Tensor and Matrix Inversions with Applications

Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we derived new tensor decompositions which we have shown to be related to the well-known canonical polyadic decomposition and multilinear SVD. Moreover, within this group structure framework, multilinear systems are derived, specifically, for solving high dimensional PDEs and large discrete quantum models. We also address multilinear systems which do not fit the framework in the least-squares sense, that is, when the tensor has an odd number of modes or when the tensor has distinct dimensions in each modes. With the notion of tensor inversion, multilinear systems are solvable. Numerically we solve multilinear systems using iterative techniques, namely biconjugate gradient and Jacobi methods in tensor format

Recognition of human activities and expressions in video sequences using shape context descriptor

The recognition of objects and classes of objects is of importance in the field of computer vision due to its applicability in areas such as video surveillance, medical imaging and retrieval of images and videos from large databases on the Internet. Effective recognition of object classes is still a challenge in vision; hence, there is much interest to improve the rate of recognition in order to keep up with the rising demands of the fields where these techniques are being applied. This thesis investigates the recognition of activities and expressions in video sequences using a new descriptor called the spatiotemporal shape context. The shape context is a well-known algorithm that describes the shape of an object based upon the mutual distribution of points in the contour of the object; however, it falls short when the distinctive property of an object is not just its shape but also its movement across frames in a video sequence. Since actions and expressions tend to have a motion component that enhances the capability of distinguishing them, the shape based information from the shape context proves insufficient. This thesis proposes new 3D and 4D spatiotemporal shape context descriptors that incorporate into the original shape context changes in motion across frames. Results of classification of actions and expressions demonstrate that the spatiotemporal shape context is better than the original shape context at enhancing recognition of classes in the activity and expression domains

A novel approach to handwritten character recognition

A number of new techniques and approaches for off-line handwritten character recognition are presented which individually make significant advancements in the field. First. an outline-based vectorization algorithm is described which gives improved accuracy in producing vector representations of the pen strokes used to draw characters. Later. Vectorization and other types of preprocessing are criticized and an approach to recognition is suggested which avoids separate preprocessing stages by incorporating them into later stages. Apart from the increased speed of this approach. it allows more effective alteration of the character images since more is known about them at the later stages. It also allows the possibility of alterations being corrected if they are initially detrimental to recognition. A new feature measurement. the Radial Distance/Sector Area feature. is presented which is highly robust. tolerant to noise. distortion and style variation. and gives high accuracy results when used for training and testing in a statistical or neural classifier. A very powerful classifier is therefore obtained for recognizing correctly segmented characters. The segmentation task is explored in a simple system of integrated over-segmentation. Character classification and approximate dictionary checking. This can be extended to a full system for handprinted word recognition. In addition to the advancements made by these methods. a powerful new approach to handwritten character recognition is proposed as a direction for future research. This proposal combines the ideas and techniques developed in this thesis in a hierarchical network of classifier modules to achieve context-sensitive. off-line recognition of handwritten text. A new type of "intelligent" feedback is used to direct the search to contextually sensible classifications. A powerful adaptive segmentation system is proposed which. when used as the bottom layer in the hierarchical network. allows initially incorrect segmentations to be adjusted according to the hypotheses of the higher level context modules

A novel approach to handwritten character recognition

A number of new techniques and approaches for off-line handwritten character recognition are presented which individually make significant advancements in the field. First. an outline-based vectorization algorithm is described which gives improved accuracy in producing vector representations of the pen strokes used to draw characters. Later. Vectorization and other types of preprocessing are criticized and an approach to recognition is suggested which avoids separate preprocessing stages by incorporating them into later stages. Apart from the increased speed of this approach. it allows more effective alteration of the character images since more is known about them at the later stages. It also allows the possibility of alterations being corrected if they are initially detrimental to recognition. A new feature measurement. the Radial Distance/Sector Area feature. is presented which is highly robust. tolerant to noise. distortion and style variation. and gives high accuracy results when used for training and testing in a statistical or neural classifier. A very powerful classifier is therefore obtained for recognizing correctly segmented characters. The segmentation task is explored in a simple system of integrated over-segmentation. Character classification and approximate dictionary checking. This can be extended to a full system for handprinted word recognition. In addition to the advancements made by these methods. a powerful new approach to handwritten character recognition is proposed as a direction for future research. This proposal combines the ideas and techniques developed in this thesis in a hierarchical network of classifier modules to achieve context-sensitive. off-line recognition of handwritten text. A new type of "intelligent" feedback is used to direct the search to contextually sensible classifications. A powerful adaptive segmentation system is proposed which. when used as the bottom layer in the hierarchical network. allows initially incorrect segmentations to be adjusted according to the hypotheses of the higher level context modules

