On Nonrigid Shape Similarity and Correspondence

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape comparison. Here, we explore the applicability of related shape similarity measures to the problem of shape correspondence, adopting spectral type distances. We propose to evaluate the spectral kernel distance, the spectral embedding distance and the novel spectral quasi-conformal distance, comparing the manifolds from different viewpoints. By matching the shapes in the spectral domain, important attributes of surface structure are being aligned. For the purpose of testing our ideas, we introduce a fully automatic framework for finding intrinsic correspondence between two shapes. The proposed method achieves state-of-the-art results on the Princeton isometric shape matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks

Person re-identification via efficient inference in fully connected CRF

In this paper, we address the problem of person re-identification problem, i.e., retrieving instances from gallery which are generated by the same person as the given probe image. This is very challenging because the person's appearance usually undergoes significant variations due to changes in illumination, camera angle and view, background clutter, and occlusion over the camera network. In this paper, we assume that the matched gallery images should not only be similar to the probe, but also be similar to each other, under suitable metric. We express this assumption with a fully connected CRF model in which each node corresponds to a gallery and every pair of nodes are connected by an edge. A label variable is associated with each node to indicate whether the corresponding image is from target person. We define unary potential for each node using existing feature calculation and matching techniques, which reflect the similarity between probe and gallery image, and define pairwise potential for each edge in terms of a weighed combination of Gaussian kernels, which encode appearance similarity between pair of gallery images. The specific form of pairwise potential allows us to exploit an efficient inference algorithm to calculate the marginal distribution of each label variable for this dense connected CRF. We show the superiority of our method by applying it to public datasets and comparing with the state of the art.Comment: 7 pages, 4 figure

k-Nearest Neighbour Classifiers: 2nd Edition (with Python examples)

Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours to determine the class of the query. This approach to classification is of particular importance because issues of poor run-time performance is not such a problem these days with the computational power that is available. This paper presents an overview of techniques for Nearest Neighbour classification focusing on; mechanisms for assessing similarity (distance), computational issues in identifying nearest neighbours and mechanisms for reducing the dimension of the data. This paper is the second edition of a paper previously published as a technical report. Sections on similarity measures for time-series, retrieval speed-up and intrinsic dimensionality have been added. An Appendix is included providing access to Python code for the key methods.Comment: 22 pages, 15 figures: An updated edition of an older tutorial on kN

A Survey on Metric Learning for Feature Vectors and Structured Data

The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This has led to the emergence of metric learning, which aims at automatically learning a metric from data and has attracted a lot of interest in machine learning and related fields for the past ten years. This survey paper proposes a systematic review of the metric learning literature, highlighting the pros and cons of each approach. We pay particular attention to Mahalanobis distance metric learning, a well-studied and successful framework, but additionally present a wide range of methods that have recently emerged as powerful alternatives, including nonlinear metric learning, similarity learning and local metric learning. Recent trends and extensions, such as semi-supervised metric learning, metric learning for histogram data and the derivation of generalization guarantees, are also covered. Finally, this survey addresses metric learning for structured data, in particular edit distance learning, and attempts to give an overview of the remaining challenges in metric learning for the years to come.Comment: Technical report, 59 pages. Changes in v2: fixed typos and improved presentation. Changes in v3: fixed typos. Changes in v4: fixed typos and new method