RECONSTRUCTION OF 3D OBJECTS FROM 2D VIEWS: SIMULATION, APPLICATIONS AND ERROR ANALYSIS

Abstract

Recovering, reconstructing and recognizing 3D objects from a set of 2D images has been one of the core topics of interest for many researchers in the field of computer vision. Most researchers had concentrated their efforts on obtaining the structural parameters of 3D objects from one or more views. The methodologies proposed in this thesis involve mathematical models for reconstruction of algebraic curves from arbitrary perspective images and its error analysis in the absence of motion. The 2D image obtained from the projection of a 3D object depends on the calibration parameters of the corresponding cameras. A hybrid approach is also presented for stereo camera calibration. This thesis, comprising of eight chapters, is concerned with the formulation of appropriate mathematical model for reconstruction of algebraic curves, camera cali-bration, integration of reconstruction techniques and some applications of these tech-niques in various fields. The first chapter presents a brief description of various reconstruction problems in 3D space. This is followed by the motivation for the stud-ies and a brief review of some salient work in the related field. The second chapter iii iv contains some necessary concepts, definitions and algorithms from stereo reconstruc-tion, camera calibration, artificial neural network (ANN) and genetic algorithm (GA) that will be used in subsequent chapters. In chapter 3, a novel approach is introduced for reconstruction of algebraic curve in 3D space from arbitrary perspective views. This approach takes care of unique-ness, generaliiatibn and noisy environment. The main advantage of the proposed technique is to overcome the matching problem that occurs in pair of projections of the curve. This chapter also contains the estimation of error in this reconstruction ap-proach. Simulation results are presented to evaluate and demonstrate reconstruction methodology using synthetic as well as real data. In chapter 4, the camera calibration problem is modeled as a nonlinear optimiza-tion problem and solved using a Laplace crossover and power mutation (LX-PM) based real coded GA. The results obtained from GA are used as seed of the weight vectors of feed-forward neural network. It can be seen from the simulation results that the proposed hybridization of GA and ANN is more accurate and robust to solve the camera calibration problem. In chapter 5, a neural network based integration of shape from shading (SFS) and stereo has been proposed. In some of the existing algorithms, the systems that integrate SFS and stereo vision into one system use stereo vision for the initialization and SFS for the boundary conditions. However, these approaches may allow the propagation of errors from stereo vision to the solution of SFS. In this chapter, stereo vision and shape from shading have been used as constraints on the depth map information simultaneously. A feed-forward neural network has been used for the integration. Divide and conquer technique have been used in the network training process for reducing the computational cost of proposed integration algorithm. In chapter 6, an application of 3D reconstruction in stereo image coding via digital watermarking is presented. The original (left) image is degraded by means of ZIG-ZAG sequence and transformed into fractional Fourier transform (FrFT) domain. Singular value decomposition (SVD) is performed on the transform degrAned image as well as watermark. Right disparity map has been used as a watermark. The effects of various watermark attacks have been studied. In chapter 7, an application of stereo vision in robot control is presented. The task under consideration is to control the manipulator, such that the tip of a tool grasped by the end-effector follows an unknown path on a surface with the help of a pair of stereo cameras mounted on the manipulator and pressure sensor at the end-effector. The control algorithm utilizes pressure information and visual sensors simultaneously. Inverse kinematics has been solved for a redundant manipulator for tracking the resultant path. An optimization based approach is presented to solve inverse kinematics by converting it into a nonlinear optimization problem. An improved energy function is defined to solve the optimization problem even in the case when the matrix associated with objective function is not positive definite. The stability analysis has been done for the proposed algorithm using Lyapunov method. vi The result has been illustrated through simulation of inverse kinematics solution for a seven arm redundant manipulator. In chapter 8, the salient contributions of the work described in this thesis are given, with the future scope of work in this field.