Co-localization with Category-Consistent CNN Featuresand Geodesic Distance Propagation

Co-localization with Category-Consistent CNN Features
and Geodesic Distance Propagation

Hieu Le hle@cs.stonybrook.edu Department of Computer Science, Stony Brook University Chen-Ping Yu Department of Psychology, Harvard University Gregory Zelinsky Dimitris Samaras Department of Computer Science, Stony Brook University
Abstract

Co-localization is the problem of localizing objects of the same class using only the set of images that contain them. This is a challenging task because the object detector must be built without negative examples that can lead to more informative supervision signals. The main idea of our method is to cluster the feature space of a generically pre-trained CNN, to find a set of CNN features that are consistently and highly activated for an object category, which we call category-consistent CNN features. Then, we propagate their combined activation map using superpixel geodesic distances for co-localization. In our first set of experiments, we show that the proposed method achieves state-of-the-art performance on three related benchmarks: PASCAL 2007, PASCAL-2012, and the Object Discovery dataset. We also show that our method is able to detect and localize truly unseen categories, on six held-out ImageNet categories with accuracy that is significantly higher than previous state-of-the-art. Our intuitive approach achieves this success without any region proposals or object detectors, and can be based on a CNN that was pre-trained purely on image classification tasks without further fine-tuning.

1 Introduction

Figure 1: Object co-localization with CCFs and geodesic distance propagation. From a set of images containing a common object, first we find the CCFs - the group of features that consistently have high responses to the object images of the same class. The CCFs then are used to form an activation map for each image, followed by geodesic distance propagation to highlight the exact regions of the objects.

In recent years, deep learning methods have dominated state-of-the-art results in object detection and localization tasks [32, 30, 7, 35, 5, 27, 37, 22, 26]. However, one major drawback for deep learning methods is that they require a large amount of labeled training data, and data labels are expensive as they depend on extensive human efforts [33, 34]. Therefore, there is great value and importance if deep learning methods can learn to detect and localize objects accurately with unlabeled data. Object co-localization is one such problem that is close to the goal of learning with unlabeled data. In the problem of object co-localization, one must learn to detect and localize the common object from a set of same-class images, without any other image information. Successful methods for the co-localization problem should be able to localize an object through image search using a single class-name keyword, without the need of any pixel-level labels (e.g. bounding box and segmentation) or negative examples. Such ability can be useful for automatically generating large-scale datasets.

Recent co-localization methods typically utilize existing region proposal methods for generating a number of candidate regions for objects and object parts [16, 33, 6, 21]. From the bag of candidate proposals, the set of object-related proposals are determined based on different criteria, such as those having high mutual similarity scores [21, 33] or those minimizing the entropy of the score distribution of a classifier [6]. Using object proposals significantly increases processing time and hinders the scalability of the algorithms as they depend on the quality of the object proposals. In fact, region and object proposals are part of a research problem of its own, and have drawbacks such as lack of repeatability, reduced detection performance with a large number of proposals, and difficulties in balancing precision and recall [12].

Our method, however, does not require any object proposals to perform co-localization, but only utilizes features from a CNN that has been pre-trained on classification tasks. The main idea in our work is that objects of the same class share common features or parts. Moreover, these commonalities are central to both category representation and detection and localization of the object. By finding those object categorical features, their joint locations can act as a single-shot object detector. This idea is also grounded in human visual learning, where it is suggested that people detect common features from examples of the category, as part of the object-learning process [38]. We do this by obtaining the CNN features of the provided set of positive images, in order to select the features that are highly and consistently activated, which we denote as Category-Consistent CNN Features (CCFs). We then use these CCFs to discover the rough object locations, and demonstrate an effective way to propagate the feature activations into a stable object for precise co-localization, using the output of the boundary detection algorithm [25]. Figure 1 illustrates the pipeline of our proposed framework.

In more detail, our approach begins with a CNN that has been pre-trained for image classification on ImageNet. Then, the images of the target category are passed through the network. From the set of the CNN kernels, we group them based on their maximum activations across the whole set of images. In fact, since these images all contain the categorical object, all CCFs tend to have high and similar activations, which encourage them to be grouped into the same cluster. Thus, we simply identify the group of kernels with the highest average activation score as CCFs and compute a single normalized activation probability map that associates to this CCF set. Then, we employ an over-segmentation into superpixels of the input image to propagate the values in the activation probability map to the entire image, weighted by the similarities between superpixels. Such similarities are computed via a boundary detection algorithm and are presented as geodesic distances between superpixels. Finally, the precise object location can be obtained by placing a tight bounding box around the thresholded object-likelihood map.

