Original: ODAM: G RADIENT - BASED I NSTANCE -S PECIFIC V ISUAL E XPLANATIONS FOR O BJECT D ETECTION
Revised: ODAM: G RADIENT - BASED I NSTANCE -S PECIFIC V ISUAL E XPLANATIONS FOR O BJECT D ETECTION

Original: Anonymous authors
Revised: Anonymous authors

Original: Paper under double-blind review
Revised: Paper under double-blind review

Original: A BSTRACT
Revised: A BSTRACT

Original: We propose the gradient

Original: -weighted

Original:  Object Detector Activation Maps (ODAM), a visualized explanation technique for interpreting the predictions of object detectors
Revised: We propose the gradient-weighted Object Detector Activation Maps (ODAM), a visualized explanation technique for interpreting the predictions of object detectors.

Original: Utilizing the gradients of detector targets flowing into the intermediate feature maps
Revised: Utilizing the gradients of detector targets ﬂowing into the intermediate feature maps

Original: ODAM pro duces heat maps that show the influence of regions on the detector’s decision for each predicted attribute.
Revised: ODAM produces heat maps that show the inﬂuence of regions on the detector’s decision for each predicted attribute.

Original: Compared to previous works classification activation maps (CAM),
Revised: Compared to previous works classiﬁcation activation maps (CAM)

Original: ODAM generates instance-specific explanations rather than class-specific ones.
Revised: ODAM generates instance-speciﬁc explanations rather than class-speciﬁc ones.

Original: We show that ODAM is applicable to both one-stage detectors and two-stage detectors with different types of detector backbones and heads, and produces higher-quality visual explanations than the state -of-the-art both effectively and efficiently.
Revised: We show that ODAM is applicable to both one-stage detectors and two-stage detectors with different types of detector backbones and heads and produces higher-quality visual explanations than the state-of-the-art both effectively and efﬁciently

Original: We next propose a training scheme, Odam-Train, to improve the explanation ability on object discrimination of the detector through encouraging consistency between explanations for detections on the same object and distinct explanations for detections on different objects.
Revised: We next propose a training scheme Odam-Train, to improve the explanation ability on object discrimination of the detector through encouraging consistency between explanations for detections on the same object and distinct explanations for detections on different objects

Original: Based on the heat maps produced by ODAM with Odam-Train, we propose Odam-NMS, which considers the information of the model’s explanation for each prediction to distinguish the duplicate detected objects.
Revised: Based on the heat maps produced by ODAM with Odam-Train we propose Odam-NMS which considers the information of the model’s explanation for each prediction to distinguish the duplicate detected objects

Original: We present a detailed analysis of the visualized explanations of detectors and carry out extensive experiments to validate the effectiveness of the proposed ODAM
Revised: We present a detailed analysis of the visualized explanations of detectors and carry out extensive experiments to validate the effectiveness of the proposed ODAM.

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Significant breakthroughs have been made in object detection and other computer vision tasks due to the development of deep neural networks (DNN) (Girshick et al., 2014b).
Revised: Signiﬁcant breakthroughs have been made in object detection and other computer vision tasks due to the development of deep neural networks (DNN) (Girshick et al., 2014b).

Original: However, the unintuitive and opaque process of DNNs makes them hard to interpret.
Revised: However, the unintuitive and opaque process of DNNs makes them hard to interpret.

Original: As spatial convolution is a frequent component of state-of-the-art models for vision tasks, class-specific attention has emerged to interpret CNNs, which has been used to identify failure modes (Agrawal et al., 2016; Hoiem et al., 2012), debug models (Koh & Liang, 2017) and establish appropriate users’ confidence about models (Selvaraju et al., 2017).
Revised: As spatial convolution is a frequent component of state-of-the-art models for vision tasks, class-speciﬁc attention has emerged to interpret CNNs, which has been used to identify failure modes (Agrawal et al., 2016; Hoiem et al., 2012), debug models (Koh & Liang, 2017) and establish appropriate users’ conﬁdence about models (Selvaraju et al., 2017).

Original: These explanation approaches produce heat maps locating the regions in the input images that the model looked at, representing the influence of different pixels on the model’s decision.
Revised: These explanation approaches produce heat maps locating the regions in the input images that the model looked at, representing the inﬂuence of different pixels on the model’s decision.

Original: Gradient visualization (Simonyan et al., 2013), Perturbation (Ribeiro et al., 2016), and
Revised: Gradient visualization (Simonyan et al., 2013), Perturbation (Ribeiro et al., 2016), and

Original: Class Activation Map (CAM) (Zhou et al., 2016) are three widely adopted methods to generate the visual explanation map.
Revised: Class Activation Map (CAM) (Zhou et al., 2016) are three widely adopted methods to generate the visual explanation map.

Original: However, these methods have primarily focused on image classification (Petsiuk et al., 2018; Fong & Vedaldi, 2017; Selvaraju et al., 2017; Chattopadhay et al., 2018; Wang et al., 2020b;a), or its variants, e.g., visual question answering (Park et al., 2018), video captioning (Ramanishka et al., 2017; Bargal et al., 2018), and video activity recognition (Bargal et al., 2018).
Revised: However, these methods have primarily focused on image classiﬁcation (Petsiuk et al., 2018; Fong & Vedaldi, 2017; Selvaraju et al., 2017; Chattopadhay et al., 2018; Wang et al., 2020b;a), or its variants, e.g., visual question answering (Park et al., 2018), video captioning (Ramanishka et al., 2017; Bargal et al., 2018), and video activity recognition (Bargal et al., 2018).

Original: Generating explanation heat maps for object detectors is an under-explored area.
Revised: Generating explanation heat maps for object detectors is an under-explored area.

Original: The first work in this area is D-RISE (Petsiuk et al., 2021), which extends RISE (Petsiuk et al., 2018) for explaining image classifiers to object detectors.
Revised: The ﬁrst work in this area is D-RISE (Petsiuk et al., 2021), which extends RISE (Petsiuk et al., 2018) for explaining image classiﬁers to object detectors.

Original: As a perturbation-based approach, D-RISE first randomly generates a large number of binary masks, resizes them to the image size, and then perturbs the original input to observe the change in the model’s prediction.
Revised: As a perturbation-based approach, D-RISE ﬁrst randomly generates a large number of binary masks, resizes them to the image size, and then perturbs the original input to observe the change in the model’s prediction.

Original: However, the large number of inference calculations makes the D-RISE computationally intensive, and the quality of the heat maps is influenced by the mask resolution (e.g., see Fig. 1b).
Revised: However, the large number of inference calculations makes the D-RISE computationally intensive, and the quality of the heat maps is inﬂuenced by the mask resolution (e.g., see Fig. 1b).

Original: Furthermore, D-RISE only generates an overall heat map for the predicted object, which is unable to show the influence of regions on the specific attributes of a prediction, e.g., class probability and regressed bounding box corner coordinates.
Revised: Furthermore, D-RISE only generates an overall heat map for the predicted object, which is unable to show the inﬂuence of regions on the speciﬁc attributes of a prediction, e.g., class probability and regressed bounding box corner coordinates.

Original: The popular CAM-based methods for image classification are not directly applicable to object detectors.
Revised: The popular CAM-based methods for image classiﬁcation are not directly applicable to object detectors.

Original: CAM methods generate heat maps for classification via a linear combination of the weights and the activation maps, such as the popular Grad-CAM (Selvaraju et al., 2017) and its variants.
Revised: CAM methods generate heat maps for classiﬁcation via a linear combination of the weights and the activation maps, such as the popular Grad-CAM (Selvaraju et al., 2017) and its variants.

Original: However, Grad-CAM provides class-specific explanations, and thus produces heat maps that high-
Revised: However, Grad-CAM provides class-speciﬁc explanations, and thus produces heat maps that high-

Original: [Figure]
Revised: [Figure]

Original: light all objects of in a category instead of explaining a single detection (e.g., see Fig. 1a).
Revised: light all objects of in a category instead of explaining a single detection (e.g., see Fig. 1a).

Original: For object detection, the explanations should be instance-specific rather than class-specific, so as to discriminate each individual object.
Revised: For object detection, the explanations should be instance-speciﬁc rather than class-speciﬁc, so as to discriminate each individual object.

Original: Exploring the spatial importance of different objects can help interpret the models’ decision and show the important area in the feature maps for each prediction.
Revised: Exploring the spatial importance of different objects can help interpret the models’ decision and show the important area in the feature maps for each prediction.

Original: Considering that direct application of existing CAM methods to object detectors is infeasible and the drawbacks of the current state-of-the-art D-RISE, we propose gradient-weighted Object Detector
Revised: Considering that direct application of existing CAM methods to object detectors is infeasible and the drawbacks of the current state-of-the-art D-RISE, we propose gradient-weighted Object Detector

Original: Activation Maps (ODAM).
Revised: Activation Maps (ODAM).

Original: ODAM adopts a similar assumption as Grad-CAM that feature maps correlate with some concept for making the final outputs.
Revised: ODAM adopts a similar assumption as Grad-CAM that feature maps correlate with some concept for making the ﬁnal outputs.

Original: Thus ODAM uses the gradients w.r.t.
Revised: Thus ODAM uses the gradients w.r.t.

Original: each pixel in the feature map to obtain the explanation heat map for each attribute of the object prediction.
Revised: each pixel in the feature map to obtain the explanation heat map for each attribute of the object prediction.

Original: Compared with the perturbation-based D-RISE, ODAM is more efficient and generates less noisy heat maps (see Fig. 1c), while also explaining each attribute separately.
Revised: Compared with the perturbation-based D-RISE, ODAM is more efﬁcient and generates less noisy heat maps (see Fig. 1c), while also explaining each attribute separately.

Original: We also explore a unique explanation task for object detectors, object discrimination , which aims to indicate which object was detected.
Revised: We also explore a unique explanation task for object detectors, object discrimination , which aims to explain which object was detected.

Original: This is different fromexplaining the object class by visualizing the object parts.
Revised: This is different from the traditional explanation task of what features are important for class prediction (i.e., object specﬁcation ).

Original: We propose a training scheme, Odam-Train, to improve the explanation ability for object discrimination by introducingboth consistency and separation losses.
Revised: We propose a training scheme, Odam-Train, to improve the explanation ability for object discrimination by introducing consistency and separation losses.

Original: The training encourages the model to produce consistent heat maps for the same object, and distinctive heat maps for different objects (see Fig. 1d).
Revised: The training encourages the model to produce consistent heat maps for the same object, and distinctive heat maps for different objects (see Fig. 1d).

Original: We further propose Odam-NMS, which uses the instance-level heat maps from ODAMand Odam-Train to aid the non-maximum suppression (NMS) process of removing duplicate predictions of the same object.
Revised: We further propose OdamNMS, which uses the instance-level heat maps from ODAM to aid the non-maximum suppression (NMS) process of removing duplicate predictions of the same object.

Original: The contributions of our paper are summarized as follows:
Revised: The contributions of our paper are summarized as follows:

Original: We propose ODAM, a gradient-based visual explanation approach to produce instance-specific heat maps for explaining prediction attributes of object detectors, which is more efficient and robust compared with the current state-of-the-art.
Revised: We propose ODAM, a gradient-based visual explanation approach to produce instance-speciﬁc heat maps for explaining prediction attributes of object detectors, which is more efﬁcient and robust compared with the current state-of-the-art.

Original: We demonstrate the generalizability of ODAM by exhibiting explanations on both one-stage and two-stage detectors with different types of backbones and detector heads.
Revised: We demonstrate the generalizability of ODAM by exhibiting explanations on one- and twostage, and transformer-based detectors with different types of backbones and detector heads.

