Shape recognition and classification in electro-sensing

This paper aims at advancing the field of electro-sensing. It exhibits the physical mechanism underlying shape perception for weakly electric fish. These fish orient themselves at night in complete darkness by employing their active electrolocation system. They generate a stable, high-frequency, weak electric field and perceive the transdermal potential modulations caused by a nearby target with different admittivity than the surrounding water. In this paper, we explain how weakly electric fish might identify and classify a target, knowing by advance that the latter belongs to a certain collection of shapes. Our model of the weakly electric fish relies on differential imaging, i.e., by forming an image from the perturbations of the field due to targets, and physics-based classification. The electric fish would first locate the target using a specific location search algorithm. Then it could extract, from the perturbations of the electric field, generalized (or high-order) polarization tensors of the target. Computing, from the extracted features, invariants under rigid motions and scaling yields shape descriptors. The weakly electric fish might classify a target by comparing its invariants with those of a set of learned shapes. On the other hand, when measurements are taken at multiple frequencies, the fish might exploit the shifts and use the spectral content of the generalized polarization tensors to dramatically improve the stability with respect to measurement noise of the classification procedure in electro-sensing. Surprisingly, it turns out that the first-order polarization tensor at multiple frequencies could be enough for the purpose of classification. A procedure to eliminate the background field in the case where the permittivity of the surrounding medium can be neglected, and hence improve further the stability of the classification process, is also discussed.Comment: 10 pages, 15 figure

Visualization and analysis of diffusion tensor fields

technical reportThe power of medical imaging modalities to measure and characterize biological tissue is amplified by visualization and analysis methods that help researchers to see and understand the structures within their data. Diffusion tensor magnetic resonance imaging can measure microstructural properties of biological tissue, such as the coherent linear organization of white matter of the central nervous system, or the fibrous texture of muscle tissue. This dissertation describes new methods for visualizing and analyzing the salient structure of diffusion tensor datasets. Glyphs from superquadric surfaces and textures from reactiondiffusion systems facilitate inspection of data properties and trends. Fiber tractography based on vector-tensor multiplication allows major white matter pathways to be visualized. The generalization of direct volume rendering to tensor data allows large-scale structures to be shaded and rendered. Finally, a mathematical framework for analyzing the derivatives of tensor values, in terms of shape and orientation change, enables analytical shading in volume renderings, and a method of feature detection important for feature-preserving filtering of tensor fields. Together, the combination of methods enhances the ability of diffusion tensor imaging to provide insight into the local and global structure of biological tissue

Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores

Multimodal Three Dimensional Scene Reconstruction, The Gaussian Fields Framework

The focus of this research is on building 3D representations of real world scenes and objects using different imaging sensors. Primarily range acquisition devices (such as laser scanners and stereo systems) that allow the recovery of 3D geometry, and multi-spectral image sequences including visual and thermal IR images that provide additional scene characteristics. The crucial technical challenge that we addressed is the automatic point-sets registration task. In this context our main contribution is the development of an optimization-based method at the core of which lies a unified criterion that solves simultaneously for the dense point correspondence and transformation recovery problems. The new criterion has a straightforward expression in terms of the datasets and the alignment parameters and was used primarily for 3D rigid registration of point-sets. However it proved also useful for feature-based multimodal image alignment. We derived our method from simple Boolean matching principles by approximation and relaxation. One of the main advantages of the proposed approach, as compared to the widely used class of Iterative Closest Point (ICP) algorithms, is convexity in the neighborhood of the registration parameters and continuous differentiability, allowing for the use of standard gradient-based optimization techniques. Physically the criterion is interpreted in terms of a Gaussian Force Field exerted by one point-set on the other. Such formulation proved useful for controlling and increasing the region of convergence, and hence allowing for more autonomy in correspondence tasks. Furthermore, the criterion can be computed with linear complexity using recently developed Fast Gauss Transform numerical techniques. In addition, we also introduced a new local feature descriptor that was derived from visual saliency principles and which enhanced significantly the performance of the registration algorithm. The resulting technique was subjected to a thorough experimental analysis that highlighted its strength and showed its limitations. Our current applications are in the field of 3D modeling for inspection, surveillance, and biometrics. However, since this matching framework can be applied to any type of data, that can be represented as N-dimensional point-sets, the scope of the method is shown to reach many more pattern analysis applications

Representations for Cognitive Vision : a Review of Appearance-Based, Spatio-Temporal, and Graph-Based Approaches

The emerging discipline of cognitive vision requires a proper representation of visual information including spatial and temporal relationships, scenes, events, semantics and context. This review article summarizes existing representational schemes in computer vision which might be useful for cognitive vision, a and discusses promising future research directions. The various approaches are categorized according to appearance-based, spatio-temporal, and graph-based representations for cognitive vision. While the representation of objects has been covered extensively in computer vision research, both from a reconstruction as well as from a recognition point of view, cognitive vision will also require new ideas how to represent scenes. We introduce new concepts for scene representations and discuss how these might be efficiently implemented in future cognitive vision systems

Spatial mapping of translational diffusion coefficients using diffusion tensor imaging: A mathematical description

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain

Tomographic PIV measurement of coherent dissipation scale structures

Movie files referred to in Appendix D (p.213) not included in e-thesis.Further understanding the small scale coherent structures which occur in high Reynolds number turbulence would be of enormous benefit. Therefore, the aim of the current project was to make well resolved three-dimensional flow measurements of the mixing flow between counter rotating impellers, using Tomographic Particle Image Velocimetry (TPIV). TPIV software was developed, with a novel approach permitting a significant reduction in processing time, and a series of numerical accuracy studies contributing to the fundamental understanding of this new technique. Basic flow characterisation determined the local isotropy, homogeneity and expected Reynolds number scaling. A favourable comparison between planar PIV and TPIV increased confidence in the latter, which was used to assess the dynamics and topology of the dissipation scale structures. In support of previous investigations similar topology, strain rate alignment, scale-invariance, and clustering behaviours are demonstrated. Correlated high enstrophy and dissipation regions occur in the periphery of larger structures, resulting in intermittency. Geometry characterisation indicates a predominance of tube-like structures, which are observed to form from larger ribbon-like structures through unsteady breakdown and vortex roll-up. Significant correlation between intermittent fields of dissipation and enstrophy describe the fine scales effects. These relationships should pave the way for more accurate models, capable of relating small scales and large scales during the prediction of dynamically important quantities.The author wishes to acknowledge funding from the Engineering and Physical Sciences Research Council through Grant No. GR/S78667/01 and a Cambridge University Doctoral Training Award