We test our method on three popular datasets for the co-localization problem. To show that our method is able to generalize to truly unseen categories, we test our method on six held-out Imagenet categories that were unseen, and not part of the pre-trained CNN’s training categories. Our experimental results show that our method achieves state-of-the-art co-localization scores even on these ”unseen” categories.

We make three contributions in this work:

  1. We propose a novel CCF extraction method that can automatically select a set of representative features for a category using only positive images. To the best of our knowledge, our method is the first successful framework for extracting representative features inside a CNN framework.

  2. We show that the set of CCFs highlights the rough initial object regions, and can act as a single-shot detector. This result is further refined with an effective feature propagation method using superpixel geodesic distances, that results in a distinctive object region using superpixel on the original image.

  3. Our method achieves state-of-the-art performance for object co-localization on the VOC 2007 and 2012 datasets [9], the Object Discovery dataset [28], and the six held-out ImageNet subset categories, demonstrating that we are able to accurately localize objects obviating the need for region proposals.

2 Related work

Co-localization is related to work on weakly supervised object localization (WSOL) [32, 30, 7, 35, 5, 27, 37, 39] since both share the same objective: to localize objects from an image. However, since WSOL allows the use of negative examples, designing the objective function to discover the information of the object-of-interest is less challenging: WSOL-based methods achieve higher performance on the same datasets as compared to co-localization methods, due to the allowed supervised training. For instance, Wang et al. [35] uses image labels to evaluate the discrimination of discovered categories in order to localize the objects. Ren et al. [27] adopts a discriminative multiple instance learning scheme to compensate for the lack of object-level annotations to localize the objects based on the most discriminative instances. Two recent works using CNN that share the objective with our work are GAP [39] and GMP [23], which both try to obtain the activation map from a CNN representation. However, both GAP & GMP learn to find discriminative features for object locations using additional supervised learning, while the features discovered through our CCF framework are representative in nature (representative may or may not be discriminative, and are similar in concept to generative models). Our method obviates the need for negative examples, and does not require additional training as in GAP and GMP. Because of the supervision that is required by those methods, it is not trivial for WSOL approaches to be directly applied to the co-localization scenarios.

One challenge of co-localization is to define the criteria for discovering the objects without any negative examples. To fill the gap, state-of-the-art co-localization methods such as [21, 33, 6, 16] employ object proposals as part of their object discovery and co-localization pipelines. Tang et al. [33] use the measure of objectness [2] to generate multiple bounding boxes for each image, followed by an objective function to simultaneously optimize the image-level labels and box-level labels. Such settings allow the use of a discriminative cost function [14]. This is also used in the work of co-localization on video frames [16]. Cho et al. [6]’s method also starts from object proposals, sharing the same spirit with deformable part models [10] where objects are discovered and localized by matching common object parts. Most recently, Li et al. [21] study the confidence score distribution of a supervised object detector over the set of object proposals to define an objective function, that learns a common object detector with similar confidence score distribution. All the aforementioned methods heavily depend on the quality of object proposals.

Our work approaches the problem from a different perspective. Instead of trying to fill in the gap of the negative data and annotations that are unavailable, we find the common features shared by the objects from the positive images. Then, we use the joint locations of those features as our single-shot object detector. Our subsequent step refines the detected object features into a stable object by propagating their activations together. We describe the details of our 2-step approach in the following sections.

3 Extracting Category-Consistent CNN Features

Our proposed method consists of two main steps. The first step is to find the CCFs of a category, and obtain their combined feature map that contains aggregated CCF activations over the rough object region. Then, the CCF activations are co-propagated into a stable object using superpixel geodesic distances on the original images.

Given a set of object images from the same class and a CNN that has been pre-trained to contain sufficient visual features, we first compute the feature maps from the last-layer convolutional kernels over the images. Then, we obtain an activation matrix with each row being the activation vector of a kernel containing the maximum values of the kernel’s feature maps.

Specifically, for each kernel: , where is the feature map of kernel , given image that has been forward-passed through the CNN. The activation matrix therefore describes the max-response distributions of all kernels to all category images.

