameterize different aspects such as the amount of coma, astigmatism or defocus.

Original: The base PSF’s wavefront aberrationdescription therefore consists of three different sets of the first 20 Zernike-Fringe coefficients,which are then assigned to the different RGB color channels.

Original: To show directional dependence,oblique astigmatism A − 2is varied, which may also lead to chromatic aberration: The originalwavefront aberration W  depends on wavelength.
Revised: To show directional dependence, oblique astigmatism A − 2 2 is added to the original wavefront aberration W λ , which may also lead to chromatic aberration as the wavefront aberration W λ depends on wavelength.

Original: The experimentally determined parameterization A − 2∈ { 1 , 1 . 4 , 2 , 3 , 3 . 8 } λ i leads to optical kernels comparable to the corruption kernels both interms of PSF metrics (MTF50, AUC, MTF curves) as well as IMG metrics (SSIM,MSE).
Revised: The experimentally determined parameterization A − 2 2 ∈ { 1 , 1 . 4 , 2 , 3 , 3 . 8 } λ i leads to optical kernels comparable to the corruption kernels both in terms of PSF metrics (MTF50, AUC, MTF curves) as well as IMG metrics (SSIM, MSE). Note that the central PSF contains little aberration and the resulting shape is mainly controlled by the parameterization.

Original: We also include two additional studies in appendix C for "straight" astigmatism and a closer matchedversion for oblique astigmatism.
Revised: We also include two additional studies in appendix C for "straight" astigmatism and a closer matched version for oblique astigmatism with comparable trend.

Original:  Experiments on ImageNet
Revised:  Experiments on ImageNet

Original: We select 12 pretrained neural networks for classification with common architectures [16] from Tab.1.
Revised: We select 12 pretrained neural networks for classification with common architectures [16] from Tab.

Original: All models are pretrained on ImageNet and publicly available from pytorch vision’s model zoo.
Revised: All models are pretrained on ImageNet and publicly available from pytorch vision’s model zoo.

Original: Wealso include three models with ResNet50 architecture from the RobustBench’s model zoo [7] rankedunder the top-5 networks at the ImageNet leaderboard for corruptions.[7]
Revised: We also include three models with ResNet50 architecture from the RobustBench’s model zoo [7] ranked under the top-5 networks at the ImageNet leaderboard for corruptions.[7]

Original: These neural networks arerobust on ImageNet-C [8] and ImageNet-3DC [9] corruptions respectively.
Revised: These neural networks are robust on ImageNet-C [8] and ImageNet-3DC [9] corruptions respectively.

Revised: Hendrycks2020AugMix is trained on ImageNet together with AugMix, which randomly mixes different augmentations based on AutoAugment [17], such as posterizing, rotation and translation, while ImageNet-C corruptions are excluded.[18] Hendrycks2020Many augments ImageNet with DeepAugment, which stochastically perturbates images by zeroing, convolving, changing activation functions and others in the augmentation network’s forward pass and weights.

Revised: This creates visually diverse distortions, which preserve semantics.[19] Geirhos2020SIN+IN is trained on Stylized-ImageNet (SIN) and ImageNet (IN).[20]

Original: The exact listing of thenetwork architectures can be found in the appendix D in Tab. 1. 
Revised: The exact listing of the network architectures can be found in the appendix D in Tab. 1. [Figure]

Original: 3.1 PSF comparisons
Revised: 3.1 PSF comparisons

Original: Here, the complex optical kernels shall first be compared to the optical kernels visually in Fig 1 forall severities.
Revised: Here, the complex optical kernels shall first be compared to the optical kernels visually in Fig 1 for all severities.

Original: Visually, the severities are comparable, even though there is a dependence on the colorchannel, as well as a break in rotational symmetry.
Revised: Visually, the severities are comparable, even though there is a dependence on the color channel, as well as a break in rotational symmetry.

Original: A criterion to quantify the similarity are also the
Revised: A criterion to quantify the similarity are also the

Original: MTF50 values in  Fig. 
Revised: MTF50 values in appendix B, Fig. 8.

Original: The values are similar and indicate an averaged comparability between thekernels.
Revised: The values are similar and indicate an averaged comparability between the kernels.

Original: The MTF curves for the kernels can also be found in the appendix B. Note that for the opticalkernels six different curves exist, which occur because of the direction dependence and wavelengthdependence, whereas the complexity of the corruption kernels can be reduced to a single MTF curve.
Revised: The MTF curves for the kernels can also be found in the appendix B. Note that for the optical kernels six different curves exist, which occur because of the direction dependence and wavelength dependence, whereas the complexity of the corruption kernels can be reduced to a single MTF curve.

Original: Astigmatic behavior can be read, for example, in severity 1 in appendix B, Fig. 6 in the red and bluechannels, where either the 45 ◦ or the − 45 ◦ curves proceed low.
Revised: Astigmatic behavior can be read, for example, in severity 1 in appendix B, Fig.in the red and blue channels, where either the 45 ◦ or the − 45 ◦ curves proceed low.

Original: In addition, the orientations are justreversed, resulting in chromatic aberrations.
Revised: In addition, the orientations are just reversed, resulting in chromatic aberrations.