Original: We explore a unique explanation task for detector, object discrimination, for showing which object was detected, and propose Odam-Train to improve object discrimination ability.
Revised: We explore a unique explanation task for detector, object discrimination, for explaining which object was detected, and propose Odam-Train to improve object discrimination ability.

Original: We propose Odam-NMS, which uses the instance-level heat maps generated by ODAM with Odam-Train to remove duplicate predictions during NMS, and its effectiveness verifies the object discrimination ability of ODAM with Odam-Train.
Revised: We propose Odam-NMS, which uses the instance-level heat maps generated by ODAM with Odam-Train to remove duplicate predictions during NMS, and its effectiveness veriﬁes the object discrimination ability of ODAM with Odam-Train.

Original:  R ELATED WORKS
Revised:  R ELATED WORKS

Original: Object detection Object detectors are generally composed of a backbone, neck and head.
Revised: Object detection Object detectors are generally composed of a backbone, neck and head.

Original: Based on the type of head, detectors can be mainly divided into one-stage and two-stage methods.
Revised: Based on the type of head, detectors can be mainly divided into one-stage and two-stage methods.

Original: Twostage approaches perform two steps: generating region candidates (proposals) and then using RoI (Region of Interest) features for the subsequent object classification and location regression.
Revised: Twostage approaches perform two steps: generating region candidates (proposals) and then using RoI (Region of Interest) features for the subsequent object classiﬁcation and location regression.

Original: The representative two-stage works are the R-CNN family, including R-CNN (Girshick et al., 2014a),
Revised: The representative two-stage works are the R-CNN family, including R-CNN (Girshick et al., 2014a),

Original: Fast R-CNN (Girshick, 2015),
Revised: Fast R-CNN (Girshick, 2015),

Original: Faster-RCNN (Ren et al., 2015), and Mask R-CNN (He et al., 2017).
Revised: Faster-RCNN (Ren et al., 2015), and Mask R-CNN (He et al., 2017).

Original: One-stage methods remove the RoI feature extraction and directly perform classification and regression on the entire feature map, and typical methods are YOLO (Redmon et al., 2016), RetinaNet (Lin et al., 2017b), and FCOS (Tian et al., 2019).
Revised: One-stage methods remove the RoI feature extraction and directly perform classiﬁcation and regression on the entire feature map, and typical methods are YOLO (Redmon et al., 2016), RetinaNet (Lin et al., 2017b), and FCOS (Tian et al., 2019).

Original: Our ODAM can generate heat maps for both one-stage and two-stage detectors with no limitation of the types of backbones and heads, and we adopt Faster R-CNN and FCOS in our experiments.
Revised: Our ODAM can generate heat maps for both one- and two-stage detectors with no limitation of the types of backbones and heads, as well as transformer-based detectors. We mainly adopt Faster R-CNN and FCOS in our experiments.

Original: Explanation by visualization Since visualizing the importance of input features is a straightforward approach to interpret a model, many works visualize the internal representations of image classifier CNNs with heat maps.
Revised: Explanation by visualization Since visualizing the importance of input features is a straightforward approach to interpret a model, many works visualize the internal representations of image classiﬁer CNNs with heat maps.

Original: Gradient visualization methods (Simonyan et al., 2013) backpropagate the gradient of a target class score to the input image to highlight the “important” pixels, and other works (Springenberg et al., 2014; Zeiler & Fergus, 2014; Adebayo et al., 2018a) manipulate this gradient to improve the results qualitatively (see comparison in (Mahendran & Vedaldi, 2016)).
Revised: Gradient visualization methods (Simonyan et al., 2013) backpropagate the gradient of a target class score to the input image to highlight the “important” pixels, and other works (Springenberg et al., 2014; Zeiler & Fergus, 2014; Adebayo et al., 2018a) manipulate this gradient to improve the results qualitatively (see comparison in (Mahendran & Vedaldi, 2016)).

Original: The visualizations are fine-grained but not class-specific.
Revised: The visualizations are ﬁne-grained but not class-speciﬁc.

Original: Perturbation-based methods (Petsiuk et al., 2018; Ribeiro et al., 2016; Lundberg & Lee, 2017; Dabkowski & Gal, 2017; Chang et al., 2018; Fong & Vedaldi, 2017; Wagner et al., 2019) perturb the original input and observe the changes in output scores to determine the importance of regions.
Revised: Perturbation-based methods (Petsiuk et al., 2018; Ribeiro et al., 2016; Lundberg & Lee, 2017; Dabkowski & Gal, 2017; Chang et al., 2018; Fong & Vedaldi, 2017; Wagner et al., 2019; Lee et al., 2021) perturb the original input and observe the changes in output scores to determine the importance of regions.

Original: These black-box methods are intuitive and highly generalizable, but computationally intensive.
Revised: Most black-box methods are intuitive and highly generalizable, but computationally intensive.

Original: Furthermore, the type or resolution of the perturbation greatly influences the quality of visualization results.
Revised: Furthermore, the type or resolution of the perturbation greatly inﬂuences the quality of visualization results.

Original: CAM-based explanations, e.g. CAM (Zhou et al., 2016), Grad-CAM (Selvaraju et al., 2017), and
Revised: CAM-based explanations, e.g. CAM (Zhou et al., 2016), Grad-CAM (Selvaraju et al., 2017), and

Original: Grad-CAM++ (Chattopadhay et al., 2018), produce a heat map from a selected intermediate layer by linearly combining its feature activation maps with weights that indicate each feature’s importance.
Revised: Grad-CAM++ (Chattopadhay et al., 2018), produce a heat map from a selected intermediate layer by linearly combining its feature activation maps with weights that indicate each feature’s importance.

Original: For example, Grad-CAM defines the weights as the global average pooling of the corresponding gradient map, computed using back-propagation.
Revised: For example, Grad-CAM deﬁnes the weights as the global average pooling of the corresponding gradient map, computed using back-propagation.

Original: Some gradient-free CAMs (Ramaswamy et al., 2020; Wang et al., 2020b;a) adopt the perturbation to generate weights from class score changes.
Revised: Some gradient-free CAMs (Ramaswamy et al., 2020; Wang et al., 2020b;a) adopt the perturbation to generate weights from class score changes.

Original: Although Grad-CAM has been adopted to study adversarial context patches in single-shot object detectors (Saha et al., 2020), the explanations are still category-specific.
Revised: Although Grad-CAM has been adopted to study adversarial context patches in single-shot object detectors (Saha et al., 2020), the explanations are still category-speciﬁc.

Original: (Petsiuk et al., 2021) describes the reasons that make direct application of existing classifier explanation methods infeasible for object detector, and then proposes D-RISEbased on RISE (Petsiuk et al., 2018), a black-box perturbation-based method.
Revised: Petsiuk et al. (2021) describes the reasons that make direct application of existing classiﬁer explanation methods infeasible for object detector, and then proposes D-RISE (Petsiuk et al., 2018), a black-box perturbation-based method.

Original: Hence, D-RISE inheritsboth the pros and cons of RISE, namely highgeneralizability due to the black-box nature but time-consuming and noisy due to the inference procedure.
Revised: Hence, D-RISE inherits the pros and cons of RISE: high-generalizability due to the blackbox nature, but time-consuming and noisy due to the inference procedure.

Original: Aiming to explorethe possibility of white-box explanation of detectors, we propose ODAM, which utilizes gradient information to generate importance heat map for instance-specific detector explanations.
Revised: To explore white-box explanations of detectors, we propose ODAM, which uses gradient information to generate importance heat map for instance-speciﬁc detector explanations.

Original: Based on ODAM, we also propose Odam-Train training to improve the object discrimination of the instance-specific explanations, which is infeasible with the class-specific heat maps and the classification task.
Revised: Based on ODAM, we also propose OdamTrain training to improve the object discrimination of the instance-speciﬁc explanations, which is infeasible with the class-speciﬁc heat maps and the classiﬁcation task.

Revised: Finally, Wu & Song (2019) estimates a latent-part model of each detected instance to explain its high-level semantic structure.

Original: Advanced NMS Classic NMS assumes that multiple instances rarely overlap, and thus high IoU (intersection over union) of two bounding boxes indicates duplicate detections.
Revised: Advanced NMS Classic NMS assumes that multiple instances rarely overlap, and thus high IoU (intersection over union) of two bounding boxes indicates duplicate detections.

Original: Several advanced
Revised: More advanced

Original: NMS are proposed to mitigate the overdependence on IoU, e.g., SoftNMS (Bodla et al., 2017),
Revised: NMS are proposed to mitigate the overdependence on IoU:

Original:  AdaptiveNMS (Liu et al., 2019), Visibility Guided NMS (G¨ahlert et al., 2020),and Relation Network
Revised: SoftNMS (Bodla et al., 2017), AdaptiveNMS (Liu et al., 2019), Visibility Guided NMS (G ¨ ahlert et al., 2020),

Original: Hu et al.
Revised: RelationNet (Hu et al., 2018), and Gnet (Hosang et al., 2017).

Original: These methods either use extra predicted cues, but still assume that high IoU correspond to duplicate detections, or modify the detectors to be more complex.
Revised: These methods either use extra predicted cues, but still assume that high IoU correspond to duplicate detections, or modify the detectors to be more complex.

Original: Relying on IoU is not enough in crowded scenes where objects partially occlude each other, and thus their IoUs are naturally large.
Revised: Relying on IoU is not enough in crowded scenes where objects partially occlude each other, and thus their IoUs are naturally large.

Original: In these cases, internal information about the predictions is required.
Revised: In these cases, internal information about the predictions is required.

Original: FeatureNMS Salscheider (2021) encodes feature embeddings for predictions and trains their distances between the same object to be smaller than those of different objects.
Revised: FeatureNMS (Salscheider, 2021) encodes features for predictions, and trains their distances between the same object to be smaller than those of different objects.

Original: In contrast, we propose Odam-NMS, which uses the correlations between instance-level heat maps together with IoUs to remove duplicate proposals of the same object.
Revised: In contrast, we propose Odam-NMS, which uses the correlations between instance-level heat maps and the their box IoUs to remove duplicate proposals of the same object.

Original: Compared with Salscheider (2021), our Odam-NMS is more stable and can also be interpreted to explain which objects were detected (i.e., object discrimination).
Revised: Compared with Salscheider (2021), our Odam-NMS is more stable and can also be interpreted to explain which objects were detected (i.e., object discrimination).

Original:  M ETHOD
Revised:  M ETHOD

Original: We propose our ODAM for explaining object detection(Sec 3.1) with instance-level heat maps,
Revised: We propose our ODAM for explaining object detection with instance-level heat maps (Sec 3.1),

Original: Odam-Train(Sec. 3.2) for improving explanations for object discrimination, and Odam-NMS(Sec. 3.3) for NMS in crowd scenarios using these explanations.
Revised: Odam-Train for improving explanations for object discrimination (Sec. 3.2), and Odam-NMS for NMS in crowd scenarios using these explanations (Sec. 3.3).

Original: 3. ODAM: O BJECT D ETECTOR A CTIVATION M APS
Revised: 3. ODAM: O BJECT D ETECTOR A CTIVATION M APS

Original: Given an image I , the detector model outputs multiple predictions, with each prediction p consisting of the class score s ( p ) c and bounding box B ( p ) =
Revised: Given an image I , the detector model outputs multiple predictions, with each prediction p consisting of the class score s ( p ) c and bounding box B ( p ) =

Original: ( x ( p ) 1 , y ( p ) 1 , x ( p ) 2 , y ( p ) 2 ) .
Revised: ( x ( p ) 1 , y ( p ) 1 , x ( p ) 2 , y ( p ) 2 ) .

