On the Geometry of Visual Correspondence

(Also cross-refernced as CAR-TR-732) Image displacement fieldsoptical flow fields, stereo disparity fields, normal flow fieldsdue to rigid motion possess a global geometric structure which is independent of the scene in view. Motion vectors of certain lengths and directions are constraine d to lie on the imaging surface at particular loci whose location and form depends solely on the 3D motion parameters. If optical flow fields or stereo disparity fields are considered, then equal vectors are shown to lie on conic sections. Similarly, for normal motion fields, equal vectors lie within regions whose boundaries also constitute conics. By studying various properties of these curves and regions and their relationships, a characterization of the structure of rigid motion fields is given. The go al of this paper is to introduce a concept underlying the global structure of image displacement fields. This concept gives rise to various constraints that could form the basis of algorithms for the recovery of visual information from multiple views

3D Video Object Detection with Learnable Object-Centric Global Optimization

We explore long-term temporal visual correspondence-based optimization for 3D video object detection in this work. Visual correspondence refers to one-to-one mappings for pixels across multiple images. Correspondence-based optimization is the cornerstone for 3D scene reconstruction but is less studied in 3D video object detection, because moving objects violate multi-view geometry constraints and are treated as outliers during scene reconstruction. We address this issue by treating objects as first-class citizens during correspondence-based optimization. In this work, we propose BA-Det, an end-to-end optimizable object detector with object-centric temporal correspondence learning and featuremetric object bundle adjustment. Empirically, we verify the effectiveness and efficiency of BA-Det for multiple baseline 3D detectors under various setups. Our BA-Det achieves SOTA performance on the large-scale Waymo Open Dataset (WOD) with only marginal computation cost. Our code is available at https://github.com/jiaweihe1996/BA-Det.Comment: CVPR202

Visualisation, navigation and mathematical perception: a visual notation for rational numbers mod1

There are three main results in this dissertation. The first result is the construction of an abstract visual space for rational numbers mod1, based on the visual primitives, colour, and rational radial direction. Mathematics is performed in this visual notation by defining increasingly refined visual objects from these primitives. In particular, the existence of the Farey tree enumeration of rational numbers mod1 is identified in the texture of a two-dimensional animation. ¶ The second result is a new enumeration of the rational numbers mod1, obtained, and expressed, in abstract visual space, as the visual object coset waves of coset fans on the torus. Its geometry is shown to encode a countably infinite tree structure, whose branches are cosets, nZ+m, where n, m (and k) are integers. These cosets are in geometrical 1-1 correspondence with sequences kn+m, (of denominators) of rational numbers, and with visual subobjects of the torus called coset fans. ¶ The third result is an enumeration in time of the visual hierarchy of the discrete buds of the Mandelbrot boundary by coset waves of coset fans. It is constructed by embedding the circular Farey tree geometrically into the empty internal region of the Mandelbrot set. In particular, coset fans attached to points of the (internal) binary tree index countably infinite sequences of buds on the (external) Mandelbrot boundary

UGC 3995: A Close Pair of Spiral Galaxies

UGC 3995 is a close pair of spiral galaxies whose eastern component hosts a Seyfert 2 nucleus. We present a detailed analysis of this system using long slit spectroscopy and narrow (\ha + \nii) as well as broad band (B, R) imaging and an archive WFPC2 image. The component galaxies reveal surprisingly small signs of interaction considering their spatial proximity and almost identical recession velocities, as the bright filament is probably an optical illusion due to the superposition of the bar of the Seyfert galaxy and of the spiral arms of the companion. The broad band morphology, a B--R color map, and a continuum-subtracted \ha + \nii image demonstrate that the western component UGC 3995B is in front of the Seyfert-hosting component UGC 3995A, partly obscuring its western side. The small radial velocity difference leaves the relative motion of the two galaxies largely unconstrained. The observed lack of major tidal deformations, along with some morphological peculiarities, suggests that the galaxies are proximate in space but may have recently approached each other on the plane of the sky. The geometry of the system and the radial velocity curve at P. A. = 106 suggest that the encounter may be retrograde or, alternatively, prograde before perigalacticon. The partial overlap of the two galaxies allows us to estimate the optical thickness of the disk of component B. We derive an extinction = 0.18 visual magnitudes in the infra-arms parts of the foreground galaxy disk, and >= 1-1.5 visual magnitudes in correspondence of the spiral arms.Comment: Accepted for publication in the Astronomical Journal (June 1999 issue

Heritability maps of human face morphology through large-scale automated three-dimensional phenotyping

The human face is a complex trait under strong genetic control, as evidenced by the striking visual similarity between twins. Nevertheless, heritability estimates of facial traits have often been surprisingly low or difficult to replicate. Furthermore, the construction of facial phenotypes that correspond to naturally perceived facial features remains largely a mystery. We present here a large-scale heritability study of face geometry that aims to address these issues. High-resolution, three-dimensional facial models have been acquired on a cohort of 952 twins recruited from the TwinsUK registry, and processed through a novel landmarking workflow, GESSA (Geodesic Ensemble Surface Sampling Algorithm). The algorithm places thousands of landmarks throughout the facial surface and automatically establishes point-wise correspondence across faces. These landmarks enabled us to intuitively characterize facial geometry at a fine level of detail through curvature measurements, yielding accurate heritability maps of the human face (www.heritabilitymaps.info)