Original: 3.2 Image comparisons
Revised: 3.2 Image comparisons

Original: The different filter kernels are then used to convolve the images from ImageNet and yield ten datasetsof 50k images each.
Revised: The different filter kernels are then used to convolve the images from ImageNet and yield ten datasets of 50k images each.

Original: Both, images from corruption kernels and optical kernels are saved with thesame slight JPEG compression as in ImageNet-C to avoid a corruption bias between lossless andlossy image data compression and to keep the processing of 500k images manageable.
Revised: Both, images from corruption kernels and optical kernels are saved with the same slight JPEG compression as in ImageNet-C to avoid a corruption bias between lossless and lossy image data compression and to keep the processing of 500k images manageable.

Original: The usualtransformations center crop and downscale to RGB images of size 224 × 224 are done as preprocessingstep to the bigger original ImageNet images to ensure that no additional smoothing by the scalingoperation is applied to the filtered images.
Revised: The usual transformations center crop and downscale to RGB images of size 224 × 224 are done as preprocessing step to the bigger original ImageNet images to ensure that no additional smoothing by the scaling operation is applied to the filtered images.

Original: The image samples in Fig.
Revised: The image samples in Fig.

Original: 1 visualize differences in thedatasets corruption datasets and optical datasets.
Revised: 1 visualize differences in the corruption datasets and optical datasets.

Original: The blur in the images increases significantly withseverities.
Revised: The blur in the images increases significantly with severities.

Original: Looking at optical datasets2-4 color fringes at edges are readily visible and directionaldependent blur occurs.
Revised: Looking at optical datasets 2-4 color fringes at edges are readily visible and directional dependent blur occurs.

Original: However, the mean values mMSE and mSSIM listed in 2 are very close to each other, which indicatesimilar and comparable image quality.[Figure] [Figure]
Revised: However, the mean values mMSE and mSSIM listed in 2 are very close to each other, which indicate similar and comparable image quality.

Original: 3.2.1 Classification on ImageNet
Revised: 3.3 Classification on ImageNet

Original: The images from  corruption datasets and optical datasets are then processed with the differentneural networks for classification from  Tab. 1.
Revised: The images from the corruption datasets and optical datasets are then processed with the different neural networks for classification from appendix D, Tab. 1.

Original: Again, the processing is set such that no additionaltransformation besides image normalization is done, because the input size is already the target sizeof 224 × 224 . 
Revised: Again, the processing is set such that no additional transformation besides image normalization is done, because the input size matches already the target size of 224 × 224 . Fig.

Original: The classification results for 50k images each in Figs.
Revised: 20 visualizes the absolute accuracies for all studies, which shows a clear trend. While the neural networks of the PytorchVision model zoo were trained only on ImageNet, the networks of the RobustBench model zoo marked with red labels are additionally trained with different augmentations. As a result, these networks stand out as the most robust. Further, to directly compare the effect of the optical kernels to the corruption kernels Fig.

Original: 2b and 2c show differences oftop1-errors for the selected  neural networks.
Revised: 2b shows the differences of Accuracies for the selected 12 neural networks and all severities.

Original: Looking at the meanvalues of the errors µ top 1 , this biascan possibly be due to the slight variation between the kernel types: The image results show slightvariations for levels 3 and 4 in mSSIM, respectively.
Revised: Looking at the mean of the deviation in accuracy µ diff , this bias can possibly be due to the small variation between the kernel types: The image results show slight variations in mSSIM for the different [Figure]

Original:  For level 3, the mSSIM for  optical datasets3 ishigher ( 1 . 11 % ) and for level 4, the mSSIM for corruption datasets4 is lower  ( − 0 .
Revised: severities. For instance, severity 3 shows for the optical datasets a higher mSSIM ( 1 . 11 % ) and for severity 4, the mSSIM for optical datasets is lower than for corruption datasets ( − 0 .

Original: However,significant differences between the networks can be found within these conditions.
Revised: However, significant differences between the networks can be found within these conditions.

Original: For example, Hendrycks2020Many[17, 18], as well as in most cases GoogLeNet[19], can handle the blur of opticalkernels better than that of corruption kernels (lower top1-error).
Revised: For example, Hendrycks2020Many (red dot) [19, 21], as well as in most cases GoogLeNet (green dot) [22], can handle the blur of optical kernels better than that of corruption kernels (higher Accuracy).

Original: Hendrycks2020AugMix[20, 18] doesmostly the opposite.
Revised: Hendrycks2020AugMix (red triangle) [18, 21] does mostly the opposite.

Original: All severities are visualized in appendix F. Note that the differences in mSSIM,mMSE, MTF50 and AUC are for severities 1-2 greater, but the top1-error deviation is smaller forthese less blurred images.
Revised: The total deviation in accuracy between these two neural networks is above 7% for severity 4 . Comparing the ImageNet only trained networks, indicated by blue and

Original:  Conclusion
Revised:  Conclusion

Original: This article compares the ImageNet validation dataset in several modified versions degraded withcorruption kernels from ImageNet-C and optical kernels, which are directional and wavelengthdependent.
Revised: This article compares the ImageNet validation dataset in several modified versions degraded with corruption kernels from ImageNet-C and optical kernels, which are directional and wavelength dependent.

