In this paper, we present a non parametric modeling for phase maps of interferometric SAR. Cosine and Sine projections maps are generated from the SAR phase map, and each of them are individually modeled by fitting 2D basis functions. The coefficients of these basis functions describe a "smoothed" version of the original phase map. Several applications can be derived from this noise filtered phase map: better phase unwrapping and SAR image compression are to of the applications that we will be discussing in the paper. The approach can be extended to other imaging domains that involve large maps of directional or phase data, such as modeling of phase MRI images, modeling of wind directions in meteorological data, etc.

Independent component analysis (ICA) has found a wide range of applications in signal processing and multimedia, ranging from speech cleaning to face recognition. This paper presents a non-parametric approach to the ICA problem that is robust towards outlier effects. The algorithm, for the first time in the field of ICA, adopts an intuitive and direct approach, focusing on the very definition of independence itself; i.e. the joint probability density function (pdf) of independent sources is factorial over the marginal distributions. This is contrary to traditional independent component analysis (ICA) algorithms, which achieve the objective by attempting to fulfill necessary conditions (but not sufficient) for independence. For example, the Jade algorithm attempts to approximate independence by minimizing higher order statistics. In the proposed algorithm, kernel density estimation is employed to provide a good approximation of the distributions that are required to be estimated. This estimation technique is inherently robust towards outlier effects. The application of kernel density estimation also enables the algorithm to be free from the assumptions of source distributions. Experimental results show that the algorithm is able to perform separation of sources in the presence of outliers, whereas existing algorithms like Jade and Info max break down under such conditions. The results have also shown that the proposed non-parametric approach is generally source distribution independent. In addition, it is able to separate non-Gaussian zero-kurtotic signals unlike the traditional ICA algorithms like Jade and Infomax.

Presents a solution to a particular curve (surface) fitting problem and demonstrate its application in modeling objects from monocular image sequences. The curve-fitting algorithm is based on a modified nonparametric regression method, which forms the core contribution of this work. This method is far more effective compared to standard estimation techniques, such as the maximum likelihood estimation method, and can take into account the discontinuities present in the curve. Next, the theoretical results of this 1D curve estimation technique ate extended significantly for an object modeling problem. The input to the algorithm is a monocular image sequence of an object undergoing rigid motion. By using the affine camera projection geometry and a given choice of an image frame pair in the sequence, we adopt the KvD (Koenderink and van Doorn, 1991) model to express the depth at each point on the object as a function of the unknown out-of-plane rotation, and some measurable quantities computed directly from the optical flow. This is repeated for multiple image pairs (keeping one fixed image frame which we formally call the base image and choosing another frame from the sequence). The depth map is next estimated from these equations using the modified nonparametric regression analysis. We conducted experiments on various image sequences to verify the effectiveness of the technique. The results obtained using our curve-fitting technique can be refined further by hierarchical techniques, as well as by nonlinear optimization techniques in structure from motion.

We present the theory of modified nonparametric regression for estimating the 3D face structure of a human from a monocular image sequence. In the preprocessing stage, the face region is segmented from the background using both color and motion information, by using a hierarchical block motion estimation method. By using the affine camera projection geometry, and a given choice of an image frame pair in the sequence, we adopt the KvD model to express the depth at each point on the face region as a function of the unknown out-of-plane rotation, and some measurable quantities computed directly from the optical flow. This is repeated for multiple image pairs (keeping one fixed image frame which we formally call the "base" image, and choosing another frame from the sequence). The true depth map is next estimated from these equations using a modified nonparametric regression technique, and this forms the core contribution of this paper. We conducted experiments on various image sequences to verify the effectiveness of the technique, and propose to extend it for photorealistic modeling of arbitrary (non-face) objects from image sequences.