Our goal in this step is to identify a subset of representative kernels from the global set of candidate kernels, that contain common features from the positive images of the same class. This implies that the activation vectors of the kernels should have high values over all vector elements, since there is at least one instance of the object on every image. Conceptually, the kernels that we seek correspond to object parts, or some object-associated features. To find the CCFs, we compute the pair-wise similarities between all pairs of kernels’ activation vectors, and cluster them using k-means. The kernels from the cluster with the highest mean activation correspond to the CCFs. The similarity between two CNN kernels and , can be defined as the distance between two activation vectors and .

The sets of positive images are only required for the identification of the CCF kernels. The CCF kernels can then be used to generate the rough object location in an image in a single-shot: given an image from the target category, the feature maps of the CCFs are combined to form a single activation map. Since each CCF corresponds to an object part of object-associate features, the densely activated area of the activation map indicates the rough location of the target object. The final activation map is normalized into a probability map that sums to 1. In Figure 2 we show the identified CCFs for the bus category, where the activated regions describe bus-related features and all fall within the spatial extent of the objects.

Figure 2: Examples of our CCFs for bus category. Each row is a different example image, and each column is the activation (in violet) of a single CNN feature in the set of our CCFs. The last column shows the final co-localization results.

4 Stable Object Completion via Co-Propagating CCF Activations

The activation probability map from the CCFs automatically points out only the rough location of the object. It does not ensure a reliable object localization because:

  1. The higher layer of a CNN does not guarantee a kernel’s receptive-field size to cover the area of an entire object.

  2. While the feature maps contain spatial information, they have imprecise object locations due to previous max-pooling layers.

  3. The CNN was trained discriminatively. Hence, only the discriminative features of each object may be localized rather than the the whole object.

The geodesic distance has been shown to be effective for many segmentation problems [18, 3, 36, 20]. Given the locations of some representative parts of the object, we utilize the superpixels of the input image and their geodesic distances computed using the image boundary map. The boundary map and the superpixels of the input image can then be used to effectively propagate the initial activation probability values into a complete object region. The geodesic distance between two superpixels is the shortest path between two superpixels where the edge weight is the likelihood of an object boundary between two adjacent superpixels, computed from the boundary probability map. In essence, the geodesic distance compactly encodes the similarity relationship between the two superpixels’ image contents. Therefore, the smaller the geodesic distance between the two superpixels, the more likely that they belong to the same object. Based on this characteristic, we propose a simple and effective method to highlight the object region from the activation probability map, that is both low-resolution and contains non-smooth feature activations.

Next, we proceed to localize the object by combining superpixels that belong to the same object using their geodesic distances, which we call geodesic distance propagation. The main idea is that if two superpixels belong to the same object, they should have 1. a small geodesic distance, and 2. similar activation values. These concepts have been similarly adopted by various works in terms of interactive image segmentation and matting [4, 11], and are especially useful in producing well differentiated object regions in this case. Specifically, we seek to obtain a resulting global activation map that has clear and highly boosted target object regions, by propagating activations based on superpixel geodesic distances.

Given an input image, we oversegment it into superpixels using [24]. We take the combined activation map that was obtained in the CCF identification step, and assign an energy value to each superpixel by averaging its corresponding pixel values found in the activation map. For superpixels, we denote the resulting flattened superpixel activation vector as . Vector can be considered as the initial likelihood of each superpixel being within the object. Then, We compute a propagation matrix , such that is the normalized amount of propagation between superpixel and , with their geodesic distance denoted as , and a parameter for controlling the amount of activation diffusion:

(1)

The propagation matrix can then be applied to the activation vector directly:

(2)

where is the propagated activation vector of the image, containing the globally boosted activations of the superpixels based on their pair-wise geodesic distances to all other superpixels. This allows us to fill in each superpixel on the image with their respective values from , and normalize the propagated superpixel map by dividing every pixel by the max value of the map. The result is an object-likelihood map, on which we apply a global threshold to obtain the region as our final object co-localization result. Finally, a tight bounding box is placed around the maximum coverage of the thresholded regions within an image.