Original: Our goal is to generate heat maps to indicate the important regions that have a positive influence on the output of each prediction.
Revised: Our goal is to generate heat maps to indicate the important regions that have a positive inﬂuence on the output of each prediction.

Original: In Grad-CAM (Selvaraju et al., 2017) and its generalization Grad-CAM++ (Chattopadhay et al., 2018), the final score for a particular class Y c is predicted from the whole image and the algorithm[Figure] ignores distinguishing object instances within.
Revised: In Grad-CAM (Selvaraju et al., 2017) and its generalization Grad-CAM++ (Chattopadhay et al., 2018), the ﬁnal score for a particular class Y c is predicted from the whole image and the algorithm ignores distinguishing object instances within.

Original: Their explanation starts from the assumption that the score to be interpreted can be written as a linear combination of its global pooled last convolutionallayer feature maps { A k } k , Y c
Revised: Their explanation starts from the assumption that the score to be interpreted can be written as a linear combination of its global pooled last convolutional

Original:  = (cid:80) k w ck (cid:80) ij A ijk = (cid:80) ij (cid:80)
Revised: [Figure] layer feature maps { A k } k , Y c = (cid:80) k w ck (cid:80) ij A ijk = (cid:80) ij (cid:80)

Original: k w ck A ijk , where A ijk indexes location ( i, j ) of A k .
Revised: k w ck A ijk , where A ijk indexes location ( i, j ) of A k .

Original: Thus, the class-specific heat map H cij = (cid:80)
Revised: Thus, the class-speciﬁc heat map H c ij = (cid:80)

Original: k w ck A ijk summarizes the feature maps with w ck capturing the importance of the k-th feature.
Revised: k w ck A ijk summarizes the feature maps with w ck capturing the importance of the k-th feature.

Original: To obtain the importance of each feature channel, Grad-CAM estimates w ck by global average pooling the gradient map ∂Y c /∂A k , while
Revised: To obtain the importance of each feature channel, Grad-CAM estimates w ck by global average pooling the gradient map ∂Y c /∂A k , while

Original: Grad-CAM++ uses a weighted global pooling.
Revised: Grad-CAM++ uses a weighted global pooling.

Original: However, both methods are limited to class-specific explanations, due to computing a channel-wise importance, which ignores the spatial discrimination information that is essential for interpreting different object instances.
Revised: However, both methods are limited to class-speciﬁc explanations, due to computing a channel-wise importance, which ignores the spatial discrimination information that is essential for interpreting different object instances.

Original: Based on the above analysis, we assume that any predicted object attribute scalar Y ( p ) of a particular instance p can be written as a linear element-wise weighted combination of the feature map, and then the instance-specific heat map H ( p ) ij can be produced by summarizing the feature maps with weight w ( p ) ijk that captures the importance of each pixel and each channel ,
Revised: Based on the above analysis, we assume that any predicted object attribute scalar Y ( p ) of a particular instance p can be written as a linear element-wise weighted combination of the feature map, and then the instance-speciﬁc heat map H ( p ) ij can be produced by summarizing the feature maps with weight w ( p ) ijk that captures the importance of each pixel and each channel ,

Original: [Equation]
Revised: [Equation]

Original: Previous gradient-based works (Simonyan et al., 2013; Springenberg et al., 2014; Selvaraju et al., 2017; Chattopadhay et al., 2018) have shown that the partial derivative w.r.t.
Revised: Previous gradient-based works (Simonyan et al., 2013; Springenberg et al., 2014; Selvaraju et al., 2017; Chattopadhay et al., 2018) have shown that the partial derivative w.r.t.

Original: A ijk can reflect the influence of the k -th feature at ( i, j ) on the final output.
Revised: A ijk can reﬂect the inﬂuence of the k -th feature at ( i, j ) on the ﬁnal output.

Original: However, such pixel-wise gradient maps are typically noisy, as visualized in (Simonyan et al., 2013).
Revised: However, such pixel-wise gradient maps are typically noisy, as visualized in (Simonyan et al., 2013).

Original: Thus, we set the importance weight map w ( p ) k according to the gradient map ∂Y ( p ) /∂A
Revised: Thus, we set the importance weight map w ( p ) k according to the gradient map ∂Y ( p ) /∂A

Original: k after a local smoothing operation Φ , and the corresponding heat map for scalar output Y ( p ) is obtained through a pixel-weighted mechanism:
Revised: k after a local smoothing operation Φ , and the corresponding heat map for scalar output Y ( p ) is obtained through a pixel-weighted mechanism:

Original: [Equation]
Revised: [Equation]

Original: where ◦ is element-wise multiplication.
Revised: where ◦ is element-wise multiplication.

Original: Here, local pooling is utilized on the gradient map to produce a smooth weight map, while maintaining the important spatial discrimination information.
Revised: Here, local pooling is utilized on the gradient map to produce a smooth weight map, while maintaining the important spatial discrimination information.

Original: We adopt a Gaussian kernel for Φ in the experiments, and adaptively decide the size of the kernel based on the size of predicted object in the feature map. 
Revised: We adopt a Gaussian kernel for Φ in the experiments, and adaptively decide the size of the kernel based on the size of predicted object in the feature map. Fig.

Original:  When the scalar output Y ( p ) is a class score, ODAM highlights the important feature regions used by the detector to classify the instance p .
Revised: 2a shows our ODAM framework. When the scalar output Y ( p ) is a class score, ODAM highlights the important feature regions used by the detector to classify the instance p .

Original: Note that Y ( p ) could be any differentiable attribute of the predictions.
Revised: Note that Y ( p ) could be any differentiable attribute of the predictions.

Original: For example, in our experiments we also examine the heat maps related to the predicted coordinates of the regressed bounding box (see Fig. 3).
Revised: For example, in our experiments we also examine the heat maps related to the predicted coordinates of the regressed bounding box (see Fig. 3).

Original: In addition to the fine-grained explanations for each predicted attribute, we also generate the heat map for the entire prediction by combining heat maps from classification and bounding box regression results using element-wise maximum,

Original: H ( p ) comb = max { H ( p ) class , H ( p ) IoU } , where H ( p ) class is the heat map for the predicted class, and H ( p ) IoU is the heat map for the IoU (intersection over union) score between B ( p ) and the ground-truth box

Original: Our work is the first analysis and successful attempt to use the white-box method to generate instance-level explanations for object detector predictions, rather than only class-level explanations.
Revised: Our work is the ﬁrst analysis and successful attempt to use a white-box method to generate instancelevel explanations for object detector predictions, rather than only class-level explanations.

Original: With a PyTorch implementation, gradients of any scalar targets w.r.t.
Revised: using PyTorch, gradients of any scalar targets w.r.t.

Original: intermediate features can be calculated automatically Paszke et al.
Revised: intermediate features can be calculated automatically (Paszke et al., 2017).

Original: In this way, generating an ODAM explanation for one prediction takes about 2ms, which is much faster than the perturbation-basedblack-box method D-RISE, where using 5000 masks requires about 3 minutes to process one image with FCOS.
Revised: In this way, generating an ODAM explanation for one prediction takes about 2ms, which is much faster than the perturbation-based D-RISE, where using 5000 masks requires ∼minutes to process one image with FCOS.

Original: In 
Revised: In Secs.

Original: Sec. 4.1 and Sec.4.2, we qualitatively and quantitatively verify that the gradient-based method can effectively explain the predicted results for each detection proposal.
Revised: 4.1 and 4.2, we qualitatively and quantitatively verify that our ODAM can effectively explain the predicted results for each detection proposal.

Original: 3. O DAM -T RAIN
Revised: 3. O DAM -T RAIN

Original: Since the instance-specific heat maps may still “leak” onto other neighboring objects, especially in crowded scenes (e.g., see Fig. 4a), we propose a training method Odam-Train for improving the explanation ability of object discrimination to better show which object was being detected.
Revised: Since the instance-speciﬁc heat maps may still “leak” onto other neighboring objects, especially in crowded scenes (e.g., see Fig. 4a), we propose a training method Odam-Train for improving the heat maps for object discrimination, to better explain which object was being detected.

Original: In order to focus the detector to be more concentrated on a specific object area, and not overlapped with other objects, Odam-Train encourages similar attention for different predictions of the same object, and separate attentions for different objects.
Revised: In order to focus the detector to be better localized on a speciﬁc object area, and not overlapped with other objects, Odam-Train encourages similar attention for different predictions of the same object, and separate attentions for different objects (see Fig. 2b).

Original: Specifically, we propose a heat-map consistency loss L con and a separation loss L sep as auxiliary losses during detector training.
Revised: Speciﬁcally, we propose a heat-map consistency loss L con and a separation loss L sep as auxiliary losses during detector training.

Original: Heat maps are first calculated by ODAM for all the positive proposals, and then resized to the same size, and vectorized.The
Revised: Using the predicted con- ﬁdence scores as explanation targets, heat maps are ﬁrst calculated by ODAM for all the positive proposals, and then resized to the same size, and vectorized.

Original:  ODAM vectors are then organized by ground-truth  object, where P ( p ) =
Revised: The ODAM vectors are then organized by ground-truth (GT) object, where P ( p ) =

Original: { H ( p ) n } n is the set of ODAM vectors for positive predictions of the p -th ground-truth (GT) object.
Revised: { H ( p ) n } n is the set of ODAM vectors for positive predictions of the p -th GT object.

Original: For each GT object, the best prediction H ( p ) best is selected in P ( p ) that has the highest IoU between its predicted bounding box and the GT box.
Revised: For each GT object, the best prediction H ( p ) best is selected from P ( p ) that has the highest IoU with the GT box.

Original: Then, the consistency and separation losses are defined so that the ODAM vectors of the same object are consistent, while those of different objects are distinctive,
Revised: The consistency and separation losses are deﬁned as:

Original: [Equation]
Revised: [Equation]

Original: p ) best , H ( p ) n ) , L sep = (cid:88) p ∈ GT (cid:88) m/ ∈P ( p ) − log (cid:0) 1 − cos( H ( p ) best , H ( ¬ p ) m ) (cid:1) , (3) where H ( ¬ p ) m are ODAM vectors for proposals not corresponding to the n -th GT object.
Revised: where H ( ¬ p ) m are ODAM vectors for proposals not corresponding to the n -th GT object.

Original: Finally, the auxiliary loss during detector training is: Laux =
Revised: The loss for detector training is L =

Original:  ( L con + L sep ) /N , where N is the total number of ODAM vector pairs during the loss calculation.
Revised: L detector + ( L con + L sep ) /N , where N is the total number of ODAM vector pairs during the loss calculation.

Revised: Finally, we note that the proposed Odam-Train is a fair design because the supervision of the heat map affects all layers of the detector via the top-down gradient computation of ODAM.

Revised: Therefore, changes in the heat maps from learning (e.g., better localized on the object) are reﬂected as changes in the detector’s strategy (using only features on the object).

Original: 3. O DAM -NMS
Revised: 3. O DAM -NMS

Original: In object detection, duplicated detections are removed in post-processing using NMS, which is based on theempirical assumption: two bounding boxes  that are overlapped (high IoU) are likely to be duplicated, and the box with lower-score (less confidence) should be removed.
Revised: In object detection, duplicated detections are removed in post-processing using NMS, which is based on the assumption: two bounding boxes (bboxes) that are overlapped (high IoU) are likely to be duplicated, and the bbox with lower-score (less conﬁdence) should be removed.

Original: In particular, for classical NMS, the predictions in list P are sorted by their confidence scores, then each prediction p ∈ P is compared to the currently selected detections d ∈ D .
Revised: In particular, for classical NMS, the predictions in list P are sorted by their conﬁdence scores, then each prediction p ∈ P is compared to the currently selected detections d ∈ D .

