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The approximate degree of a Boolean function is the least degree of a real multilinear polynomial approximating it in the $\ell_\infty$-norm over the Boolean hypercube. We show that the approximate degree of the Bipartite Perfect Matching function, which is the indicator over all bipartite graphs having a perfect matching, is $\widetilde{\Theta}(n^{3/2})$. The upper bound is obtained by fully characterizing the unique multilinear polynomial representing the Boolean dual of the perfect matching function, over the reals. Crucially, we show that this polynomial has very small $\ell_1$-norm -- only exponential in $\Theta(n \log n)$. The lower bound follows by bounding the spectral sensitivity of the perfect matching function, which is the spectral radius of its cut-graph on the hypercube \cite{aaronson2020degree, huang2019induced}. We show that the spectral sensitivity of perfect matching is exactly $\Theta(n^{3/2})$.

In the last years, unmanned aerial vehicles are becoming a reality in the context of precision agriculture, mainly for monitoring, patrolling and remote sensing tasks, but also for 3D map reconstruction. In this paper, we present an innovative approach where a fleet of unmanned aerial vehicles is exploited to perform remote sensing tasks over an apple orchard for reconstructing a 3D map of the field, formulating the covering control problem to combine the position of a monitoring target and the viewing angle. Moreover, the objective function of the controller is defined by an importance index, which has been computed from a multi-spectral map of the field, obtained by a preliminary flight, using a semantic interpretation scheme based on a convolutional neural network. This objective function is then updated according to the history of the past coverage states, thus allowing the drones to take situation-adaptive actions. The effectiveness of the proposed covering control strategy has been validated through simulations on a Robot Operating System.

This paper tackles the problem of accurately matching the points of two 3D point clouds. Most conventional methods improve their performance by extracting representative features from each point via deep-learning-based algorithms. On the other hand, the correspondence calculation between the extracted features has not been examined in depth, and non-trainable algorithms (e.g. the Sinkhorn algorithm) are frequently applied. As a result, the extracted features may be forcibly fitted to a non-trainable algorithm. Furthermore, the extracted features frequently contain stochastically unavoidable errors, which degrades the matching accuracy. In this paper, instead of using a non-trainable algorithm, we propose a differentiable matching network that can be jointly optimized with the feature extraction procedure. Our network first constructs graphs with edges connecting the points of each point cloud and then extracts discriminative edge features by using two main components: a shared set-encoder and an edge-selective cross-concatenation. These components enable us to symmetrically consider two point clouds and to extract discriminative edge features, respectively. By using the extracted discriminative edge features, our network can accurately calculate the correspondence between points. Our experimental results show that the proposed network can significantly improve the performance of point cloud matching. Our code is available at //github.com/yanarin/ESFW

Image-text matching plays a central role in bridging vision and language. Most existing approaches only rely on the image-text instance pair to learn their representations, thereby exploiting their matching relationships and making the corresponding alignments. Such approaches only exploit the superficial associations contained in the instance pairwise data, with no consideration of any external commonsense knowledge, which may hinder their capabilities to reason the higher-level relationships between image and text. In this paper, we propose a Consensus-aware Visual-Semantic Embedding (CVSE) model to incorporate the consensus information, namely the commonsense knowledge shared between both modalities, into image-text matching. Specifically, the consensus information is exploited by computing the statistical co-occurrence correlations between the semantic concepts from the image captioning corpus and deploying the constructed concept correlation graph to yield the consensus-aware concept (CAC) representations. Afterwards, CVSE learns the associations and alignments between image and text based on the exploited consensus as well as the instance-level representations for both modalities. Extensive experiments conducted on two public datasets verify that the exploited consensus makes significant contributions to constructing more meaningful visual-semantic embeddings, with the superior performances over the state-of-the-art approaches on the bidirectional image and text retrieval task. Our code of this paper is available at: //github.com/BruceW91/CVSE.

Most conditional generation tasks expect diverse outputs given a single conditional context. However, conditional generative adversarial networks (cGANs) often focus on the prior conditional information and ignore the input noise vectors, which contribute to the output variations. Recent attempts to resolve the mode collapse issue for cGANs are usually task-specific and computationally expensive. In this work, we propose a simple yet effective regularization term to address the mode collapse issue for cGANs. The proposed method explicitly maximizes the ratio of the distance between generated images with respect to the corresponding latent codes, thus encouraging the generators to explore more minor modes during training. This mode seeking regularization term is readily applicable to various conditional generation tasks without imposing training overhead or modifying the original network structures. We validate the proposed algorithm on three conditional image synthesis tasks including categorical generation, image-to-image translation, and text-to-image synthesis with different baseline models. Both qualitative and quantitative results demonstrate the effectiveness of the proposed regularization method for improving diversity without loss of quality.

