Periodic Motion Detection and Estimation via Space-Time Sampling

A novel technique to detect and localize periodic movements in video is presented. The distinctive feature of the technique is that it requires neither feature tracking nor object segmentation. Intensity patterns along linear sample paths in space-time are used in estimation of period of object motion in a given sequence of frames. Sample paths are obtained by connecting (in space-time) sample points from regions of high motion magnitude in the first and last frames. Oscillations in intensity values are induced at time instants when an object intersects the sample path. The locations of peaks in intensity are determined by parameters of both cyclic object motion and orientation of the sample path with respect to object motion. The information about peaks is used in a least squares framework to obtain an initial estimate of these parameters. The estimate is further refined using the full intensity profile. The best estimate for the period of cyclic object motion is obtained by looking for consensus among estimates from many sample paths. The proposed technique is evaluated with synthetic videos where ground-truth is known, and with American Sign Language videos where the goal is to detect periodic hand motions.National Science Foundation (CNS-0202067, IIS-0308213, IIS-0329009); Office of Naval Research (N00014-03-1-0108

Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning or robust PCA (RPCA). For long data sequences, if one tries to use a single lower dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition (S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an entire data vector is either an outlier or an inlier. The S+LR formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201

Representation, space and Hollywood Squares: Looking at things that aren't there anymore

It has been argued that the human cognitive system is capable of using spatial indexes or oculomotor coordinates to relieve working memory load (Ballard, Hayhoe, Pook & Rao, 1997) track multiple moving items through occlusion (Scholl & Pylyshyn, 1999) or link incompatible cognitive and sensorimotor codes (Bridgeman and Huemer, 1998). Here we examine the use of such spatial information in memory for semantic information. Previous research has often focused on the role of task demands and the level of automaticity in the encoding of spatial location in memory tasks. We present five experiments where location is irrelevant to the task, and participants' encoding of spatial information is measured implicitly by their looking behavior during recall. In a paradigm developed from Spivey and Geng (submitted), participants were presented with pieces of auditory, semantic information as part of an event occurring in one of four regions of a computer screen. In front of a blank grid, they were asked a question relating to one of those facts. Under certain conditions it was found that during the question period participants made significantly more saccades to the empty region of space where the semantic information had been previously presented. Our findings are discussed in relation to previous research on memory and spatial location, the dorsal and ventral streams of the visual system, and the notion of a cognitive-perceptual system using spatial indexes to exploit the stability of the external world