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 ordinal relation



Single-Image Depth Perception in the Wild

Neural Information Processing Systems

This paper studies single-image depth perception in the wild, i.e., recovering depth from a single image taken in unconstrained settings. We introduce a new dataset "Depth in the Wild" consisting of images in the wild annotated with relative depth between pairs of random points. We also propose a new algorithm that learns to estimate metric depth using annotations of relative depth. Compared to the state of the art, our algorithm is simpler and performs better. Experiments show that our algorithm, combined with existing RGB-D data and our new relative depth annotations, significantly improves single-image depth perception in the wild.


Ordinal Constrained Binary Code Learning for Nearest Neighbor Search

AAAI Conferences

Recent years have witnessed extensive attention in binary code learning, a.k.a. hashing, for nearest neighbor search problems. It has been seen that high-dimensional data points can quantize into binary codes to give an efficient similarity approximation via Hamming distance. Among the existing schemes, ranking-based hashing is recent promising that targets at preserving ordinal relations of ranking in the Hamming space to minimize retrieval loss. However, the size of the ranking tuples that show the ordinal relations, is quadratic or cubic to the size of training samples. It is so very expensive to embed such ranking tuples in binary code learning, especially given a large-scale training data set. Besides, it remains difficult to build ranking tuples efficiently for most ranking-preserving hashing, which are deployed over an ordinal graph-based setting. To handle these problems, we propose a novel ranking-preserving hashing method, dubbed Ordinal Constraint Hashing (OCH), which efficiently learns the optimal hashing functions with a graph-based approximation to embed the ordinal relations. The core idea is to reduce the size of ordinal graph with ordinal constraint projection, which preserves the ordinal relations through a small data set (such as clusters or random samples). In particular, to learn such hash functions effectively, we further relax the discrete constraints and design a specific stochastic gradient decent algorithm for optimization. Experimental results on three large-scale visual search benchmark datasets, i.e. LabelMe, Tiny100K and GIST1M, show that the proposed OCH method can achieve superior performance over the state-of-the-arts approaches.


Single-Image Depth Perception in the Wild

arXiv.org Artificial Intelligence

This paper studies single-image depth perception in the wild, i.e., recovering depth from a single image taken in unconstrained settings. We introduce a new dataset "Depth in the Wild" consisting of images in the wild annotated with relative depth between pairs of random points. We also propose a new algorithm that learns to estimate metric depth using annotations of relative depth. Compared to the state of the art, our algorithm is simpler and performs better. Experiments show that our algorithm, combined with existing RGB-D data and our new relative depth annotations, significantly improves single-image depth perception in the wild.


Single-Image Depth Perception in the Wild

Neural Information Processing Systems

This paper studies single-image depth perception in the wild, i.e., recovering depth from a single image taken in unconstrained settings. We introduce a new dataset "Depth in the Wild" consisting of images in the wild annotated with relative depth between pairs of random points. We also propose a new algorithm that learns to estimate metric depth using annotations of relative depth. Compared to the state of the art, our algorithm is simpler and performs better. Experiments show that our algorithm, combined with existing RGB-D data and our new relative depth annotations, significantly improves single-image depth perception in the wild.


Towards Optimal Binary Code Learning via Ordinal Embedding

AAAI Conferences

Binary code learning, a.k.a., hashing, has been recently popular due to its high efficiency in large-scale similarity search and recognition. It typically maps high-dimensional data points to binary codes, where data similarity can be efficiently computed via rapid Hamming distance. Most existing unsupervised hashing schemes pursue binary codes by reducing the quantization error from an original real-valued data space to a resulting Hamming space. On the other hand, most existing supervised hashing schemes constrain binary code learning to correlate with pairwise similarity labels. However, few methods consider ordinal relations in the binary code learning process, which serve as a very significant cue to learn the optimal binary codes for similarity search. In this paper, we propose a novel hashing scheme, dubbed Ordinal Embedding Hashing (OEH), which embeds given ordinal relations among data points to learn the ranking-preserving binary codes. The core idea is to construct a directed unweighted graph to capture the ordinal relations, and then train the hash functions using this ordinal graph to preserve the permutation relations in the Hamming space. To learn such hash functions effectively, we further relax the discrete constraints and design a stochastic gradient decent algorithm to obtain the optimal solution. Experimental results on two large-scale benchmark datasets demonstrate that the proposed OEH method can achieve superior performance over the state-of-the-arts approaches.At last, the evaluation on query by humming dataset demonstrates the OEH also has good performance for music retrieval by using user's humming or singing.


The Fidelity of Local Ordinal Encoding

Neural Information Processing Systems

A key question in neuroscience is how to encode sensory stimuli such as images and sounds. Motivated by studies of response properties of neurons in the early cortical areas, we propose an encoding scheme that dispenses with absolute measures of signal intensity or contrast and uses, instead, only local ordinal measures. In this scheme, the structure of a signal is represented by a set of equalities and inequalities across adjacent regions. In this paper, we focus on characterizing the fidelity of this representation strategy. We develop a regularization approach for image reconstruction from ordinal measures and thereby demonstrate that the ordinal representation scheme can faithfully encode signal structure. We also present a neurally plausible implementation of this computation that uses only local update rules.


The Fidelity of Local Ordinal Encoding

Neural Information Processing Systems

A key question in neuroscience is how to encode sensory stimuli such as images and sounds. Motivated by studies of response properties of neurons in the early cortical areas, we propose an encoding scheme that dispenses with absolute measures of signal intensity or contrast and uses, instead, only local ordinal measures. In this scheme, the structure of a signal is represented by a set of equalities and inequalities across adjacent regions. In this paper, we focus on characterizing the fidelity of this representation strategy. We develop a regularization approach for image reconstruction from ordinal measures and thereby demonstrate that the ordinal representation scheme can faithfully encode signal structure. We also present a neurally plausible implementation of this computation that uses only local update rules.