Image-Based View Synthesis

We present a new method for rendering novel images of flexible 3D objects from a small number of example images in correspondence. The strength of the method is the ability to synthesize images whose viewing position is significantly far away from the viewing cone of the example images ("view extrapolation"), yet without ever modeling the 3D structure of the scene. The method relies on synthesizing a chain of "trilinear tensors" that governs the warping function from the example images to the novel image, together with a multi-dimensional interpolation function that synthesizes the non-rigid motions of the viewed object from the virtual camera position. We show that two closely spaced example images alone are sufficient in practice to synthesize a significant viewing cone, thus demonstrating the ability of representing an object by a relatively small number of model images --- for the purpose of cheap and fast viewers that can run on standard hardware.

Image Based Rendering Using Algebraic Techniques

This paper presents an image-based rendering system using algebraic relations between different views of an object. The system uses pictures of an object taken from known positions. Given three such images it can generate "virtual'' ones as the object would look from any position near the ones that the two input images were taken from. The extrapolation from the example images can be up to about 60 degrees of rotation. The system is based on the trilinear constraints that bind any three view so fan object. As a side result, we propose two new methods for camera calibration. We developed and used one of them. We implemented the system and tested it on real images of objects and faces. We also show experimentally that even when only two images taken from unknown positions are given, the system can be used to render the object from other view points as long as we have a good estimate of the internal parameters of the camera used and we are able to find good correspondence between the example images. In addition, we present the relation between these algebraic constraints and a factorization method for shape and motion estimation. As a result we propose a method for motion estimation in the special case of orthographic projection.

On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications

This paper investigates the linear degeneracies of projective structure estimation from point and line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) in the case when the scene is a Linear Line Complex (set of lines in space intersecting at a common line) and is 21 when the scene is planar. The LLC situation is only linearly degenerate, and we show that one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice.

Diffusion tensor of water in model articular cartilage

We used Monte Carlo simulations of Brownian dynamics of water to study anisotropic water diffusion in an idealised model of articular cartilage. The main aim was to use the simulations as a tool for translation of the fractional anisotropy of the water diffusion tensor in cartilage into quantitative characteristics of its collagen fibre network. The key finding was a linear empirical relationship between the collagen volume fraction and the fractional anisotropy of the diffusion tensor. Fractional anisotropy of the diffusion tensor is potentially a robust indicator of the microstructure of the tissue because, in the first approximation, it is invariant to the inclusion of proteoglycans or chemical exchange between free and collagen-bound water in the model. We discuss potential applications of Monte Carlo diffusion-tensor simulations for quantitative biophysical interpretation of MRI diffusion-tensor images of cartilage. Extension of the model to include collagen fibre disorder is also discussed.

XML documents clustering using tensor space model - A preliminary study

A hierarchical structure is used to represent the content of the semi-structured documents such as XML and XHTML. The traditional Vector Space Model (VSM) is not sufficient to represent both the structure and the content of such web documents. Hence in this paper, we introduce a novel method of representing the XML documents in Tensor Space Model (TSM) and then utilize it for clustering. Empirical analysis shows that the proposed method is scalable for a real-life dataset as well as the factorized matrices produced from the proposed method helps to improve the quality of clusters due to the enriched document representation with both the structure and the content information.

Digital processing of diffusion-tensor images of avascular tissues

Diffusion is the process that leads to the mixing of substances as a result of spontaneous and random thermal motion of individual atoms and molecules. It was first detected by the English botanist Robert Brown in 1827, and the phenomenon became known as ‘Brownian motion’. More specifically, the motion observed by Brown was translational diffusion – thermal motion resulting in random variations of the position of a molecule. This type of motion was given a correct theoretical interpretation in 1905 by Albert Einstein, who derived the relationship between temperature, the viscosity of the medium, the size of the diffusing molecule, and its diffusion coefficient. It is translational diffusion that is indirectly observed in MR diffusion-tensor imaging (DTI). The relationship obtained by Einstein provides the physical basis for using translational diffusion to probe the microscopic environment surrounding the molecule.

XML documents clustering using Tensor Space Model

The traditional Vector Space Model (VSM) is not able to represent both the structure and the content of XML documents. This paper introduces a novel method of representing XML documents in a Tensor Space Model (TSM) and then utilizing it for clustering. Empirical analysis shows that the proposed method is scalable for large-sized datasets; as well, the factorized matrices produced from the proposed method help to improve the quality of clusters through the enriched document representation of both structure and content information.

Modelling word meaning using efficient tensor representations

Models of word meaning, built from a corpus of text, have demonstrated success in emulating human performance on a number of cognitive tasks. Many of these models use geometric representations of words to store semantic associations between words. Often word order information is not captured in these models. The lack of structural information used by these models has been raised as a weakness when performing cognitive tasks. This paper presents an efficient tensor based approach to modelling word meaning that builds on recent attempts to encode word order information, while providing flexible methods for extracting task specific semantic information.

Tensor query expansion : a cognitively motivated relevance model

In information retrieval, a user's query is often not a complete representation of their real information need. The user's information need is a cognitive construction, however the use of cognitive models to perform query expansion have had little study. In this paper, we present a cognitively motivated query expansion technique that uses semantic features for use in ad hoc retrieval. This model is evaluated against a state-of-the-art query expansion technique. The results show our approach provides significant improvements in retrieval effectiveness for the TREC data sets tested.

Clustering of web users using the tensor decomposed models

We propose to use the Tensor Space Modeling (TSM) to represent and analyze the user’s web log data that consists of multiple interests and spans across multiple dimensions. Further we propose to use the decomposition factors of the Tensors for clustering the users based on similarity of search behaviour. Preliminary results show that the proposed method outperforms the traditional Vector Space Model (VSM) based clustering.

A people-to-people recommendation system using Tensor Space Models

Existing recommendation systems often recommend products to users by capturing the item-to-item and user-to-user similarity measures. These types of recommendation systems become inefficient in people-to-people networks for people to people recommendation that require two way relationship. Also, existing recommendation methods use traditional two dimensional models to find inter relationships between alike users and items. It is not efficient enough to model the people-to-people network with two-dimensional models as the latent correlations between the people and their attributes are not utilized. In this paper, we propose a novel tensor decomposition-based recommendation method for recommending people-to-people based on users profiles and their interactions. The people-to-people network data is multi-dimensional data which when modeled using vector based methods tend to result in information loss as they capture either the interactions or the attributes of the users but not both the information. This paper utilizes tensor models that have the ability to correlate and find latent relationships between similar users based on both information, user interactions and user attributes, in order to generate recommendations. Empirical analysis is conducted on a real-life online dating dataset. As demonstrated in results, the use of tensor modeling and decomposition has enabled the identification of latent correlations between people based on their attributes and interactions in the network and quality recommendations have been derived using the 'alike' users concept.

A tensor encoding model for semantic processing

This paper develops and evaluates an enhanced corpus based approach for semantic processing. Corpus based models that build representations of words directly from text do not require pre-existing linguistic knowledge, and have demonstrated psychologically relevant performance on a number of cognitive tasks. However, they have been criticised in the past for not incorporating sufficient structural information. Using ideas underpinning recent attempts to overcome this weakness, we develop an enhanced tensor encoding model to build representations of word meaning for semantic processing. Our enhanced model demonstrates superior performance when compared to a robust baseline model on a number of semantic processing tasks.

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0◦ to 90◦. The corresponding diffusion ellipsoids are prolate for θ < θMA, spherical for θ ≈ θMA, and oblate for θ > θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.