Original: If the IoU between p and any d ∈ D is larger than a threshold T iou , p is considered a duplicate and discarded.
Revised: If the IoU between p and any d ∈ D is larger than a threshold T iou , p is considered a duplicate and discarded.

Original: Otherwise p is added to D .
Revised: Otherwise p is added to D .

Original: The classical NMS has shortcomings in crowded scenes because the key assumption does not hold when objects are partially occluded by neighboring objects.
Revised: The classical NMS has shortcomings in crowded scenes because the key assumption does not hold when objects are partially occluded by neighboring objects.

Original: We propose Odam-NMS to mitigate this problem based on an observation that with Odam-Train, the ODAM heat maps for different objects can be distinctive, even though their bounding boxes are heavily overlapped (see the left and center heat maps in Fig. 2c).
Revised: We propose Odam-NMS to mitigate this problem based on an observation that with Odam-Train, the ODAM heat maps for different objects can be distinctive, even though their bboxes are heavily overlapped (see the left and center heat maps in Fig. 2c).

Original: Meanwhile, even if the IoU of two predicted bounding boxes for the same object does not exceed the threshold, their explanation may be similar indicating the same object instance is detected.
Revised: Meanwhile, even if the IoU of two predicted bboxes is small, their explanations may be similar indicating the same object instance is detected.

Original: For example, in Fig.
Revised: For example, in Fig.

Original: 2c, the center and right predictions have lowbox IoU(0.44) but have heat maps with high correlation (0.81).
Revised: 2c, the center and right predictions have low IoU but have heat maps with high correlation.

Original: In other words, ODAM shows which object the model looked at to make the prediction, which can intuitively assist NMS to better identify duplicate object predictions.
Revised: In other words, ODAM shows which object the model looked at to make the prediction, which can intuitively assist NMS to better identify duplicate object predictions.

Original: In particular, after the inference stage of the detector, we use ODAM to generate heat maps for each prediction.
Revised: After the inference stage of the detector, we use ODAM to generate heat maps for each prediction with the predicted conﬁdence score.

Original: All the heat maps are resized to the same size with a short edge length of 50, then vectorized.
Revised: All the heat maps are resized to the same size with a short edge length of 50, then vectorized.

Original: Normalized correlation is calculated between each pair of vectors to represent the probability that the two predictions correspond to the same object.
Revised: Normalized correlation is calculated between each pair of vectors to represent the probability that the two predictions correspond to the same object.

Original: Odam-NMS uses both the IoUs and heat map correlations between p and d ∈ D when considering whether a prediction should be removed or kept.
Revised: Odam-NMS uses both the IoUs and heat map correlations between p and d ∈ D when considering whether a prediction should be removed or kept.

Original: If the IoU is larger than T iou while the correlation is very small ( corr ≤ T l ), then p is not a duplicate; On the contrary, if the IoU is small but the correlation is very near to one ( corr > T h ), then pand the d are predicting the same object, which means p is a duplicate.
Revised: If the IoU is large ( IoU ≥ T iou ) and the correlation is very small ( corr ≤ T l ), then p is not a duplicate; If the IoU is small ( IoU < T iou ) and the correlation is very large ( corr > T h ), then p is a duplicate.

Original: Through these two conditions, Odam-NMS keeps more proposals in the high-IoU range for detecting highly-overlapped crowded objects, and removes more proposals in the low-IoU range for reducing duplicates.
Revised: Through these two conditions, Odam-NMS keeps more proposals in the high-IoU range for detecting highly-overlapped crowded objects, and removes more proposals in the low-IoU range for reducing duplicates.

Original: The pseudo codeof Odam-NMS is in the Appendix. [Figure]
Revised: The pseudo code is in the App. A.1.

Original:  E XPERIMENTS
Revised:  E XPERIMENTS

Original: In this section we conduct experiments on ODAM to: 1) evaluate its visual explanations qualitatively and quantitatively, and compare with the current state-of-the-art method D-RISE (Petsiuk et al., 2021); 2) evaluate the proposed Odam-NMS on crowded scenes.
Revised: In this section we conduct experiments on ODAM to: 1) evaluate its visual explanations qualitatively and quantitatively, and compare with the current state-of-the-art method D-RISE (Petsiuk et al., 2021); 2) evaluate the proposed Odam-NMS on crowded scenes.

Original: We mainly conduct the experiments withboth one-stage detector FCOS (Tian et al., 2019) and two-stage detector Faster 
Revised: We mainly conduct the experiments with one-stage detector FCOS (Tian et al., 2019) and two-stage detector Faster R-CNN, (Ren et al., 2015) using ResNet-50 (He et al., 2016) as the backbone and FPN (Lin et al., 2017a) as Q: The robot has detected the object inside the blue bounding box, and gives four attention heat maps to explain why the robot found the object. Please rank the Explanation A to Explanation D by the order of the most reasonable to the most unreasonable.

Original: R-CNN, (Ren et al., 2015) using ResNet-50 (He et al., 2016) as the backbone and FPN (Lin et al., 2017a) as the neck.
Revised: Detected Object A B C

Revised: D Detected Object Detected Object

Revised: A

Revised: B

Revised: C

Revised: D A

Revised: B

Revised: C

Revised: D Examples of Questionnaire

Revised: Examples of Questionnaire 2 Detected Object

Revised: Robot

Revised: Robot 2 Detected Object

Revised: Robot

Revised: Robot 2 Detected Object

Revised: Robot

Revised: Robot 2 Q: Two robots have detected the object inside the blue bounding box, and give us the attention heat maps to explain why they found the object.

Revised: Please choose the robot that has a more reasonable explanation.

Original:  Two datasets are adopted for evaluation: MS COCO (Lin et al., 2014), a standard object detection dataset, and CrowdHuman (Shao et al., 2018), containing scenes with heavily overlapped objects.
Revised: [Figure] the neck. Two datasets are adopted for evaluation: MS COCO (Lin et al., 2014), a standard object detection dataset, and CrowdHuman (Shao et al., 2018), containing scenes with heavily overlapped objects.

Original: Experiments are performed using PyTorch and an RTX 3090 GPU.
Revised: Experiments are performed using PyTorch and an RTX 3090 GPU.

Original: The training and testing hyperparameters are the same as those of the baseline detectors.
Revised: The training and testing hyperparameters are the same as those of the baseline detectors.

Original: 4. Q UALITATIVE EVALUATION OF VISUAL EXPLANATIONS
Revised: 4. Q UALITATIVE EVALUATION OF VISUAL EXPLANATIONS

Original: Evaluation via visualization In order to verify the interpretability of visualizations, we generate visual explanations for different prediction targets (class score, bounding box regression values and their combination) of two specific instances using various detector architectures with the two types of backbones. 
Revised: Evaluation via visualization In order to verify the interpretability of visualizations, we generate visual explanations for different prediction attributes (class score, bbox regression values) of two speciﬁc instances using various detector architectures with the two types of backbones. To obtain a holistic view of the explanations generated by different models, we compute a combined heat map based on element-wise maximum of heat maps for the predicted class and bbox regression, H comb = max( H class , H x 1 , H y 1 , H x 2 , H y 2 ) .

Original: Here we adopt the original baseline detector models (Odam-Train results are visualized in the next experiment).
Revised: Here we adopt the original baseline detector models (Odam-Train results are visualized in the next experiment).

Original: A set of example results are presented in Fig.
Revised: A set of example results are presented in Fig.

Original: 3, and we have the following observations from examining many such examples: 1) When predicting the object class, the model attends to the central areas of the object; 2) when regressing the bounding box, the model focuses on the extent of the object, while sometimes also looking at context information (e.g., for FCOSResNet50, the prediction of x 2 (right coordinate) of the horse uses its head on the left); 3)
Revised: 3 (left), and we have the following observations from examining many such examples (see App. A.5.5): 1) When predicting the object class, the model attends to the central areas of the object; 2) when regressing the bbox, the model focuses on the extent of the object, (see App. A.5.

Original:  For the same target, models from different detectors show attention on different regions, even through they all detect the same instance with a high confidence.
Revised: for more examples); 3) For the same target, models from different detectors show attention on different regions, even though they all detect the same instance with a high conﬁdence.

Original: Thus, developers can have an intuitive judgment about the model through explanation maps. 
Revised: Thus, developers can have an intuitive judgment about the model through explanation maps. [Figure]

Original: From the combination maps, which consider both classification and bounding box regression, the leg of the horse and the head of the dog are commonly important for the detectors, although theconcrete heat maps look different. 
Revised: From the combination maps (Fig. 3 right), which consider both classiﬁcation and bbox regression, the right arm of the person and the head of the dog are commonly important for the detectors, although the heat maps look different. More examples are in App.

Original: [Figure]
Revised: A.5.7.

Original: Furthermore, we compare theinstance-specific visualizations of Grad-CAM, D-RISE and our ODAM (w/o and w/ Odam-Train) in Fig.
Revised: We further compare the visualizations of Grad-CAM, D-RISE and our ODAM (w/o and w/ Odam-Train) in Fig.

Original: The results are all generated with FCOS with FPN, and both Grad-CAM and ODAM use class score targets, while D-RISE uses the same mask settings as Petsiuk et al. (2021) to find the attention area of predictions.
Revised: The results are all generated with FCOS with FPN, and both Grad-CAM and ODAM use class score targets, while D-RISE uses the same mask settings as Petsiuk et al. (2021) to ﬁnd the attention area of predictions.

Original: Our ODAM demonstrates a strong ability of generating clear and distinct instance-specific heat maps.
Revised: Our ODAM demonstrates a strong ability of generating clear and distinct instance-speciﬁc heat maps.

Original: In contrast, Grad-CAM is class-specific (highlighting all the people for each detected person), and D-RISE contains “speckles” in the background due to the random masking mechanism.
Revised: In contrast, Grad-CAM is class-speciﬁc (highlighting all the people for each detected person), and D-RISE contains “speckles” in the background due to the random masking mechanism.

Original: See Appendix for more examples.
Revised: See App. A.5.4 for more examples.

Original: Visualization w/ and w/o Odam-Train
Revised: Visualization w/ and w/o Odam-Train

Original: Next we compare the heat maps from ODAM using the baseline detector trained with and without Odam-Train.
Revised: Next we compare the heat maps from ODAM using the baseline detector trained with and without Odam-Train.

Original: The heat maps for each proposal are computed by ODAM with their confidence score as the explanation targets.
Revised: The heat maps for each proposal are computed by ODAM with its conﬁdence score as the explanation target.

Original: We find that although the original heat maps without Odam-Train (Fig. 4a) can locate the object well, the attention 
Revised: Although the original heat maps without Odam-Train (Fig. 4a) can locate the object well, the attention is spread to its overlapping

Original: (b) (a)Target object (d)Ours (b)Grad-CAM (c)D-RISE Del.
Revised: (b) (a)Target object (d)Ours (b)Grad-CAM (c)D-RISE Del.

Original: Insertion
Revised: Insertion

Original: [Figure]
Revised: [Figure]

Original: [Table]

Original: [Table]
Revised: [Table]

Original: is spread to its overlapping neighbors, which makes the correlations between them relatively high.
Revised: neighbors, which makes the correlations between them relatively high.

Original: Using the consistency and separation losses in (3), Odam-Train yields concentrated heat maps for the same object and distinctive heat maps for different objects, which better shows which object was being detected, improving object discrimination.
Revised: Using the consistency and separation losses in (3), Odam-Train yields well-localized heat maps for the same object and distinctive heat maps for different objects, which better shows which object was being detected, improving object discrimination.

