Properties and Applications of Shape Recipes

In low-level vision, the representation of scene properties such as shape, albedo, etc., are very high dimensional as they have to describe complicated structures. The approach proposed here is to let the image itself bear as much of the representational burden as possible. In many situations, scene and image are closely related and it is possible to find a functional relationship between them. The scene information can be represented in reference to the image where the functional specifies how to translate the image into the associated scene. We illustrate the use of this representation for encoding shape information. We show how this representation has appealing properties such as locality and slow variation across space and scale. These properties provide a way of improving shape estimates coming from other sources of information like stereo.

Synthesis, Optical properties and Applications of Water Soluble Conjugated PPPs for Biosensors

In recent years, application of fluorescent conjugated polymers to sense chemical and biological analytes has received much attention owing to its technological significance. Water soluble conjugated polymers are interesting towards the developing sensors for biomolecules. In this present contribution, we describe the syntheses and characterization of a series of water soluble conjugated polymers with sulfonic acid groups in the side chain. Such anionic conjugated polymers are designed to interact with biomolecules such as cytochrome-C. All polymers are water soluble and showed strong blue emission. Significant quenching of the fluorescence from our functionalized PPP was observed upon addition of viologen derivatives or cytochrome -C.

Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

The Quadric Reference Surface: Theory and Applications

The conceptual component of this work is about "reference surfaces'' which are the dual of reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.

On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications

This paper investigates the linear degeneracies of projective structure estimation from point and line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) in the case when the scene is a Linear Line Complex (set of lines in space intersecting at a common line) and is 21 when the scene is planar. The LLC situation is only linearly degenerate, and we show that one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice.

Support Vector Machines: Training and Applications

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.