Original: Although the blur kernels are of comparable size and produce similar image datasets,some classification results differ significantly.
Revised: Although the blur kernels are of comparable size and produce similar image datasets, some classification results differ significantly.

Original: We conclude that realistic optical corruptions shouldbe considered in our standard benchmarks towards model robustness. 
Revised: We conclude that realistic optical corruptions should be considered in our standard benchmarks towards model robustness. A PSFs

Original: B MTF curves
Revised: The different used kernels are visualized in Figs. 3, 4 and 5. [Figure] [Figure]

Original: [Figure]
Revised: [Figure]

Original: Here, the direction in coordinate axes is denoted with ( x, y ) and the diagonal direction is denoted with± 45 ◦ .
Revised: Here, the direction in coordinate axes is denoted with ( x, y ) and the diagonal direction is denoted with ± 45 ◦ .

Original: Note that sometimes curves for the optical kernels in different directions proceed differently.
Revised: Note that sometimes curves for the optical kernels in different directions proceed differently.

Original: This astigmatic behaviour is color channel dependent and therefore creates chromatic aberrations.
Revised: This astigmatic behaviour is color channel dependent and therefore creates chromatic aberrations.

Original: [Figure]
Revised: [Figure]

Original: [Figure]
Revised: [Figure]

Original: B.1 Aggregated MTF metrics - differences for MTF 
Revised: B.1 Aggregated MTF metrics - differences for MTF

Original: [Figure]
Revised: [Figure]

Original: C Additional studies for different optical kernels 
Revised: C Additional studies for different optical kernels C.1 Oblique astigmatism (higher match quality)

Original: [Figure] C.1 Oblique astigmatism (higher match quality)

Original: [Figure] We provide here a version with closer match in mSSIM, mMSE, MTF50 and AUC for all severitieswith the parameterization A − 2 2 ∈ { 0 . 9 , 1 . 3 , 2 . 1 , 2 . 8 , 3 . 6 } λ i .
Revised: We provide here a version with closer match in mSSIM, mMSE, MTF50 and AUC for all severities with the parameterization A − 2 2 ∈ { 0 . 9 , 1 . 3 , 2 . 1 , 2 . 8 , 3 . 6 } λ i .

Original: The mSSIM for severities 3-5 is below0 .
Revised: The mSSIM for severities 3-5 is below 0 .

Original: 5 % , but although significantly smaller differences occur compared to Fig.
Revised: 5 % , but although significantly smaller differences occur compared to Fig.

Original: 14 still the DNNs canhandle the blur types differently well, which indicates a distribution shift.
Revised: 14 still the DNNs can handle the blur types differently well, which indicates a distribution shift.

Original: Lower severities tend to bemore robust to changes in mSSIM and the improved match quality has little effect
Revised: Lower severities tend to be more robust to changes in mSSIM and the improved match quality has little effect

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: [Figure]
Revised: [Figure]

Original: C.2 Oblique astigmatism
Revised: C.2 Oblique astigmatism

Original: We include here the study on oblique astigmatic optical kernels as used in the main article.
Revised: We include here the study on oblique astigmatic optical kernels as used in the main article.

Original: The sizeof the kernels in Fig.
Revised: The size of the kernels in Fig.

Original: 3 look very similar to Fig. 4, but create a slightly larger mSSIM ≤ 1 . 1 % forseverities 3-5.
Revised: 3 look very similar to Fig. 4, but create a slightly larger mSSIM ≤ 1 . 1 % for severities

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: [Figure]
Revised: [Figure]

Original: C.3 Straight astigmatism
Revised: C.3 Straight astigmatism

Original: This study shows the effect of the parameterization of straight astigmatism A + ∈{ 1 . 0 , 1 . 4 , 2 . 2 , 2 . 8 , 3 . 6 } λ i , which leads to comparable results as in Fig.
Revised: This study shows the effect of the parameterization of straight astigmatism A + ∈ { 1 . 0 , 1 . 4 , 2 . 2 , 2 . 8 , 3 . 6 } λ i , which leads to comparable results as in Fig.

Original: [Figure]
Revised: [Figure]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: D Additional tables
Revised: D Additional tables

Original: [Table]
Revised: [Table]

Original: E Additional image examples
Revised: E Additional image examples

Original: [Figure]
Revised: [Figure]

Original: [Figure]

Original: [Figure]
Revised: [Figure]

Original: F.1 Classification results for
Revised: F Absolute classification Accuracies on the different modified dataset versions

Original: all severities for additional studies

Original: [Figure]
Revised: Below Fig.

Original: [Figure]
Revised: 20 shows the classification accuracies for all studies from appendix C. Note that while AlexNet (blue triangle downward) has always the worst accuracy, Hendrycks2020Many (red dot) achieves in all cases the best results. Additionally, the pretrained models from RobustBench’s model zoo (red markers) outperfom most of the PyTorch Vision models.

Original: [Figure]
Revised: [Figure]

Original: [Figure] [Figure] 
Revised: [Figure] [Figure] [Figure]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]