Recognition of human body posture from a cloud of 3D data points using wavelet transform coefficients

Addresses the problem of recognizing a human body posture from a cloud of 3D points acquired by a human body scanner. Motivated by finding a representation that embodies a high discriminatory power between posture classes, a new type of feature is suggested, namely the wavelet transform coefficients (WTC) of the 3D data-point distribution projected on to the space of spherical harmonics. A feature selection technique is developed to find those features with high discriminatory power. Integrated within a Bayesian classification framework and compared with other standard features, the WTC showed great capability in discriminating between close postures. The qualities of the WTC features were also reflected in the experimental results carried out with artificially generated postures, where the WTC obtained the best classification rat

Analysis Tools for Discovering Strong Parity Violation at Hadron Colliders

Several arguments suggest parity violation may be observable in high energy strong interactions. We introduce new analysis tools for describing the azimuthal dependence of multi-particle distributions, or "azimuthal flow." Analysis uses the representations of the orthogonal group O(2) and dihedral groups $D_{N}$ necessary to define parity correctly in two dimensions. Classification finds that collective angles used in event-by-event statistics represent inequivalent tensor observables that cannot generally be represented by a single "reaction plane". Many new parity-violating observables exist that have never been measured, while many new parity-conserving observables formerly lumped together are now distinguished. We use the concept of "event shape sorting" to suggest separating right- and left-handed events, and we discuss the effects of transverse and longitudinal spin. The analysis tools are statistically robust, and can be applied equally to low or high multiplicity events at the Tevatron, $RHIC$ or $RHIC\, Spin$, and the $LHC$.Comment: 18 pages, 2 figures. Final version, accepted for publication in PRD. Updated references. Modified presentation and discussion of previous wor

Deformable Prototypes for Encoding Shape Categories in Image Databases

We describe a method for shape-based image database search that uses deformable prototypes to represent categories. Rather than directly comparing a candidate shape with all shape entries in the database, shapes are compared in terms of the types of nonrigid deformations (differences) that relate them to a small subset of representative prototypes. To solve the shape correspondence and alignment problem, we employ the technique of modal matching, an information-preserving shape decomposition for matching, describing, and comparing shapes despite sensor variations and nonrigid deformations. In modal matching, shape is decomposed into an ordered basis of orthogonal principal components. We demonstrate the utility of this approach for shape comparison in 2-D image databases.Office of Naval Research (Young Investigator Award N00014-06-1-0661

Direct Object Recognition Using No Higher Than Second or Third Order Statistics of the Image

Novel algorithms for object recognition are described that directly recover the transformations relating the image to its model. Unlike methods fitting the typical conventional framework, these new methods do not require exhaustive search for each feature correspondence in order to solve for the transformation. Yet they allow simultaneous object identification and recovery of the transformation. Given hypothesized % potentially corresponding regions in the model and data (2D views) --- which are from planar surfaces of the 3D objects --- these methods allow direct compututation of the parameters of the transformation by which the data may be generated from the model. We propose two algorithms: one based on invariants derived from no higher than second and third order moments of the image, the other via a combination of the affine properties of geometrical and the differential attributes of the image. Empirical results on natural images demonstrate the effectiveness of the proposed algorithms. A sensitivity analysis of the algorithm is presented. We demonstrate in particular that the differential method is quite stable against perturbations --- although not without some error --- when compared with conventional methods. We also demonstrate mathematically that even a single point correspondence suffices, theoretically at least, to recover affine parameters via the differential method

On selecting the best features in a noisy environment

summary:This paper introduces a novel method for selecting a feature subset yielding an optimal trade-off between class separability and feature space dimensionality. We assume the following feature properties: (a) the features are ordered into a sequence, (b) robustness of the features decreases with an increasing order and (c) higher-order features supply more detailed information about the objects. We present a general algorithm how to find under those assumptions the optimal feature subset. Its performance is demonstrated experimentally in the space of moment-based descriptors of 1-D signals, which are invariant to linear filtering

Moments of the Wigner Distribution and a Generalized Uncertainty Principle

The nonnegativity of the density operator of a state is faithfully coded in its Wigner distribution, and this places constraints on the moments of the Wigner distribution. These constraints are presented in a canonically invariant form which is both concise and explicit. Since the conventional uncertainty principle is such a constraint on the first and second moments, our result constitutes a generalization of the same to all orders. Possible application in quantum state reconstruction using optical homodyne tomography is noted.Comment: REVTex, no figures, 9 page

Recognizing trace graphs of closed braids

To a closed braid in a solid torus we associate a trace graph in a thickened torus in such a way that closed braids are isotopic if and only if their trace graphs can be related by trihedral and tetrahedral moves. For closed braids with a fixed number of strands, we recognize trace graphs up to isotopy and trihedral moves in polynomial time with respect to the braid length