Hausdorff-Distance Enhanced Matching of Scale Invariant Feature Transform Descriptors in Context of Image Querying

Reliable and effective matching of visual descriptors is a key step for many vision applications, e.g. image retrieval. In this paper, we propose to integrate the Hausdorff distance matching together with our pairing algorithm, in order to obtain a robust while computationally efficient process of matching feature descriptors for image-to-image querying in standards datasets. For this purpose, Scale Invariant Feature Transform (SIFT) descriptors have been matched using our presented algorithm, followed by the computation of our related similarity measure. This approach has shown excellent performance in both retrieval accuracy and speed

Human face recognition using a spatially weighted Hausdorff distance

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Gromov-Monge quasi-metrics and distance distributions

Applications in data science, shape analysis and object classification frequently require maps between metric spaces which preserve geometry as faithfully as possible. In this paper, we combine the Monge formulation of optimal transport with the Gromov-Hausdorff distance construction to define a measure of the minimum amount of geometric distortion required to map one metric measure space onto another. We show that the resulting quantity, called Gromov-Monge distance, defines an extended quasi-metric on the space of isomorphism classes of metric measure spaces and that it can be promoted to a true metric on certain subclasses of mm-spaces. We also give precise comparisons between Gromov-Monge distance and several other metrics which have appeared previously, such as the Gromov-Wasserstein metric and the continuous Procrustes metric of Lipman, Al-Aifari and Daubechies. Finally, we derive polynomial-time computable lower bounds for Gromov-Monge distance. These lower bounds are expressed in terms of distance distributions, which are classical invariants of metric measure spaces summarizing the volume growth of metric balls. In the second half of the paper, which may be of independent interest, we study the discriminative power of these lower bounds for simple subclasses of metric measure spaces. We first consider the case of planar curves, where we give a counterexample to the Curve Histogram Conjecture of Brinkman and Olver. Our results on plane curves are then generalized to higher dimensional manifolds, where we prove some sphere characterization theorems for the distance distribution invariant. Finally, we consider several inverse problems on recovering a metric graph from a collection of localized versions of distance distributions. Results are derived by establishing connections with concepts from the fields of computational geometry and topological data analysis.Comment: Version 2: Added many new results and improved expositio

Learning Inductive Biases with Simple Neural Networks

People use rich prior knowledge about the world in order to efficiently learn new concepts. These priors - also known as "inductive biases" - pertain to the space of internal models considered by a learner, and they help the learner make inferences that go beyond the observed data. A recent study found that deep neural networks optimized for object recognition develop the shape bias (Ritter et al., 2017), an inductive bias possessed by children that plays an important role in early word learning. However, these networks use unrealistically large quantities of training data, and the conditions required for these biases to develop are not well understood. Moreover, it is unclear how the learning dynamics of these networks relate to developmental processes in childhood. We investigate the development and influence of the shape bias in neural networks using controlled datasets of abstract patterns and synthetic images, allowing us to systematically vary the quantity and form of the experience provided to the learning algorithms. We find that simple neural networks develop a shape bias after seeing as few as 3 examples of 4 object categories. The development of these biases predicts the onset of vocabulary acceleration in our networks, consistent with the developmental process in children.Comment: Published in Proceedings of the 40th Annual Meeting of the Cognitive Science Society, July 201

Multi-scale active shape description in medical imaging

Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed

Joint Image Reconstruction and Segmentation Using the Potts Model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data

Dynamic motion coupling of body movement for input control

Touchless gestures are used for input when touch is unsuitable or unavailable, such as when interacting with displays that are remote, large, public, or when touch is prohibited for hygienic reasons. Traditionally user input is spatially or semantically mapped to system output, however, in the context of touchless gestures these interaction principles suffer from several disadvantages including memorability, fatigue, and ill-defined mappings. This thesis investigates motion correlation as the third interaction principle for touchless gestures, which maps user input to system output based on spatiotemporal matching of reproducible motion. We demonstrate the versatility of motion correlation by using movement as the primary sensing principle, relaxing the restrictions on how a user provides input. Using TraceMatch, a novel computer vision-based system, we show how users can provide effective input through investigation of input performance with different parts of the body, and how users can switch modes of input spontaneously in realistic application scenarios. Secondly, spontaneous spatial coupling shows how motion correlation can bootstrap spatial input, allowing any body movement, or movement of tangible objects, to be appropriated for ad hoc touchless pointing on a per interaction basis. We operationalise the concept in MatchPoint, and demonstrate the unique capabilities through an exploration of the design space with application examples. Finally, we explore how users synchronise with moving targets in the context of motion correlation, revealing how simple harmonic motion leads to better synchronisation. Using the insights gained we explore the robustness of algorithms used for motion correlation, showing how it is possible to successfully detect a user's intent to interact whilst suppressing accidental activations from common spatial and semantic gestures. Finally, we look across our work to distil guidelines for interface design, and further considerations of how motion correlation can be used, both in general and for touchless gestures