The per-pixel cross-entropy loss (CEL) has been widely used in structured output prediction tasks as a spatial extension of generic image classification. However, its i.i.d. assumption neglects the structural regularity present in natural images. Various attempts have been made to incorporate structural reasoning mostly through structure priors in a cooperative way where co-occuring patterns are encouraged. We, on the other hand, approach this problem from an opposing angle and propose a new framework for training such structured prediction networks via an adversarial process, in which we train a structure analyzer that provides the supervisory signals, the adversarial structure matching loss (ASML). The structure analyzer is trained to maximize ASML, or to exaggerate recurring structural mistakes usually among co-occurring patterns. On the contrary, the structured output prediction network is trained to reduce those mistakes and is thus enabled to distinguish fine-grained structures. As a result, training structured output prediction networks using ASML reduces contextual confusion among objects and improves boundary localization. We demonstrate that ASML outperforms its counterpart CEL especially in context and boundary aspects on figure-ground segmentation and semantic segmentation tasks with various base architectures, such as FCN, U-Net, DeepLab, and PSPNet.

Despite the remarkable recent progress, person Re-identification (Re-ID) approaches are still suffering from the failure cases where the discriminative body parts are missing. To mitigate such cases, we propose a simple yet effective Horizontal Pyramid Matching (HPM) approach to fully exploit various partial information of a given person, so that correct person candidates can be still identified even if some key parts are missing. Within the HPM, we make the following contributions to produce a more robust feature representation for the Re-ID task: 1) we learn to classify using partial feature representations at different horizontal pyramid scales, which successfully enhance the discriminative capabilities of various person parts; 2) we exploit average and max pooling strategies to account for person-specific discriminative information in a global-local manner; 3) we introduce a novel horizontal erasing operation during training to further resist the problem of missing parts and boost the robustness of feature representations. Extensive experiments are conducted on three popular benchmarks including Market-1501, DukeMTMC-reID and CUHK03. We achieve mAP scores of 83.1%, 74.5% and 59.7% on these benchmarks, which are the new state-of-the-arts.

Typical person re-identification (ReID) methods usually describe each pedestrian with a single feature vector and match them in a task-specific metric space. However, the methods based on a single feature vector are not sufficient enough to overcome visual ambiguity, which frequently occurs in real scenario. In this paper, we propose a novel end-to-end trainable framework, called Dual ATtention Matching network (DuATM), to learn context-aware feature sequences and perform attentive sequence comparison simultaneously. The core component of our DuATM framework is a dual attention mechanism, in which both intra-sequence and inter-sequence attention strategies are used for feature refinement and feature-pair alignment, respectively. Thus, detailed visual cues contained in the intermediate feature sequences can be automatically exploited and properly compared. We train the proposed DuATM network as a siamese network via a triplet loss assisted with a de-correlation loss and a cross-entropy loss. We conduct extensive experiments on both image and video based ReID benchmark datasets. Experimental results demonstrate the significant advantages of our approach compared to the state-of-the-art methods.

In this paper, we study the problem of image-text matching. Inferring the latent semantic alignment between objects or other salient stuffs (e.g. snow, sky, lawn) and the corresponding words in sentences allows to capture fine-grained interplay between vision and language, and makes image-text matching more interpretable. Prior works either simply aggregate the similarity of all possible pairs of regions and words without attending differentially to more and less important words or regions, or use a multi-step attentional process to capture limited number of semantic alignments which is less interpretable. In this paper, we present Stacked Cross Attention to discover the full latent alignments using both image regions and words in sentence as context and infer the image-text similarity. Our approach achieves the state-of-the-art results on the MS-COCO and Flickr30K datasets. On Flickr30K, our approach outperforms the current best methods by 22.1% in text retrieval from image query, and 18.2% in image retrieval with text query (based on Recall@1). On MS-COCO, our approach improves sentence retrieval by 17.8% and image retrieval by 16.6% (based on Recall@1 using the 5K test set).

Person re-identification (\textit{re-id}) refers to matching pedestrians across disjoint yet non-overlapping camera views. The most effective way to match these pedestrians undertaking significant visual variations is to seek reliably invariant features that can describe the person of interest faithfully. Most of existing methods are presented in a supervised manner to produce discriminative features by relying on labeled paired images in correspondence. However, annotating pair-wise images is prohibitively expensive in labors, and thus not practical in large-scale networked cameras. Moreover, seeking comparable representations across camera views demands a flexible model to address the complex distributions of images. In this work, we study the co-occurrence statistic patterns between pairs of images, and propose to crossing Generative Adversarial Network (Cross-GAN) for learning a joint distribution for cross-image representations in a unsupervised manner. Given a pair of person images, the proposed model consists of the variational auto-encoder to encode the pair into respective latent variables, a proposed cross-view alignment to reduce the view disparity, and an adversarial layer to seek the joint distribution of latent representations. The learned latent representations are well-aligned to reflect the co-occurrence patterns of paired images. We empirically evaluate the proposed model against challenging datasets, and our results show the importance of joint invariant features in improving matching rates of person re-id with comparison to semi/unsupervised state-of-the-arts.