Our propagation step can be implemented in using Johnson’s algorithm [13] to compute all pair shortest paths (where is the number of superpixels, and is the number of edges between superpixels on an image). Thus, our method can potentially be applied on real-time applications. The diffusion values from a superpixel to others are visualized in figure 3. The original image and its boundary map is shown in 2(a). In figure 2(b), we select two representative superpixels to illustrate the propagation values from each superpixel to others under the effect of different values of . The two chosen superpixels are marked as yellow in the leftmost column of figure 2(b).The top row corresponds to the case of a background superpixel. This superpixel has small geodesic distances to a large set of other superpixels. In the second row, we consider a superpixel corresponding to the bird. The next columns illustrate the activation propagating from the selected superpixel to all other superpixels with a varying degree of controlling parameter set at , and , where redder values indicate higher activations. It can be seen from the second column that since the background superpixel has small geodesic distances to many other superpixels, the activations being propagated from this superpixel to others are equally small; in contrast, the activations propagated from the bottom superpixel mostly fall into its close neighboring superpixels and ones that belong to the object’s region. As increases, the amount of propagation is more evenly and widely spread, but with a lower overall magnitude.

(a) The original image and the corresponding boundary map detected using [25]
(b) Two rows illustrate the diffusion amounts from each of the two yellow superpixels to others under the effect of the different values of . The original energy value of each superpixel is 1. The color represents the true value of the energy of the superpixel (increasing from cold to warm). The boundary map is overlaid.
Figure 3: Geodesic distance propagation. (a) is the original image and the boundary map extracted by [25]. The leftmost column of (b) marks the position and initial activation of each of the two selected superpixels, to illustrate the effect of our activation propagation for a single superpixel. The top superpixel is located in the background while the bottom one is located inside the category object (bird). The remaining columns of (b) illustrate the propagated activations from the two superpixels to all other superpixels, with the controlling parameter set at , and , respectively.

5 Experiments

We evaluate our proposed 2-step framework with different parameter settings to illustrate different characteristics of our method. We also evaluate our method on multiple benchmarks, with intermediate and final results to show the localization effects of our proposed method. In all of our experiments, we used two different CNN models: AlexNet[19] and VGG-19[31], both pre-trained on ImageNet [29]. We use the fc6 of AlexNet and the last convolutional layer of a VGG-19 network [31] as variable pool. We used for k-means clustering in the CCF identification step. The final global threshold for obtaining the object region from the object-likelihood map was set at for all images. It is worth mentioning that the recent state-of-the-art co-localization method of Li et al. [21] also uses the fc6 feature of AlexNet and employs the output of EdgeBox[40] in their experiments, which is a direct application of [25]. Our experiments using AlexNet fc6 features therefore are directly comparable to theirs. There is, unfortunately, no publicly available implementation of their method using VGG19.

5.1 Evaluation metric and datasets

We use the conventional CorLoc metric [8] to evaluate our co-localization results. The metric measures the percentage of images that contain correctly localized results. An image is considered correctly localized if there is at least one ground truth bounding box of the object-of-interest having more than a 50% Intersection-over-Union (IoU) score with the predicted bounding box. To benchmark our method performance, we evaluate our method on three commonly used datasets for the problem of co-localization. These are the VOC 2007 and 2012 [9], and the Object Discovery dataset [28]. We also follow [21] to test our method on the six held-out ImageNet subsets. For experiments on the VOC datasets, we followed previous work [6, 16, 21] that used all images on the trainval set excluding the images that only contain the object instances annotated as difficult or truncated. For experiments on the Object Discovery dataset, we used the 100-image subset following [28] in order to make an appropriate comparison with related methods. The ground truth bounding box for each image in the Object Discovery dataset is defined as the smallest bounding box covering all the segmentation ground truth of the object.

Method aero bicy bird boat bottle bus car cat chair cow table dog horse mbike person plant sheep sofa train tv mean Joulin et al. [16] 32.80 17.30 20.90 18.20 4.50 26.90 32.70 41.00 5.80 29.10 34.50 31.60 26.10 40.40 17.90 11.80 25.00 27.50 35.60 12.10 24.60 Cho et al. [6] 50.30 42.80 30.00 18.50 4.00 62.30 64.50 42.50 8.60 49.00 12.20 44.00 64.10 57.20 15.30 9.40 30.90 34.00 61.60 31.50 36.60 Li et al. [21] - AlexNet 73.10 45.00 43.40 27.70 6.80 53.30 58.30 45.00 6.20 48.00 14.30 47.30 69.40 66.80 24.30 12.80 51.50 25.50 65.20 16.80 40.00 Ours - AlexNet 69.60 51.67 43.80 30.05 5.11 55.74 60.00 58.50 6.20 49.00 16.30 51.26 58.74 67.38 22.60 11.60 47.06 27.40 58.93 16.20 40.36 Ours - VGG19 71.90 61.67 48.20 27.66 11.90 63.90 59.30 71.50 5.70 37.00 12.20 44.80 66.50 71.70 18.48 11.11 36.76 29.25 66.96 22.84 41.97