Original: As seen in Fig.
Revised: As seen in Fig.

Original: 4b, different people in the crowd can be separated by their low heat-map correlation, even when they have high IoU.
Revised: 4b, different people in the crowd can be separated by their low heat-map correlation, even when they have high IoU.

Original: 4. Q UANTITATIVE EVALUATION OF VISUAL EXPLANATIONS
Revised: 4. Q UANTITATIVE EVALUATION OF VISUAL EXPLANATIONS

Original: We evaluate faithfulness using Deletion, Insertion (Samek et al., 2016; Chattopadhay et al., 2018;
Revised: We evaluate faithfulness using Deletion, Insertion (Samek et al., 2016; Chattopadhay et al., 2018;

Original: Wang et al.
Revised: Wang et al.

Original: , 2020b;a; Petsiuk et al., 2021) and visual explanation accuracy (Oramas Mogrovejo et al., 2019), and also evaluate on the user trust of the produced visual explanations.
Revised: , 2020b;a; Petsiuk et al., 2021) and visual explanation accuracy (Oramas Mogrovejo et al., 2019), and also evaluate on the user trust of the produced heat maps.

Original: For evaluating localization, we adopt Pointing games (Zhang et al., 2018).
Revised: For evaluating localization, we adopt Pointing games (Zhang et al., 2018).

Original: Meanwhile, we propose an object discrimination index (ODI) for measuring the interpretation ability of object discrimination.
Revised: Meanwhile, we propose an object discrimination index (ODI) for measuring the interpretation ability of object discrimination.

Original: For comparison, we implement D-RISE using 5000 masks with resolution of 16 × 16 as in (Petsiuk et al., 2021).
Revised: For comparison, we implement D-RISE using 5000 masks with resolution of 16 × 16 as in (Petsiuk et al., 2021).

Original: FCOS is used as baseline model and the features from FPN are adopted to generate heat maps.
Revised: FCOS is used as baseline model and the features from FPN are adopted to generate heat maps.

Original: The best matched predictions of  objects  in the evaluation dataset are interpreted by each explanation method.
Revised: The best matched predictions of the well-detected objects ( IoU > 0 . 9 ) in the evaluation dataset are interpreted by each explanation method.

Revised: The conﬁdence scores of predictions are used as the explanation targets in ODAM, Grad-CAM and Grad-CAM++.

Original: Besides the MS COCO val set, results of the Pointing game and ODI are also reported on CrowdHuman validation sets.
Revised: Besides the MS COCO val set, results of the Pointing game and ODI are also reported on CrowdHuman validation sets.

Original: Deletion and Insertion A faithful visual explanation map should highlight the important context on the image.
Revised: Deletion and Insertion A faithful heat map should highlight the important context on the image.

Original: Deletion replaces input image pixels by random values step-by-step using the ordering of the heatmap (most important first), then measures the amount of the prediction score drops (in percentage).
Revised: Deletion replaces input image pixels by random values step-by-step using the ordering of the heatmap (most important ﬁrst), then measures the amount of the predicted conﬁdence score drops (in percentage).

Original: Insertion is the reverse operation of deletion, and adds image pixels to an empty image in each step (based on heatmap importance) and records the average score increase.
Revised: Insertion is the reverse operation of deletion, and adds image pixels to an empty image in each step (based on heatmap importance) and records the average score increase.

Original: Since the sizes of objects vary a lot, we consider 1% of the bounding box area in each step and record results fortotal steps.

Original: The average prediction scores on every 10 step are presented in Fig.
Revised: The average prediction score curves are presented in Fig.

Original: 5(a-b), and Tab.reports the area under the curve (AUC).
Revised: 5(a-b), and Tab. 1 reports the area under the curve (AUC).

Original: Lower Deletion AUC means steeper drops in score, while higher Insertion AUC means larger increase in score with each step.
Revised: Lower Deletion AUC means steeper drops in score, while higher Insertion AUC means larger increase in score with each step.

Original: Our methods have the fastest performance drop and largest performance increase for Deletion and Insertion, which shows that the regions highlighted in our heatmaps do have large effects on the detector predictions, as compared to other methods.
Revised: Our methods have the fastest performance drop and largest performance increase for Deletion and Insertion, which shows that the regions highlighted in our heat maps have larger effects on the detector predictions, as compared to other methods.

Revised: Interestingly, faithfulness metrics when using Odam-Train are slightly worse than without it, but still better than previous works on Insertion and VEA.

Original: Note that instance-specific explanations (ours and D-RISE) significantly surpass the classification explanation methods (Grad-CAM, Grad-CAM++).
Revised: Note that instance-speciﬁc explanations (ours and D-RISE) signiﬁcantly surpass the classiﬁcation explanation methods (Grad-CAM, Grad-CAM++).

Original: Visual explanation accuracyThe visual explanation accuracy (VEA)  measures thepixel-level IoU between the ground-truth mask and the explanation heat map thresholded at different values.
Revised: Visual explanation accuracy (VEA) VEA measures the IoU between the GT and the explanation heat map thresholded at different values.

Original: We use the MS COCO ground-truth object masks for this evaluation, and results are presented in Fig.5(c).
Revised: We use the MS COCO GT object masks for this evaluation, and results are presented in Fig.5(c).

Original: Our method obtains the highest IoU when the threshold is small ( T < 0 . 4 ), and the IoUs decrease as the threshold increases.
Revised: Our method obtains the highest IoU when the threshold is small ( T < 0 . 4 ), and the IoUs decrease as the threshold increases.

Original: This demonstrates that our heatmap energy is almost all inside the object (consistent with energy PG results in Tab. 4).
Revised: This demonstrates that our heat map energy is almost all inside the object (consistent with energy PG results in Tab. 4).

Original: In contrast, the low IoUs of the other three methods at a small threshold indicate that their heatmaps contains significant amounts of energy outside the object mask.
Revised: In contrast, the low IoUs of the previous methods at a small threshold indicate that their heatmaps contains signiﬁcant amounts of energy outside the object mask.

Original: For Grad-CAM/Grad-CAM++, the IoUs decrease when the threshold increases, which suggests that there are more large heat map values outside the object mask than inside the mask (they are not object-instance specific).
Revised: For Grad-CAM/Grad-CAM++, the IoUs decrease when the threshold increases, which suggests that there are more large heat map values outside the object mask than inside the mask (they are not object-instance speciﬁc).

Original: For D-RISE, the IoU increases as the threshold increases, which indicates that the heat map values inside the object mask are larger than those outside the mask.
Revised: For D-RISE, the IoU increases as the threshold increases, which indicates that the heat map values inside the object mask are larger than those outside the mask.

Original: Overall, our method has better IoU (0.421 at T=0.1)compared to
Revised: Overall, our method has better IoU (0.421 at T=0.1)

Original:  D-RISE (0.249 at T=0.7), which is also verified by theAUC of the VEA curve in Tab. 1.
Revised: compared to D-RISE (0.249 at T=0.7), which is also veriﬁed by the VEA AUC in Tab. 1.

Original: User Trust
Revised: User Trust

Original: The interpretability of visual explanations is evaluated through a human trust test.
Revised: The interpretability of visual explanations is evaluated through a human trust test.

Original: Heat maps are generated by D-RISE, Grad-CAM, Grad-CAM++, and ODAM for 120 correctlydetected objects out of 80 classes from the MSCOCO val set (1-2 instances for each class).
Revised: Heat maps are generated by D-RISE, Grad-CAM, Grad-CAM++, and ODAM for 120 correctlydetected objects out of 80 classes from the MSCOCO val set (1-2 instances for each class).

Original: For each object, users are asked to rank the maps from the four methods by the order of which map gives [Table] [Table] [Table]
Revised: For each object, users are asked to rank the maps from the four methods by the order of which map gives more reasonable insight about how the target object was detected.

Original: more reasonable insight about how the target object was detected.

Original: We collect 10 responses for each object from a total number of 40 users (30 objects per user), totaling 1200 responses. 
Revised: We collect 10 responses for each object from a total number of 40 users (30 objects per user), totaling 1200 responses. The results [Table]

Original: The results are presented in Tab. 2.
Revised: [Table] [Table] are presented in Tab. 2.

Original: ODAM is ranked 1st place 53.8% of trials and 2nd place 35.4%, which is significantly better than D-RISE ( χ 2 test, p < 0.001).
Revised: ODAM is ranked 1st place 53.8% of trials and 2nd place 35.4%, which is signiﬁcantly better than D-RISE ( χ 2 test, p < 0.001).

Original: Overall, ODAM has significantly better average rank of 1.6 compared to others (Wilcoxon signed-rank test, p < 0.001).
Revised: Overall, ODAM has signiﬁcantly better average rank of 1.6 compared to others (Wilcoxon signed-rank test, p < 0.001).

Original: The significantly higher human trust of ODAM demonstrate its superior instance-level interpretability for object detection.
Revised: The signiﬁcantly higher human trust of ODAM demonstrate its superior instance-level interpretability for object detection.

Original: From another aspect, previous studies evaluated trust between humans and machine learning systems by seeing if better models had better explanation maps according to humans.
Revised: From another aspect, previous studies evaluated trust between humans and machine learning systems by seeing if better models had better explanation maps according to humans.

Original: Following Selvaraju et al.
Revised: Following Selvaraju et al.

Original: ; Petsiuk et al.
Revised: ; Petsiuk et al.

Original: (2021), ODAM maps are generated for 120 objects that are correctly detected by two FCOS-ResNet50 models with different performance (36.6% mAP and 42.3% mAP).
Revised: (2021), ODAM maps are generated for 120 objects that are correctly detected by two FCOS-ResNet50 models with different performance (36.6% mAP and 42.3% mAP).

Original: Excluding the samples where users thought the explanations were similar quality, the better model (42.3% mAP) received more responses(38.2% vs. 28.6%) that its explanations were more trustworthy.
Revised: Excluding the samples where users thought the explanations were similar quality, the better model (42.3% mAP) received more responses that its explanations were more trustworthy (38.2% vs. 28.6%).

Original: More details are provided in the Appendix.
Revised: More details are provided in the Appendix A.2.

Original: Pointing Game  To quantitatively evaluate the localization ability, we report results of thePointing
Revised: Pointing Game (PG) To quantitatively evaluate the localization ability, we report results of the

Original: Game (PG) metric.
Revised: PG metric.

Original: In the PG, the maximum point in the instance-level heat map is extracted and a hit is scored if the point lies within the ground truth object region (either bounding box or segmentation mask).
Revised: For PG, the maximum point in the instance-level heat map is extracted and a hit is scored if the point lies within the GT object region (either bbox or instance mask).

Original: Then the PG accuracy is measured by averaging over the test objects.
Revised: Then the PG accuracy is measured by averaging over the test objects.

Original: Sincethe PG only considers the maximum point, but not the spread of the heat map, we also adopt the energy-based PG (Wang et al., 2020b), which calculates the proportion of heat map energy within the GT object bounding box orsegmentation mask (versus the whole map).
Revised: Since PG only considers the maximum point, but not the spread of the heat map, we also adopt the energy-based PG (Wang et al., 2020b), which calculates the proportion of heat map energy within the GT object bbox or mask (versus the whole map).

Original: Finally, to show the compactness of the heat map, we calculate the weighted standard deviation of heat-map pixels, relative to the maximum point: Comp.
Revised: Finally, to show the compactness of the heat map, we calculate the weighted standard deviation of heat-map pixels, relative to the maximum point: Comp.

