Syzygies of the polynomial invariants of the Riemann tensor

This thesis introduces a novel way of writing polynomial invariants as network graphs, and applies this diagrammatic notation scheme, in conjunction with graph theory, to derive algorithms for constructing relationships (syzygies) between different invariants. These algorithms give rise to a constructive solution of a longstanding classical problem in invariant theory.

Stereo vision and wavelets/multiwavelets analysis : 3d reconstruction using wavelets/multiwavelets theory and stereo vision

During the image formation process of the camera, explicit 3D information about the scene or objects in the scene are lost. Therefore, 3D structure or depth information has to be inferred implicitly from the 2D intensity images. This problem is com- monly referred to as 3D reconstruction. In this work a complete 3D reconstruction algorithm is presented, capable of reconstructing dimensionally accurate 3D models of the objects, based on stereo vision and multi-resolution analysis. The developed system uses a reference depth model of the objects under observation to improve the disparity maps, estimated. Only a few features are extracted from that reference model, which are the relative location of the discontinuities and the z-dimensional extremes of objects depth. The maximum error deviation of the estimated depth along the surfaces is less than 0.5mm and along the discontinuities is less than 1.5mm. The developed system is invariant to illuminative variations, and orientation, location and scaling of the objects under consideration, which makes the developed system highly robust.

Robust modular artmap for multi-class shape recognition

This paper presents a fuzzy ARTMAP (FAM) based modular architecture for multi-class pattern recognition known as modular adaptive resonance theory map (MARTMAP). The prediction of class membership is made collectively by combining outputs from multiple novelty detectors. Distance-based familiarity discrimination is introduced to improve the robustness of MARTMAP in the presence of noise. The effectiveness of the proposed architecture is analyzed and compared with ARTMAP-FD network, FAM network, and One-Against-One Support Vector Machine (OAO-SVM). Experimental results show that MARTMAP is able to retain effective familiarity discrimination in noisy environment, and yet less sensitive to class imbalance problem as compared to its counterparts.