Table 1: CorLoc scores of our approach and state-of-the-art co-localization methods on Pascal VOC 2007 dataset.

Method aero bicy bird boat bottle bus car cat chair cow table dog horse mbike person plant sheep sofa train tv mean Cho et al. [6] 57.00 41.20 36.00 26.90 5.00 81.10 54.60 50.90 18.20 54.00 31.20 44.90 61.80 48.00 13.00 11.70 51.40 45.30 64.60 39.20 41.80 Li et al. [21] - AlexNet 65.70 57.80 47.90 28.90 6.00 74.90 48.40 48.40 14.60 54.40 23.90 50.20 69.90 68.40 24.00 14.20 52.70 30.90 72.40 21.60 43.80 Ours - AlexNet 72.58 67.40 48.73 31.22 8.22 74.05 52.42 64.75 16.04 52.09 26.09 58.64 67.40 71.97 23.99 13.07 37.55 34.25 64.20 15.64 45.02 Ours - VGG19 75.94 76.20 55.70 37.56 22.24 83.97 55.41 67.63 14.08 54.88 31.88 53.65 69.28 76.26 14.04 10.23 42.86 33.70 69.96 18.94 48.22

Table 2: CorLoc scores of our approach and state-of-the-art co-localization methods on Pascal VOC 2012 dataset.

5.2 Comparison to state-of-the-art co-localization methods

We first evaluate our method on the 100-image subset of Object Discovery dataset which contains objects of three classes, namely Airplane, Car, and Horse. There are 18, 11, and 7 noisy images in each class, respectively. Table 3 reports the co-localization performance of our approach in comparison with the state-of-the-art methods on image co-localization [14, 28, 15, 16, 6, 21]. In this small scale setting, our method outperformed other methods in both in individual object classes and overall.

Methods Airplane Car Horse Mean
Kim et al. [17] 21.95 0.00 16.13 12.69
Joulin et al. [14] 32.93 66.29 54.84 51.35
Joulin et al. [15] 57.32 64.04 52.69 58.02
Rubinstein et al. [28] 74.39 87.64 63.44 75.16
Joulin et al. [16] 71.95 93.26 64.52 76.58
Cho et al. [6] 82.93 94.38 75.27 84.19
Ours - AlexNet 81.71 94.38 77.42 84.50
Ours - VGG19 84.15 94.38 79.57 86.03
Table 3: Experiment on the Object Discovery Dataset. Highest performance scores are labeled in bold.
Figure 4: Object co-localization results on the Object Discovery dataset. From the top row to the bottom row: input image, combined activation map from the identified CCFs, propagated object-likelihood map, and resulting bounding boxes. We also depict in green the pixels with the object-region that is predicted by our method. Our predicted bounding boxes are colored as white while the ground truth bounding boxes are green.

Three examples of our co-localization approach using VGG19 on the Object Discovery dataset are illustrated in figure 4. The second row shows the combined activation map from the set of identified CCFs, that acted as our single-shot object detector. It is apparent that the combined activation maps already provided object estimates that were quite accurate to the location of the actual object in the images, with different parts of each object getting high values such as the tail of the airplane, the wheel of the car, or head and tail of the horse. All these values were propagated based on the superpixel geodesic distances, resulting in the images shown in the third row. The propagated object-likelihood maps on the third row show that the sporadic activations on the background have been smoothed out evenly, and that the non-smooth object parts and their associated activations have been boosted and completed into complete and stable objects with significantly higher activation magnitudes. This shows that our two-step framework was able to generate informative single-shot object detections using the CCFs, and the subsequent stable object region via activation propagation.