Original: = (cid:0)
Revised: = (cid:0)

Original: [Table]
Revised: [Equation]

Original: 2 , where S x is the heat map value at location x , ˆ x is the maximum point of the heat map, and ( w, h ) are the width and height of the GT box.
Revised: where S x is the heat map value at location x , ˆ x is the maximum point of the heat map, and ( w, h ) are the width and height of the GT box.

Original: The denominator normalizes the distance w.r.t.
Revised: The denominator normalizes the distance w.r.t.

Original: the object size.
Revised: the object size.

Original: Smaller compactness values indicate the heat map is more concentrated around the maximum point.
Revised: Smaller compactness values indicate the heat map is more concentrated around its maximum.

Original: Both Grad-CAM and Grad-CAM++ perform poorly on both datasets since they generate classspecific heat maps.
Revised: Both Grad-CAM and Grad-CAM++ perform poorly on both datasets since they generate classspeciﬁc heat maps.

Original: Our ODAM yields significant improvements over D-RISE on all the metrics.
Revised: Our ODAM yields signiﬁcant improvements over D-RISE on all the metrics.

Original: Specifically, D-RISE cannot work well on the CrowdHuman dataset, which only contains one object category.
Revised: Speciﬁcally, D-RISE cannot work well on CrowdHuman, which only contains one object category.

Original: Since D-RISE uses the similarities between predictions of masked images and the original image to decide the mask weights, for datasets with few object categories, the predicted class probabilities provide less useful information when calculating the weights.
Revised: Since D-RISE uses the similarities between predictions of masked images and the original image to decide the mask weights, for datasets with few object categories, the predicted class probabilities provide less useful information when calculating the weights.

Original: Finally, using Odam-Train further improves the localization quality by generatingmore compact and well-localized heat maps.
Revised: Finally, using Odam-Train further improves the localization quality by generating heat maps that are well-localized on the objects.

Original: Object Discrimination To evaluate the object discrimination ability of the heat maps, we propose the object discrimination index (ODI), which measures the amount of heat map energy that leaks to other objects.
Revised: Object Discrimination To evaluate the object discrimination ability of the heat maps, we propose the object discrimination index (ODI), which measures the amount of heat map energy that leaks to other objects.

Original: Specifically, for a given target object, the ODI is the proportion of heat map energy inside all other objects’ bounding boxes (or segmentation masks) w.r.t.
Revised: Speciﬁcally, for a given target object, the ODI is the proportion of heat map energy inside all other objects’ bboxes (or segmentation masks) w.r.t.

Original: the total heat map energy inside all objects in the image (i.e., ignoring background regions).
Revised: the total heat map energy inside all objects in the image (i.e., ignoring background regions).

Original: The averaged ODIs are presented[Table] in Tab. 3.
Revised: The averaged ODIs are presented in Tab. 3a.

Original: Compared with others, ODAM consistently shows the least energy leaking out to other objects.
Revised: Compared with others, ODAM consistently shows the least energy leaking out to other objects.

Original: Note that when using the tighter GT mask on MSCOCO, ODAM obtains the largest proportion of decrease, which indicates that the heat map can better focus on the explained target, even if its bounding box overlaps with other objects.
Revised: Note that when using the tighter GT mask on MSCOCO, ODAM obtains the largest proportion of decrease, which indicates that the heat map can better focus on the explained target, even if its bbox overlaps with other objects.

Original: Using Odam-Train significantly improves object discrimination in the  crowded scenes of CrowdHuman.
Revised: Using Odam-Train signiﬁcantly improves object discrimination in the [Table] crowded scenes of CrowdHuman, although there is a tradeoff with faithfulness (see Tab. 1).

Original: 4. E VALUATING O DAM -NMS
Revised: Finally, we conduct a user study on object discrimination (details in App. A.3). The results in Tab. 3b show that users are more accurate and more conﬁdent at object discrimination using ODAM compared to previous works ( χ 2 test, p < .0001; t-test, p < .0001) [Table]

Original: We evaluate Odam-NMS for improving detection in crowded scenes.
Revised: and that using Odam-Train further improves user conﬁdence (t-test, p=.02). These results are consistent with the quantitative evalution with ODI.

Original: We use ODAM with OdamTrain to generate explanation maps that have better object discrimination ability.
Revised: We evaluate Odam-NMS with Odam-Train for improving detection in crowded scenes.

Original: To evaluate the performance of NMS on heavily overlapped situations, we adopt the CrowdHuman dataset (Shao et al., 2018), which contains an average 22.6 objects per image (2.4 overlapped objects).
Revised: To evaluate the performance of NMS on heavily overlapped situations, we adopt the CrowdHuman dataset, which contains an average 22.6 objects per image (2.4 overlapped objects).

Original: We compare Odam-NMS with NMS, SoftNMS, and FeatureNMS, using both FCOS and Faster RCNN.
Revised: We compare OdamNMS with NMS, SoftNMS, and FeatureNMS, using both FCOS and Faster RCNN.

Original: The IoU threshold is set to T iou = 0 .
Revised: The IoU threshold is set to T iou = 0 .

Original: 5 for both NMS and our method.
Revised: 5 for both NMS and our method.

Original: Soft-NMS uses Gaussian decay with σ = 0 .
Revised: Soft-NMS uses Gaussian decay with σ = 0 .and

Original: 5 and final threshold of 0.05.
Revised: ﬁnal threshold of 0.05.

Original: For FeatureNMS, the IoU range is set to (0 . 9 , 0 . 1) following Salscheider (2021).
Revised: For FeatureNMS, the IoU range is set to (0 . 9 , 0 . 1) following Salscheider (2021).

Original: The aspect ratios of the anchors in Faster R-CNN are set to H :
Revised: The aspect ratios of the anchors in Faster R-CNN are set to H :

Original: W = { 1 , 2 , 3 } based on the dataset, and other parameters are the same as in the baselines.
Revised: W = { 1 , 2 , 3 } based on the dataset, and other parameters are the same as in the baselines.

Original: Training runs forepochs.
Revised: Training runs for 30 epochs.

Original: We use T h = 0 .
Revised: We use T h = 0 .

Original: 8 , T l = 0 .
Revised: 8 , T l = 0 .

Original: 2 based on the ablation study in the Appendix.
Revised: 2 based on the ablation study in the App. A.4.1.

Original: We adopt three evaluation criteria:
Revised: We adopt three evaluation criteria:

Original: Average Precision ( AP 50 ); Log-Average Missing Rate (MR), commonly used in pedestrian detection, which is sensitive to false positives (FPs); Jaccard Index (JI).
Revised: Average Precision ( AP 50 ); Log-Average Missing Rate (MR), commonly used in pedestrian detection, which is sensitive to false positives (FPs); Jaccard Index (JI).

Original: See Chu et al.
Revised: See Chu et al.

Original: (2020) for details.
Revised: (2020) for details.

Original: Smaller MR indicates better results, while larger AP 50 and JI are better.
Revised: Smaller MR indicates better results, while larger AP 50 and JI are better.

Original: Tab. 5 shows the results.
Revised: Tab. 5 shows the results.

Original: Soft-NMS performs poorly in crowd scenes, generating many false positives in high-score region (high MR) with a long processing time.
Revised: Soft-NMS performs poorly in crowd scenes, generating many false positives in high-score region (high MR) with a long processing time.

Original: For FCOS, AP performance of
Revised: For FCOS, AP performance of

Original: FeatureNMS is much higher than NMS, while JI and MR are similar.
Revised: FeatureNMS is much higher than NMS, while JI and MR are similar.

Original: However for Faster RCNN, although FeatureNMS obtains a high recall, the others are worse than NMS, indicating that the feature embeddings trained with the cropped features in two-stage detectors are not distinctive enough, and there are many false positives in detections.
Revised: However for Faster RCNN, although FeatureNMS obtains a high recall, the others are worse than NMS, indicating that the feature embeddings trained with the cropped features in two-stage detectors are not distinctive enough, and there are many false positives in detections.

Original: The learned embeddings in FeatureNMS have no explicit meaning except the relative distance between each pair, while Odam-NMS directly uses heat maps that offer explanations of the detector model.
Revised: The learned embeddings in FeatureNMS have no explicit meaning except the relative distance between each pair, while Odam-NMS directly uses heat maps that offer explanations of the detector model.

Original: With the default IoU threshold, our OdamNMS achieves better JI and MR than NMS and FeatureNMS for both detectors (FCOS and Faster RCNN).
Revised: With the default IoU threshold, our Odam-NMS achieves better JI and MR than NMS and FeatureNMS for both detectors (FCOS and Faster RCNN).

Original: Meanwhile, Odam-NMS also achieves the best AP with Faster RCNN.
Revised: Meanwhile, Odam-NMS also achieves the best AP with Faster RCNN.

Original: The limitation of Odam-NMS is that generating heat maps for dense predictions costs a slightly longer processing time.
Revised: The limitation of OdamNMS is that generating heat maps for dense predictions takes slightly longer.

Original: Overall, these results verify the object discrimination interpretation ability of ODAM with Odam-Train and demonstrate that the instance-level explanation for predictions can help improve NMS in crowd scenes.
Revised: Overall, these results verify the object discrimination interpretation ability of ODAM with Odam-Train and demonstrate that the instance-level explanation for predictions can help improve NMS in crowd scenes.

Original:  C ONCLUSION
Revised:  C ONCLUSION

Original: In this paper, we propose ODAM, a white-box gradient-based instance-level visualized explanation technique for interpreting the predictions of object detectors.
Revised: In this paper, we propose ODAM, a white-box gradient-based instance-level visualized explanation technique for interpreting the predictions of object detectors.

Original: ODAM can produce instance-specific heat maps for any prediction attribute, including object class and bounding box coordinates, to show the important regions that the model uses to make its prediction.
Revised: ODAM can produce instance-speciﬁc heat maps for any prediction attribute, including object class and bounding box coordinates, to show the important regions that the model uses to make its prediction.

Original: Our method is general and applicable to both one-stage and two-stage  detectors with different detector backbones, and heads.
Revised: Our method is general and applicable to one- and two-stage and transformer-based detectors with different detector backbones and heads.

Original: Qualitative and quantitative evaluations demonstrate the advantages of our method compared with the class-specific (Grad-CAM) or black-box works (D-RISE).
Revised: Qualitative and quantitative evaluations demonstrate the advantages of our method compared with the class-speciﬁc (Grad-CAM) or black-box works (D-RISE).

Original: We also propose a training scheme, OdamTrain, which trains the detector to produce more consistent explanations for the same detected object, and distinct explanations for different objects, thus improving object discrimination.
Revised: We also propose a training scheme, OdamTrain, which trains the detector to produce more consistent explanations for the same detected object, and distinct explanations for different objects, thus improving object discrimination.

Original: Experiments show that Odam-Train is effective at improving localization in the explanation map and object discrimination.
Revised: Experiments show that Odam-Train is effective at improving localization in the explanation map and object discrimination.

Original: Finally, we propose Odam-NMS, which utilizes the explainability of ODAM to identify and remove duplicate predictions in crowd scenarios.
Revised: Finally, we propose Odam-NMS, which utilizes the explainability of ODAM to identify and remove duplicate predictions in crowd scenarios.

Original: Experiments on different detector architectures confirm its effectiveness, and further verify the interpretability provided by ODAM.
Revised: Experiments on different detectors conﬁrm its effectiveness, and further verify the interpretability provided by ODAM for both object speciﬁcation and object discrimination.

Revised: Finally, we note that there appears a tradeoff between faithfulness and object discrimination in the explanation maps, since high object discrimination implies not using context information.

Revised: Future work will consider how to manage this tradeoff.

