RECONSTRUCTION OF 3-D OBJECTS USING SHAPE FROM SHADING ALGORITHMS

Abstract

Computer Vision is a nice mimicry of human vision system and its aim is to provide visual system to the Computers. In human vision system, the real world scene is projected onto the retina, essentially two dimensional but human being perceives the scene in three-dimensional world with the help of nervous system attached with it. Similarly, in Computer Vision, one tries to recover the 3-D shape of the scene from the 2-D projected images captured by the camera. Thus the Computer Vision can be considered as inverse problem of one of the topics of Computer Graphics in which the images are rendered by projecting a 3-D scene or object onto 2-D image planes. Computer Vision has broad spectrum of applications e.g. in medical sciences, vehicle guidance, visual surveying, industrial manufacturing, robot navigation, oceanography etc. The Computer Vision techniques are developed on the basis of available visual cues in the images and according to the application requirements. There are various techniques of Computer Vision, collectively called Shape from-X-techniques, where X stands for stereo, shading, texture, motion, contour, focus and so on. Out of these, Shape from Shading is one of the well known techniques and its applicability in real life is very wide as it recovers the 3-D shape of an object from its single shaded image unlike other techniques which use the multiple images. Shape from Shading, as popularly called as SfS, was first introduced by B.K.P. Horn in early seventies. Shading variation mainly depends upon surface orientation, albedo (microstructure) of the surface material and the light source direction etc. The basic goal of SfS is to solve the image irradiance equation which relates im-age irradiance to scene radiance. Image irradiance is a first order Hamilton Jacobi 11 type equation. SfS techniques are mainly categorized into four approaches, namely minimization, local, propagation and linear. In minimization approaches, the energy function along with some constraints is minimized to obtain the shape information. In local approaches, the local shape of the object is assumed e.g. spherical and based on local shape the entire shape of the object is calculated. In propagation approaches, solution propagates from some known points usually known as singular points and the entire shape is obtained. In linear approaches, usually reflectance map is linearized in terms of depth and the shape of the object is calculated. The present thesis mainly deals with the minimization, linear and propagation approaches. The aim of the present thesis is to present a series of discussions that describe, analyze, explain and hypothesize about SfS and its usage. The work in this thesis deals with the integration of SfS with other Computer Vision techniques like Shape, from Stereo, Shape reconstruction of smooth and polyhedral objects using SfS, ap-plication of SfS on perfect gray level and defocused images, a comparative study of SfS algorithms with respect to their accuracy and efficiency and the development of SfS algorithms for perspective projected shaded images. This thesis, includes eight chapters which are mainly concerned with the development and presentation of SfS algorithms. Chapter 1 describes motivation behind the .present work, a brief introduc-, tion of the topic, classification of the work carried out in this field, a brief literature review and outline of the thesis. Chapter 2 explains some necessary concepts, defini-tions, SfS models, Artificial Neural Network, Genetic Algorithm, Dijkstra's algorithm etc. which have been used in the development of the methods given in the subsequent chapters. In chapter 3, a novel and robust approach is introduced to recover the 3-D shape of complex surfaces from their texture less stereo pair images using a generalized and linear reflectance model of SfS. For the approximation of rough surfaces, the general-ized Lambertian reflectance map with a simple linear approach is used to obtain the depth values of reconstructed surfaces. To improve the SfS results, Scale Invariant Features Transform (SIFT) index based feature matching is performed between the stereo pair of images and a multilayer feed forward neural network scheme is used to embed SIFT indexes with SfS depth values. 111 In chapter 4, three different SfS techniques based on edge detection and super-strictness problem are introduced for the reconstruction of polyhedral objects. In the first technique, the consistency of images is checked by rank conditions of shape matrix and in case of incorrect image, vertices of polyhedral image are corrected by singular value decomposition method. The second technique is a probabilistic ap-proach for the shape reconstruction of polyhedral objects using shaded information contained in the planar faces of polyhedral object's image. In the third technique, the geometrical constraints are added in image irradiance equation and the result-ing functional is minimized with the Genetic Algorithm in order to obtain the depth values at each vertex of the polyhedral object. Chapter 5 presents a very fast technique for the reconstruction of the 3-D shapes of smooth objects from their shaded images. This technique is a propagation,'„based, deterministic, non-iterative and a single pass technique known as Marching with Correctness Criterion (MCC). Obtained results and computing time of MCC are compared with a well known Fast Marching Method (FMM). In chapter 6, a fast and efficient approach is used to solve the Perspective Shape from Shading (PSfS) problem. In this problem, the object surface is assumed to be illuminated by a point light source at vertical direction, situated far away from the object. The camera is assumed to be calibrated. The MCC approach is applied or these perspective images and the 3-D shape of the objects are reconstructed. The computed time and errors are compared with the Perspective Shape from Shading case solved by FMM. In chapter 7, a robust technique for the 3-D shape reconstruction from defocusec images is given. Defocused images are diffused into a single image carrying the im-portant features of the defocused images. A wavelet Packet Transform (WPT) anc discrete contrast based fusion algorithm is used to diffuse the defocused image it a single image. On the obtained fused image, the linear and general Lambertiar approach is used for the 3-D shape reconstruction of the objects. In chapter 8, the thesis is concluded with a critical analysis of the work presentee in earlier chapters and the overall concluding observations of this study along with brief discussion on the scope of future work.