The question of how shape is represented is of central interest to understanding visual processing in cortex. While tuning properties of the cells in early part of the ventral visual stream, thought to be responsible for object recognition in the primate, are comparatively well understood, several different theories have been proposed regarding tuning in higher visual areas, such as V4. We used the model of object recognition in cortex presented by Riesenhuber and Poggio (1999), where more complex shape tuning in higher layers is the result of combining afferent inputs tuned to simpler features, and compared the tuning properties of model units in intermediate layers to those of V4 neurons from the literature. In particular, we investigated the issue of shape representation in visual area V1 and V4 using oriented bars and various types of gratings (polar, hyperbolic, and Cartesian), as used in several physiology experiments. Our computational model was able to reproduce several physiological findings, such as the broadening distribution of the orientation bandwidths and the emergence of a bias toward non-Cartesian stimuli. Interestingly, the simulation results suggest that some V4 neurons receive input from afferents with spatially separated receptive fields, leading to experimentally testable predictions. However, the simulations also show that the stimulus set of Cartesian and non-Cartesian gratings is not sufficiently complex to probe shape tuning in higher areas, necessitating the use of more complex stimulus sets.

A patient-specific model of the liver can supply accurate volume measurements for oncologists and lesion locations and liver visualisation for surgeons. Our work seeks to enable an automatic computational tool for liver quantification. To create this model, the liver shape must be segmented from 3D CT images. In doing so, we can quantify liver volume and restrict the region of interest to ease the task of tumour and vascular segmentation. The main objective of liver segmentation developed into a mission to fluently describe liver shape a priori in level-set methods. This thesis looks at the utility of an implicit shape representation based on the Poisson equation to describe highly variable shapes, with application to image segmentation. Our first contribution is analyses on four implicit shape representations based on the heat equation, the signed distance function, Poisson’s equation, and the logarithm of odds. For four separate shape case studies, we summarise the class of shapes through their shape representation using Principal Component Analysis (PCA). Each shape class is highly variable across a population, but have a characteristic structure. We quantitatively compare the implicit shape representations, within each class, by evaluating its compactness, and in the last case, also completeness. To the best of our knowledge, this study is novel in comparing several shape representations through a single dimension reduction method. Our second contribution is a hybrid region-based level set segmentation that simultaneously infers liver shape given the image data, integrates the Poisson-based shape function prior into the segmentation, and evolves the level set according to the image data. We test our algorithm on exemplary 2D liver axial slices. We compare results for each image to results from (a) level-set segmentation without a shape prior and (b) level-set segmentation with a shape prior based on the Signed Distance Transform (SDT). In both priors, shapes are projected from shape space through the sample population mean and its modes of variation (the minimum number of principal components to comprise at least 95% of the cumulative variance). We compare results on four individual cases using the Dice coefficient and the Hausdorff distance. This thesis introduces an implicit shape representation based on Poisson’s equation in the field of medical image segmentation, showing its influence on shape space summary and projection. We analyse the shape space for compactness, showing that it is more compact in each of our case studies by at least two-fold and as much as three-fold. For 3D liver shapes, we show that it is more complete than the other three implicit shape representations. We utilise its description efficiency for use in 2D liver image segmentation, implementing the first shape function prior based on the Poisson equation. We show a qualitative and quantitative improvement over segmentation results without any shape prior and comparable results to segmentation with a SDT shape prior.

We describe a new direct method for estimating structure and motion from image intensities of multiple views. We extend the direct methods of Horn- and-Weldon to three views. Adding the third view enables us to solve for motion, and compute a dense depth map of the scene, directly from image spatio -temporal derivatives in a linear manner without first having to find point correspondences or compute optical flow. We describe the advantages and limitations of this method which are then verified through simulation and experiments with real images.

In this thesis, we study the shape analysis problem and propose new methods for shape description, similarity and recognition. Firstly, we introduce a new shape descriptor in a two-step method. In the first step, the 2-D shape information is mapped into a set of 1-D functions. The mapping is based on the beams, which are originated from a boundary point, connecting that point with the rest of the points on the boundary. At each point, the angle between a pair of beams is taken as a random variable to define the statistics of the topological structure of the boundary. The third order statistics of all the beam angles is used to construct 1-D Beam Angle Statistics (BAS) functions. In the second step, we apply a set of feature extraction methods on BAS functions in order to describe it in a more compact form. BAS functions eliminate the context-dependency of the representation to the data set. BAS function is invariant to translation, rotation and scale. It is insensitive to distortions. No predefined resolution or threshold is required to define the BAS functions. Secondly, we adopt three different similarity distance methods defined on the BAS feature space, namely, Optimal Correspondence of String Subsequences, Dynamic Warping and Cyclic Sequence Matching algorithms. Main goal in these algorithms is to minimize the distance between two BAS features by allowing deformations. Thirdly, we propose a new Hidden Markov Model (HMM)topology for boundary based shape recognition. The proposed topology called Circular HMM is both ergodic and temporal. Therefore, the states can be revisited in finite time intervals while keeping the sequential information in the string, which represents the shape. It is insensitive to size changes. Since it has no starting and terminating state, it is insensitive to the starting point of the shape boundary. Experiments are done on the dataset of MPEG 7 Core Experiments Shape-1. It is observed that BAS descriptor outperforms all the methods in the literature. The Circular HMM gives higher recognition rates than the classical topologies in shape analysis applications.

The user of an image database often wishes to retrieve all images similar to the one (s)he already has. In this thesis, shape analysis methods for retrieving shape are investigated. Shape analysis methods can be classified in two groups as contour-based and region-based according to the shape information used. In such a classification, curvature scale space (CSS) representation and angular radial transform (ART) are promising methods for shape similarity retrieval respectively. The CSS representation operates by decomposing the shape contour into convex and concave sections. CSS descriptor is extracted by using the curvature zero-crossings behaviour of the shape boundary while smoothing the boundary with Gaussian filter. The ART descriptor decomposes the shape region into a number of orthogonal 2-D basis functions defined on a unit disk. ART descriptor is extracted using the magnitudes of ART coefficients. These methods are implemented for similarity comparison of binary images and the retrieval performances of descriptors for changing number of sampling points of boundary and order of ART coefficients are investigated. The experiments are done using 1000 images from MPEG7 Core Experiments Shape-1. Results show that for different classes of shape, different descriptors are more successful. When the choice of approach depends on the properties of the query shape, similarity retrieval performance increases.

[Truncated abstract] The aim of visual recognition is to identify objects in a scene and estimate their pose. Object recognition from 2D images is sensitive to illumination, pose, clutter and occlusions. Object recognition from range data on the other hand does not suffer from these limitations. An important paradigm of recognition is model-based whereby 3D models of objects are constructed offline and saved in a database, using a suitable representation. During online recognition, a similar representation of a scene is matched with the database for recognizing objects present in the scene . . . The tensor representation is extended to automatic and pose invariant 3D face recognition. As the face is a non-rigid object, expressions can significantly change its 3D shape. Therefore, the last part of this thesis investigates representations and matching techniques for automatic 3D face recognition which are robust to facial expressions. A number of novelties are proposed in this area along with their extensive experimental validation using the largest available 3D face database. These novelties include a region-based matching algorithm for 3D face recognition, a 2D and 3D multimodal hybrid face recognition algorithm, fully automatic 3D nose ridge detection, fully automatic normalization of 3D and 2D faces, a low cost rejection classifier based on a novel Spherical Face Representation, and finally, automatic segmentation of the expression insensitive regions of a face.

This master's thesis is engaged in machine vision, methods of image processing and analysis. The reason is to create application to determine relative positions of Trilobot robots in the laboratory.