Original: A A PPENDIX A.  O DAM -NMS
Revised: A A PPENDIX A. I MPLEMENTATION DETAILS : O DAM -T RAIN AND O DAM -NMS

Original: The pseudo-code for Odam-NMS is presented in Algorithm 1.
Revised: For Odam-Train on MSCOCO, the detector training pipeline is totally the same as the baseline (Tian et al., 2019; Ren et al., 2015), which uses SGD as optimizer running for 12 epochs with 16 batch size, 0.2 learning rate for two-stage Faster R-CNN and 0.1 learning rate for FCOS.

Original: A. U SER TRUST TEST
Revised: For training on

Original: We present the form of the questionnares and some samples that we used in  the two user trust tests in Fig.
Revised: CrowdHuman, the aspect ratios of the anchors in Faster R-CNN are set to H : W = { 1 , 2 , 3 } :since the dataset contains people, and training runs for 30 epochs. Other parameters are the same as in training on MSCOCO. The pseudo-code for Odam-NMS is presented in Algorithm 1.

Original: Algorithm  removed or kept based on both the IoU and the correlation between ODAM heat maps.
Revised: Algorithm 1 Odam-NMS: predictions are removed or kept based on both the IoU and the correlation between ODAM heat maps.

Original: P ← GetPredictions ( imageI ) P ← SORT ( P )
Revised: [Table]

Original: D ← ∅ while P ̸ = ∅ do p ← POP ( P ) isDuplicate ← false for d ∈ D do iou ← GetIoU ( p,d ) corr ← NormCorrelation ( S ( p ) yc ,S ( d ) yc ) if iou ≥ T iou and corr > T l then isDuplicate ← true else if iou < T iou and corr > T h then isDuplicate ← true end if end for if ¬ isDuplicate then PUSH ( p,D ) end if end while 
Revised: < T iou and corr > T h then isDuplicate ← true end if end for if ¬ isDuplicate then PUSH ( p,D ) end if end while A. U SER TRUST ON EXPLANATION FAITHFULNESS EVALUATION We present the form of the questionnares and some samples that we used in the two user trust tests in Fig.

Original: Q: The robot has detected the object inside the blue bounding box, and gives four attention heat maps to explain why the robot found the object.
Revised: Q: The robot has detected the object inside the blue bounding box, and gives four attention heat maps to explain why the robot found the object.

Original: Please rank the Explanation A to Explanation D by the order of the most reasonable to the most unreasonable.
Revised: Please rank the Explanation A to Explanation D by the order of the most reasonable to the most unreasonable.

Original: Detected Object
Revised: Detected Object

Original: A
Revised: A

Original: B
Revised: B

Original: C
Revised: C

Original: D
Revised: D

Original: Detected Object Detected Object
Revised: Detected Object Detected Object

Original: A
Revised: A

Original: B
Revised: B

Original: C
Revised: C

Original: D
Revised: D

Original: A
Revised: A

Original: B
Revised: B

Original: C
Revised: C

Original: D
Revised: D

Original: Examples of Questionnaire Examples of Questionnaire
Revised: Examples of Questionnaire Examples of Questionnaire

Original: Detected Object Robot
Revised: Detected Object Robot

Original: Robot
Revised: Robot

Original: Detected Object Robot
Revised: Detected Object Robot

Original: Robot
Revised: Robot

Original: Detected Object
Revised: Detected Object

Original: Robot Robot
Revised: Robot Robot

Original: Q: Two robots have detected the object inside the blue bounding box, and give us the attention heat maps to explain why they found the object.
Revised: Q: Two robots have detected the object inside the blue bounding box, and give us the attention heat maps to explain why they found the object.

Original: Please choose the robot that has a more reasonable explanation.
Revised: Please choose the robot that has a more reasonable explanation.

Original: A. M ORE A BLATION S TUDIES A.3. E FFECTS OF THRESHOLDS IN O DAM -NMS
Revised: A. U SER TRUST ON OBJECT DISCRIMINATION EVALUATION

Revised: Since the user trust study in Sec.

Revised: 4.2 only evaluate explanations from the faithfulness aspect, which shows how reasonable the heat maps explain the predictions, we further conduct a user study on object discrimination ability.

Revised: In this test, users are asked to draw a bounding box on the image, pointing out which object they think the AI has detected, based on the shown heat map.

Revised: Meanwhile, the users also need to provide their conﬁdence level from most uncertain (1) to most certain (5) when making the choice.

Revised: For each method (D-RISE, Grad-CAM, Grad-CAM++, ODAM and ODAM with

Revised: Odam-Train), 150 samples are sent out to 10 users with one user answering 15 images.

Revised: Since the purpose is to test whether the heat maps can effectively show which object was detected, especially in the crowded scene, we choose the samples from the CrowdHuman validation set.

Revised: Since users will have different ways to draw the box around the object, a separate marker manually inspected the user’s boxes to see if they align with the GT object box in order to determine correctness.

Revised: During this process, the marker does not know which explanation method was used for each image.

Revised: Tab. 6 presents the number of examples (in percentage) under each conﬁdence level and the accuracy of users’ decisions (the ratio of users’ correct choices) based on heat maps of each method.

Revised: The results show that the user can obtain a much higher accuracy ( χ 2 test, p < .0001) and conﬁdence (ttest, p < .0001) with heat maps from both ODAM and ODAM with Odam-Train.

Revised: Furthermore, using

Revised: Odam-Train further improves the average user conﬁdence (t-test, p=0.024).

Revised: Using Odam-Train, users have higher conﬁdence ( 83 .

Revised: 99% vs. 70 .

Revised: 68% at most certain) about their decision, which demonstrates our method is superior on object discrimination ability, especially with the model after

Revised: Odam-Train.

Revised: Some incorrect and correct user’s choices are displayed in Fig.

Revised: [Table]

Revised: [Figure]

Revised: [Table]

Revised: [Figure]

Revised: [Table]

Revised: [Table]

Revised: Fig.

Revised: 8 shows a more detailed view of the histogram of users’ correctness and conﬁdences compared with the ODIs (object discrimination index, proposed in Sec. 4.2) of the tested samples.

Revised: Higher ODI means more heat map energy is leaking out to other objects, while less energy is in the explained target object.

Revised: Except for ODAM (w/ or w/o Odam-Train), most heat maps of other methods have high ODIs (larger than 0.6).

Revised: We can ﬁnd that users tend to have lower conﬁdence and make incorrect decisions with these high-ODI heat maps from other methods.

Revised: In contrast, for ODAM (w/ and w/o

Revised: Odam-Train), users have higher conﬁdence and make correct decisions even for high ODI samples.

Revised: These results demonstrate that ODAM can improve the user trust in the object discrimination of the detector.

Revised: [Figure]

Revised: A. M ORE A BLATION S TUDIES A.4. E FFECTS OF THRESHOLDS IN O DAM -NMS

Original: Figure 7 shows the results comparing various combinations of low and high correlation thresholds,
Revised: Figure 9 shows the results comparing various combinations of low and high correlation thresholds,

Original: T l and T h , for Odam-NMS with the FCOS detector.
Revised: T l and T h , for Odam-NMS with the FCOS detector.

Original: We compare with classical NMS, corresponding to T l = 0 , T h = 1 .
Revised: We compare with classical NMS, corresponding to T l = 0 , T h = 1 .

Original: The results for all the three metrics are improved by increasing T l to 0.1-0.2, which indicates that some high-IoU crowded objects are successfully kept through their low correlation values.
Revised: The results for all the three metrics are improved by increasing T l to 0.1-0.2, which indicates that some high-IoU crowded objects are successfully kept through their low correlation values.

Original: Then with the T l further increasing, MR and JI starts to get worse, since more false positives are introduced.
Revised: Then with the T l further increasing, MR and JI starts to get worse, since more false positives are introduced.

Original: As for T h , two proposals are regarded as the same object if their correlation exceeds T h , even though their IoU is smaller than the T iou .
Revised: As for T h , two proposals are regarded as the same object if their correlation exceeds T h , even though their IoU is smaller than the T iou .

Original: Since using T h < 1 will reduce the recall rate, and AP 50 is highly depends on the recall, T h shows no benefit to AP 50 .
Revised: Since using T h < 1 will reduce the recall rate, and AP 50 is highly depends on the recall, T h shows no beneﬁt to AP 50 .

Original: MR and JI have better performance by decreasing the T h when T l is fixed.
Revised: MR and JI have better performance by decreasing the T h when T l is ﬁxed.

Original: This indicates that using a T h <can indeed remove low-IoU false positives, although the performance improvement is slight.
Revised: This indicates that using a T h <can indeed remove low-IoU false positives, although the performance improvement is slight.

Original: Based on the results in Fig.
Revised: Based on the results in Fig.

Original: 7, we adopt T h = 0 .
Revised: 9, we adopt T h = 0 .

Original: 8 and T l = 0 .
Revised: 8 and T l = 0 .

Original: 2 in the experiments.
Revised: 2 in the experiments.

Original: [Figure]
Revised: [Figure]

Revised: I

Original: [Figure] 
Revised: [Figure] l

Revised: T

Revised: [Figure]

Revised: [Figure]

Revised: T h

Revised: [Figure]

Revised: [Figure]

Revised: T

Original: [Table]
Revised: [Figure]

Original: A.3. A NALYSIS ON RECALLS WITH O DAM -NMS
Revised: A.4. A NALYSIS ON RECALLS WITH O DAM -NMS

Original: To verify that more crowded objects can be recalled using Odam-NMS, we compare the recalls of the baseline detectors with or without Odam-NMS for both crowded and uncrowded instances.
Revised: To verify that more crowded objects can be recalled using Odam-NMS, we compare the recalls of the baseline detectors with or without Odam-NMS for both crowded and uncrowded instances.

Original: Since the recall is related to the confidence score threshold, we use the thresholds corresponding to the best JI for each method for fair comparison.
Revised: Since the recall is related to the conﬁdence score threshold, we use the thresholds corresponding to the best JI for each method for fair comparison.

Original: Based on (Chu et al., 2020), we define the “crowd” set and “sparse” set, where the ground-truth boxes that overlap with some other ground truth with
Revised: Based on (Chu et al., 2020), we deﬁne the “crowd” set and “sparse” set, where the ground-truth boxes that overlap with some other ground truth with

Original: IoU > 0 .
Revised: IoU > 0 .

Original: 5 comprise the “crowd” set and the other GT boxes as the “sparse” set.
Revised: 5 comprise the “crowd” set and the other GT boxes as the “sparse” set.

Original: The results are shown in Tab. 6.
Revised: The results are shown in Tab. 7.

Original: The recall percentage on the crowd set is much lower than on the sparse set.
Revised: The recall percentage on the crowd set is much lower than on the sparse set.

Original: Using
Revised: Using

Original: Odam-NMS improves the recall percentage of crowded objects compared to the baseline, e.g., recall is improved by 4% for Faster R-CNN and 13.5% for FCOS. 
Revised: Odam-NMS improves the recall percentage of crowded objects compared to the baseline, e.g., recall is improved by 4% for Faster R-CNN and 13.5% for FCOS. [Table]

Original: A.3. O DAM -NMS WITH AND WITHOUT O DAM -T RAIN
Revised: A.4. O DAM -NMS WITH AND WITHOUT O DAM -T RAIN

Original: In Sec.
Revised: In Sec.

Original: 4.2, we evaluate Odam-NMS with the model when using Odam-Train.
Revised: 4.2, we evaluate Odam-NMS with the model when using Odam-Train.

Original: Here we provide the ablation studies evaluating Odam-NMS with and without using Odam-Train.
Revised: Here we provide the ablation studies evaluating Odam-NMS with and without using Odam-Train.

Original: The results are shown in the Tab. 7.
Revised: The results are shown in the Tab. 8.