Shape Descriptors

Every day we recognize a numerous objects and human brain can recognize objects under many conditions. The way in which humans are able to identify an object is remarkably fast even in different size, colours or other factors. Computers or robots need computational tools to identify objects. Shape descriptors are one of the tools commonly used in image processing applications. Shape descriptors are regarded as mathematical functions employed for investigating image shape information. Various shape descriptors have been studied in the literature. The aim of this thesis is to develop new shape descriptors which provides a reasonable alternative to the existing methods or modified to improve them. Generally speaking shape descriptors can be categorized into various taxonomies based on the information they use to compute their measures. However, some descriptors may use a combination of boundary and interior points to compute their measures. A new shape descriptor, which uses both region and contour information, called centeredness measure has been defined. A new alternative ellipticity measure and sensitive family ellipticity measures are introduced. Lastly familiy of ellipticity measures, which can distinguish between ellipses whose ratio between the length of the major and minor axis differs, have been presented. These measures can be combined and applied in different image processing applications such as image retrieval and classification. This simple basis is demonstrated through several examples

The computational magic of the ventral stream: sketch of a theory (and why some deep architectures work).

This paper explores the theoretical consequences of a simple assumption: the computational goal of the feedforward path in the ventral stream -- from V1, V2, V4 and to IT -- is to discount image transformations, after learning them during development

Object recognition using multi-view imaging

Single view imaging data has been used in most previous research in computer vision and image understanding and lots of techniques have been developed. Recently with the fast development and dropping cost of multiple cameras, it has become possible to have many more views to achieve image processing tasks. This thesis will consider how to use the obtained multiple images in the application of target object recognition. In this context, we present two algorithms for object recognition based on scale- invariant feature points. The first is single view object recognition method (SOR), which operates on single images and uses a chirality constraint to reduce the recognition errors that arise when only a small number of feature points are matched. The procedure is extended in the second multi-view object recognition algorithm (MOR) which operates on a multi-view image sequence and, by tracking feature points using a dynamic programming method in the plenoptic domain subject to the epipolar constraint, is able to fuse feature point matches from all the available images, resulting in more robust recognition. We evaluated these algorithms using a number of data sets of real images capturing both indoor and outdoor scenes. We demonstrate that MOR is better than SOR particularly for noisy and low resolution images, and it is also able to recognize objects that are partially occluded by combining it with some segmentation techniques

Combining shape and color. A bottom-up approach to evaluate object similarities

The objective of the present work is to develop a bottom-up approach to estimate the similarity between two unknown objects. Given a set of digital images, we want to identify the main objects and to determine whether they are similar or not. In the last decades many object recognition and classification strategies, driven by higher-level activities, have been successfully developed. The peculiarity of this work, instead, is the attempt to work without any training phase nor a priori knowledge about the objects or their context. Indeed, if we suppose to be in an unstructured and completely unknown environment, usually we have to deal with novel objects never seen before; under these hypothesis, it would be very useful to define some kind of similarity among the instances under analysis (even if we do not know which category they belong to). To obtain this result, we start observing that human beings use a lot of information and analyze very different aspects to achieve object recognition: shape, position, color and so on. Hence we try to reproduce part of this process, combining different methodologies (each working on a specific characteristic) to obtain a more meaningful idea of similarity. Mainly inspired by the human conception of representation, we identify two main characteristics and we called them the implicit and explicit models. The term "explicit" is used to account for the main traits of what, in the human representation, connotes a principal source of information regarding a category, a sort of a visual synecdoche (corresponding to the shape); the term "implicit", on the other hand, accounts for the object rendered by shadows and lights, colors and volumetric impression, a sort of a visual metonymy (corresponding to the chromatic characteristics). During the work, we had to face several problems and we tried to define specific solutions. In particular, our contributions are about: - defining a bottom-up approach for image segmentation (which does not rely on any a priori knowledge); - combining different features to evaluate objects similarity (particularly focusiing on shape and color); - defining a generic distance (similarity) measure between objects (without any attempt to identify the possible category they belong to); - analyzing the consequences of using the number of modes as an estimation of the number of mixture’s components (in the Expectation-Maximization algorithm)