The PASCAL VOC 2007 and 2012 datasets both contain realistic images of 20 object classes with significantly larger numbers of images per class. These datasets are more challenging than the Object Discovery dataset due to the diversity of viewpoints, and the complexity of the objects. Table 1 reports our performance on the VOC 2007 dataset. Our approach using VGG19 outperforms the state-of-the-art method [21] by 2% on average. Our method works particularly well on bicycle and cat with 16% and 26% higher Corloc score respectively. With AlexNet, our method still shows a mild improvement from the state-of-the-art method.

Results on VOC 2012 dataset are shown in table 2, showing a more pronounced improvement over previous methods. Notice that VOC 2012 has twice the number of images than the VOC 2007 dataset. Our method using AlexNet and VGG19 achieves significantly better results than state-of-the-art methods with 1.2% and 4.42% increase on average.

Our VGG-19 and AlexNet model was pre-trained on ImageNet’s 1000 classes. While VOC 2007 and 2012 are different datasets from ImageNet, there are significant overlaps between the object categories in VOC and ImageNet. For example, the ”motorbike” class of VOC datasets is equivalent to the ”moped” class of ILSVRC 2012 dataset. The six subsets of the ImageNet dataset, chosen by Li et al. [21], are held-out categories from the 1000-label classification task, which means they do not overlap with the 1000 classes used to train VGG-19. The images and the corresponding bounding box annotations were downloaded from ImageNet website [1]. We show that our method is generalizable to truly novel object categories with the six held-out ImageNet subset classes. Table 4 reports the co-localization of our method compares to [21] on the six ImageNet subset. The results show that our method significantly outperforms the competing methods. This result demonstrates that our method can robustly detect and localize truly unseen categories using previously learned CNN features. Our approach outperforms the state-of-the-art method by 1.3% using a pre-trained AlexNet, and 12.8% using a pre-trained VGG19 CNN model. This experiment shows that our method can perform co-localization task accurately on truly unseen classes, implying the strong generalization ability of the CNN features. For example, our results that used the pre-trained VGG19 show noticeable improvements over the state-of-the-art method with a 19% CorLoc score increase in the chipmunk class and 50% CorLoc score increase in the racoon class.

Based on our experimental results on all three datasets, our method using AlexNet performs comparably to the state-of-the-art method, and shows mild improvements on the VOC2007 and six held-out ImageNet subsets and an average of 1.2% CorLoc score increase on the VOC2012 dataset. It is worth mentioning that the performance of the previous state-of-the-art method [21] significantly relies on the object proposal algorithm, the EdgeBox method [40]. Unfortunately there is no available implementation of [21] with different base CNN models other than AlexNet, to measure how it scales with the better CNN models. Our method scales up well, and it appears to show bigger performance gains as the models and datasets get more complex.

ImageNet chipmunk rhino stoat racoon rake wheelchair mean Cho et al. [6] 26.60 81.80 44.20 30.10 8.30 35.30 37.72 Li et al. [21] - AlexNet 44.00 81.80 67.30 41.80 14.50 39.30 48.12 Ours - AlexNet 44.94 86.36 56.73 66.02 10.34 32.37 49.46 Ours - VGG19 63.29 89.77 56.73 91.26 20.69 43.93 60.95

Table 4: CorLoc scores [8] (%) of our approach and state-of-the-art co-localization methods on the 6 held-out subsets of ImageNet collected by Li et al. [21].

5.3 Category-consistent CNN features selection analysis

In this section, we provide an analysis to justify our CCF selection method, where we conduct additional experiments with the same configurations but using different subsets of CNN features for the initial object detection step. We use VGG19 for the analysis in this section. After clustering the last-layer CNN kernels based on their image-level activations, these clusters were sorted in a decreasing order by the clusters’ average activations. We then obtained the rough object locations using individual clusters and thresholded on those maps directly to obtain the object locations. Their respective average CorLoc scores on the VOC 2007 and 2012 dataset are reported in table 5. The table shows that co-localization performance correlates strongly with the level of average activations of the clusters, suggesting that the most representative features were indeed members of the top cluster. We visualize some examples in figure 5, with an image from the bus and motorbike category, respectively. For each image, the first row is the results of our method when using the first cluster (ranked by their average activation) and the second row shows the results of our method when using the third cluster. It is clear that the combined activation maps from the third cluster failed to detect and estimate the object locations, and ultimately lead to incorrect object localization results. This indicates that the selection of the top cluster is essential, and the CCFs could not be chosen arbitrarily.