Original: When using the classical NMS, the baseline detector model yields similar and comparable results with and without using Odam-Train, which demonstrates that Odam-Train will have little influence on the baseline model performance when improving the explanation ability.
Revised: When using the classical NMS, the baseline detector model yields similar and comparable results with and without using Odam-Train, which demonstrates that Odam-Train will have little inﬂuence on the baseline model performance when improving the explanation ability.

Original: This is a desirable property since we hope that providing explanations will not hinder the detector performance.
Revised: This is a desirable property since we hope that providing explanations will not hinder the detector performance.

Original: As for Odam-NMS, Odam-Train brings an obvious improvement with the same parameter setting ( T h = 0 .
Revised: As for Odam-NMS, Odam-Train brings an obvious improvement with the same parameter setting ( T h = 0 .

Original: 8 and T l = 0 . 2 )
Revised: 8 and T l = 0 . 2 )

Original: as compared to without Odam-Train.
Revised: as compared to without Odam-Train.

Original: This shows that model can be trained to give more consistent and separated explanations that benefit duplicate detection removal.
Revised: This shows that model can be trained to give more consistent and separated explanations that beneﬁt duplicate detection removal.

Original: Furthermore, without Odam-Train, Odam-NMS needs the stricter judgment conditions to make more reasonable decisions, such as increasing T h and reducing T l , to obtain better results.
Revised: Furthermore, without Odam-Train, Odam-NMS needs the stricter judgment conditions to make more reasonable decisions, such as increasing T h and reducing T l , to obtain better results.

Original: Table 8 illustrates the recalls on the “crowd” and “sparse” set when the FCOS model is trained with or without Odam-Train, and uses classical NMS or Odam-NMS in the post-processing.
Revised: Table 9 illustrates the recalls on the “crowd” and “sparse” set when the FCOS model is trained with or without Odam-Train, and uses classical NMS or Odam-NMS in the post-processing.

Original: When using
Revised: When using

Original:  NMS with Odam-Train or Odam-NMS without Odam-Train, the recall rate is improved compared with the classical NMS without Odam-Train.
Revised: [Table] NMS with Odam-Train or Odam-NMS without Odam-Train, the recall rate is improved compared with the classical NMS without Odam-Train.

Original: However, the comprehensive metrics (e.g. AP, JI and MR) are not better accordingly (shown in Tab. 7) because the number of false positives is also [Figure] [Table]
Revised: However, the comprehensive metrics (e

Original: [Table]
Revised: [Table]

Original:  increased.
Revised: g. AP, JI and MR) are not better accordingly (shown in Tab. 8) because the number of false positives is also increased.

Original: Specifically, using Odam-NMS with Odam-Train, the recall is best on the crowd set and also obtains superior performance in Tab. 7 by reducing the number of false positives. 
Revised: Speciﬁcally, using Odam-NMS with Odam-Train, the recall is best on the crowd set and also obtains superior performance in Tab. 8 by reducing the number of false positives. [Table]

Original: In summary, the ablation studies indicate that, since Odam-NMS makes decisions based on heatmap correlations, it relies on good quality explanations, and using Odam-Train is beneficial because it encourages the model to produce consistent and distinctive heat maps on detections of the same or different object.
Revised: In summary, the ablation studies indicate that, since Odam-NMS makes decisions based on heatmap correlations, it relies on good quality explanations, and using Odam-Train is beneﬁcial because it encourages the model to produce consistent and distinctive heat maps on detections of the same or different object.

Original: A. M ORE EVALUATIONS OF VISUAL EXPLANATIONS
Revised: A. M ORE EVALUATIONS OF VISUAL EXPLANATIONS

Original: Here we provide more evaluations about the visual explanations generated by ODAM.
Revised: Here we provide more evaluations about the visual explanations generated by ODAM

Original: A.4. S ANITY CHECKS
Revised: . A.5. S ANITY CHECKS

Original: Adebayo et al.
Revised: Adebayo et al.

Original: (2018b) develops sanity checks for saliency methods.
Revised: (2018b) develops sanity checks for saliency methods.

Original: Specifically, they compare explanation methods to edge detection techniques, and show that some methods are independent of both the model or training data, but still produce outputs visually similar to those of explanation methods.
Revised: Speciﬁcally, they compare explanation methods to edge detection techniques, and show that some methods are independent of both the model or training data, but still produce outputs visually similar to those of explanation methods.

Original: We adopt the model parameter randomization test proposed in (Adebayo et al., 2018b) to compare the predicted heat maps of the trained model and the untrained model.
Revised: We adopt the model parameter randomization test proposed in (Adebayo et al., 2018b) to compare the predicted heat maps of the trained model and the untrained model.

Original: The Fig.
Revised: Fig.

Original: 8 shows that the weight randomization results in totally incorrect predictions and corresponding heat maps, which means that our method is related to the predicted instances and relies on the model parameters to produce the explanations. 
Revised: 10 shows that the weight randomization results in totally incorrect predictions and corresponding heat maps, which means that our method is related to the predicted instances and relies on the model parameters to produce the explanations. [Figure]

Original: A.4. A NALYZING ERROR MODES OF DETECTOR
Revised: A.5. A NALYZING ERROR MODES OF DETECTOR

Original: We use ODAM to analyze the error modes of detector.
Revised: We use ODAM to analyze the error modes of detector.

Original: For the high confidence but poorly localized cases, we generate explanations of the wrong predicted extents and compare them with the correct localization results.
Revised: For the high conﬁdence but poorly localized cases, we generate explanations of the wrong predicted extents and compare them with the correct localization results.

Original: As shown in Fig.
Revised: As shown in Fig.

Original: 9, the model highlights that the wrong extents were misled by the leg of the person and the sea horizon. 
Revised: 11, the model highlights that the wrong extents were misled by the leg of the person and the sea horizon. [Figure]

Original: To analyze classification decisions of the model, we generate explanations of the class scores.
Revised: To analyze classiﬁcation decisions of the model, we generate explanations of the class scores.

Original: In
Revised: In

Original: Fig.
Revised: Fig.

Original: 10, when focusing on both the monitor and keyboard, the model correctly classifies the instance as “laptop”, while a fractional attention (only on the keyboard itself) results in predicting class “keyboard”.
Revised: 12, when focusing on both the monitor and keyboard, the model correctly classiﬁes the instance as “laptop”, while a fractional attention (only on the keyboard itself) results in predicting class “keyboard”.

Original: Thus we may infer that the model requires seeing the laptop screen to predict “laptop”.
Revised: Thus we may infer that the model requires seeing the laptop screen to predict “laptop”.

Original: However note that the laptop keyboard has unique features (e.g., the trackpad) compared to a normal keyboard.
Revised: However note that the laptop keyboard has unique features (e.g., the trackpad) compared to a normal keyboard.

Original: Thus, this may be a particular failure mode of the detector.
Revised: Thus, this may be a particular failure mode of the detector.

Original: [Figure]
Revised: [Figure]

Original: [Figure]

Original: The second row of Fig.
Revised: The second row of Fig.

Original: 10 shows that the model correctly predicts the “toilet” class using the lid of the toilet.
Revised: 12 shows that the model correctly predicts the “toilet” class using the lid of the toilet.

Original: However, the model predicts ”sink” on the toilet’s reflection in the glass because it can only see the toilet bowl, and the lid is partially obscured.
Revised: However, the model predicts ”sink” on the toilet’s reﬂection in the glass because it can only see the toilet bowl, and the lid is partially obscured.

Original: Again this shows a particular failure mode of the detector, where it relies too much on the toilet lid to predict the “toilet” class. 
Revised: Again this shows a particular failure mode of the detector, where it relies too much on the toilet lid to predict the “toilet” class. A C OMPARISON OF EXPLANATIONS FROM DIFFERENT FEATURE MAP LAYERS In Fig.

Revised: we visualize and compare the heat maps generated with different feature layers.

Revised: For the same target, higher-level layers (e g. FPN and RoI pooling) show more concentrated attention and generate smoother heat maps.

Original: A.4. M ORE COMPARISONS OF DIFFERENT EXPLANATION METHODS
Revised: [Figure] A.5. M ORE COMPARISONS OF DIFFERENT EXPLANATION METHODS

Original: We provide more comparisons of heat maps from D-RISE, Grad-CAM, Grad-CAM++, and
Revised: We provide more comparisons of heat maps from D-RISE, Grad-CAM, Grad-CAM++, and

Original: our
Revised: our

Original: ODAM in Fig.
Revised: ODAM in Fig.

Revised: [Figure]

Original: A.4. M ORE VISUALIZATIONS OF EACH DETECTION ATTRIBUTE
Revised: A.5. M ORE VISUALIZATIONS OF EACH DETECTION ATTRIBUTE

Original: We provide more visualized explanations by ODAM for some high-confidence true positive predictions of the baseline FCOS detector in Fig. 
Revised: We provide more visualized explanations by ODAM for some high-conﬁdence true positive predictions of the baseline FCOS detector in Fig. 15.

Original: The heat maps for the class scores and four regression values are displayed in each column.
Revised: The heat maps for the class scores and four regression values are displayed in each column.

Original: [Figure]
Revised: [Figure]

Revised: A.5. T HE EFFECT OF GRADIENT DIRECTION IN EXPLAINING BOUNDING BOX REGRESSION

Revised: The visualization of the bounding box regression in Fig.

Revised: 3 (left) is for the FCOS detector.

Revised: In FCOS, the ( x 1 , y 1 , x 2 , y 2) values are the box offsets relative to the anchor center point, i.e, positive values indicate expanding the box, and negative values indicate shrinking the box.

Revised: The corresponding visualizations in Fig.

Revised: 3 use the ReLU to truncate the negative heat map (Eq. 2), and thus it shows features important for expanding the regressed box.

Revised: These features tend to be object parts in the extremes of the object.

Revised: We can also create visualizations using other directions of the gradient or using other functions beside ReLU when computing the heat map H in (2).

Revised: Figure 16 shows visualizations for different settings:

Revised: a) using positive gradients and ReLU shows the features important for expanding the box, which tend to be on the extremes of the object.

Revised: b) using negative gradients and ReLU shows the feature for shrinking the box, which tend to be further inside the object.

Revised: c) using positive gradients without ReLU shows a summary of important features in either direction, using different colors.

Revised: d) using positive grardients and Abs instead of ReLU shows a summary of the most important features overall for the bounding box edge.

Original: [Figure]
Revised: [Figure]

Revised: 5000 masks

Revised: [Figure]

Revised: resolution 16x16)

Revised: [Figure]

Revised: [Figure]

Revised: M ORE EXAMPLES FOR EXPLANATIONS FOR VARIOUS DETECTORS

Revised: Fig.

Revised: 17 shows more visualizations of explanation heat maps generated with different detector heads and backbones.

Revised: Interestingly, transformer-based DETR appears to be more heavily focused on object parts in the extremities of the object, while ignoring other regions, compared to the CNN-based detectors.

Revised: This is likely due to the patch-set representation and transformer used as the detector head.

Revised: Regarding the attention map of the transformer in DETR and its variants, the transformer selfattention mechanism produces a bottom-up attention map (i.e., generally which features are interesting).

Revised: In contrast, the ODAM generates a top-down attention map (i.e, which features are important for the output prediction).

Revised: It should be noted that for bottom-up attention, even if a feature is highlighted in the attention map, there is no guarantee that the feature is actually used in the subsequent output prediction.

Revised: In contrast, for the top-down attention, all highlighted features should be important for generating the prediction.

Revised: Therefore, we think that top-down visual explanations are still necessary for transformer-based detectors (Jain & Wallace, 2019).

Revised: [Figure]