Dataset 1st 2nd 3rd 4th 5th
VOC07 41.97 39.55 32.15 25.44 21.40
VOC12 48.22 41.47 38.71 32.43 24.80
Table 5: Co-localization performance of our method on the VOC 2007 and 2012 dataset. Each column indicates which top cluster was taken as the CCF cluster (out of 5 total clusters), and the corresponding average CorLoc score (%) by using the selected cluster of features for co-localization.
Figure 5: Two examples illustrating the effect of our feature selection method. For each image, the first row is the results of our method when using the first cluster and the second row is the results of our method when using the third cluster. The green bounding box is the ground truth and the predicted bounding boxes are colored as white, the predicted object regions are masked as green.

We furthermore validate our feature selection method by evaluating the performance of our approach when the CCFs are not selected from the first cluster, but from the top clusters instead, where varies from 1 to 5. As shown in table 6, the results indicate that a larger number of kernels does not provide enough object specificity as the performance decreases when more clusters are added.

Dataset 1 1-2 1-3 1-4 1-5 VOC07 41.97 41.10 39.30 32.25 31.20 VOC12 48.22 46.68 42.25 40.15 38.45

Table 6: Co-localization performance of our methods on the VOC 2007 and 2012 dataset. Each column indicates how many top clusters were taken as the CCF clusters (out of 5 total clusters), and the corresponding average corLoc score (%) by using the selected clusters of features for co-localization. For example, the last column indicates that all available features were used for co-localization.

5.4 Geodesic distance propagation analysis

The geodesic distance acts as a refinement step in our pipeline to remove the background as well as to boost the activation within the object region. To evaluate the effect of geodesic distance propagation, we simply compared the performance of our method on VOC 2007 and 2012 datasets with and without geodesic distance propagation, and report the results in table 7. The results show that geodesic distance propagation significantly improved the co-localization accuracy by more than 6% in absolute CorLoc scores for both datasets, which means that it is an important step after the initial CCF object detection step.

Dataset Without GDP With GDP
VOC07 35.41 41.97
VOC12 41.20 48.22
Table 7: Co-localization performance of our methods on VOC 2007 and 2012 dataset with and without using geodesic distance propagation. Using geodesic distance propagation increased the average CorLoc score (%) of our approach by 6.56% for the VOC 2007 dataset, and 7.02% for the VOC 2012 dataset.

5.5 Qualitative results

Figure 6: Some example results of object co-localization with our CCFs and geodesic distance propagation. The results show the bounding boxes that we generate match the ground truth bounding boxes very well, even when objects are not located centrally in the image. In addition, our co-localized object pixel-level regions (pixels colored in green) show well delineated shape in most cases.

We show some examples of our co-localization results in figure 6. The results show that the bounding boxes generated by our proposed framework accurately match the ground truth bounding boxes. It is apparent that our results generate well-covered object regions, that has the potential to well delineate the objects in majority of the cases. The figures also show that the objects were able to be accurately co-localized with various sizes and locations.

Figure 7: Some failed examples of our approach. While these examples did not have significant coverage with the ground truth boudning box in terms of CorLoc, the mistakes were still accurate, in the sense that the areas were detected but not the spatial extent.

Figure 7 illustrates three failure scenarios of our approach. While these three examples did not cover the ground truth bounding box sufficiently, but they were not far off. Some analysis suggests that these failures were due to some CCFs that are shared by multiple categories, and that the object boundaries may not have been strong enough (i.e. bottle and boat).

6 Conclusion

In this work, we proposed a 2-step approach for the problem of co-localization, that uses only positive images, without any region or object proposals. Our method is motivated by human vision; people implicitly detect the common features of category examples to learn the representation of the class. We show that the identified category-consistent features can also act as an effective first-pass object detector. This idea is implemented by finding the group of CNN features that are highly and consistently activated by a given positive set of images. The result of this first step generates a rough but reliable object location, and acts as a single-shot object detector. Then, we aggregate the activations of the identified CCFs, and propagate their activations so that the activations over the true object region are boosted, while the activations over the background region are smoothed out. This effective activation refinement step allowed us to obtain accurately co-localized objects in terms of the standard CorLoc score with bounding boxes. We achieved new state-of-the-art performance on the three commonly used benchmarks. In the future, we plan to extend our method to generate object co-segmentations.

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