Image-based 3-D reconstruction of constrained environments

Nuclear power plays a important role to the United Kingdom electricity generation infrastructure, providing a reliable baseload of low carbon electricity. The Advanced Gas-cooled Reactor (AGR) design makes up approximately 50% of the existing fleet, however, many of the operating reactors have exceeding their original design lifetimes.To ensure safe reactor operation, engineers perform periodic in-core visual inspections of reactor components to monitor the structural health of the core as it ages. However, current inspection mechanisms deployed provide limited structural information about the fuel channel or defects.;This thesis investigates the suitability of image-based 3-D reconstruction techniques to acquire 3-D structural geometry to enable improved diagnostic and prognostic abilities for inspection engineers. The application of image-based 3-D reconstruction to in-core inspection footage highlights significant challenges, most predominantly that the image saliency proves insuffcient for general reconstruction frameworks. The contribution of the thesis is threefold. Firstly, a novel semi-dense matching scheme which exploits sparse and dense image correspondence in combination with a novel intra-image region strength approach to improve the stability of the correspondence between images.;This results in a percentage increase of 138.53% of correct feature matches over similar state-of-the-art image matching paradigms. Secondly, a bespoke incremental Structure-from-Motion (SfM) framework called the Constrained Homogeneous SfM (CH-SfM) which is able to derive structure from deficient feature spaces and constrained environments. Thirdly, the application of the CH-SfM framework to remote visual inspection footage gathered within AGR fuel channels, outperforming other state-of-the-art reconstruction approaches and extracting representative 3-D structural geometry of orientational scans and fully circumferential reconstructions.;This is demonstrated on in-core and laboratory footage, achieving an approximate 3-D point density of 2.785 - 23.8025NX/cm² for real in-core inspection footage and high quality laboratory footage respectively. The demonstrated novelties have applicability to other constrained or feature-poor environments, with future work looking to producing fully dense, photo-realistic 3-D reconstructions.Nuclear power plays a important role to the United Kingdom electricity generation infrastructure, providing a reliable baseload of low carbon electricity. The Advanced Gas-cooled Reactor (AGR) design makes up approximately 50% of the existing fleet, however, many of the operating reactors have exceeding their original design lifetimes.To ensure safe reactor operation, engineers perform periodic in-core visual inspections of reactor components to monitor the structural health of the core as it ages. However, current inspection mechanisms deployed provide limited structural information about the fuel channel or defects.;This thesis investigates the suitability of image-based 3-D reconstruction techniques to acquire 3-D structural geometry to enable improved diagnostic and prognostic abilities for inspection engineers. The application of image-based 3-D reconstruction to in-core inspection footage highlights significant challenges, most predominantly that the image saliency proves insuffcient for general reconstruction frameworks. The contribution of the thesis is threefold. Firstly, a novel semi-dense matching scheme which exploits sparse and dense image correspondence in combination with a novel intra-image region strength approach to improve the stability of the correspondence between images.;This results in a percentage increase of 138.53% of correct feature matches over similar state-of-the-art image matching paradigms. Secondly, a bespoke incremental Structure-from-Motion (SfM) framework called the Constrained Homogeneous SfM (CH-SfM) which is able to derive structure from deficient feature spaces and constrained environments. Thirdly, the application of the CH-SfM framework to remote visual inspection footage gathered within AGR fuel channels, outperforming other state-of-the-art reconstruction approaches and extracting representative 3-D structural geometry of orientational scans and fully circumferential reconstructions.;This is demonstrated on in-core and laboratory footage, achieving an approximate 3-D point density of 2.785 - 23.8025NX/cm² for real in-core inspection footage and high quality laboratory footage respectively. The demonstrated novelties have applicability to other constrained or feature-poor environments, with future work looking to producing fully dense, photo-realistic 3-D reconstructions

Towards large-scale geometry indexing by feature selection

We present a new approach to image indexing and retrieval, which integrates appearance with global image geometry in the indexing process, while enjoying robustness against viewpoint change, photometric variations, occlusion, and background clutter. We exploit shape parameters of local features to estimate image alignment via a single correspondence. Then, for each feature, we construct a sparse spatial map of all remaining features, encoding their normalized position and appearance, typically vector quantized to visual word. An image is represented by a collection of such feature maps and RANSAC-like matching is reduced to a number of set intersections. The required index space is still quadratic in the number of features. To make it linear, we propose a novel feature selection model tailored to our feature map representation, replacing our earlier hashing approach. The resulting index space is comparable to baseline bag-of-words, scaling up to one million images while outperforming the state of the art on three publicly available datasets. To our knowledge, this is the first geometry indexing method to dispense with spatial verification at this scale, bringing query times down to milliseconds

Key characteristics of specular stereo.

Because specular reflection is view-dependent, shiny surfaces behave radically differently from matte, textured surfaces when viewed with two eyes. As a result, specular reflections pose substantial problems for binocular stereopsis. Here we use a combination of computer graphics and geometrical analysis to characterize the key respects in which specular stereo differs from standard stereo, to identify how and why the human visual system fails to reconstruct depths correctly from specular reflections. We describe rendering of stereoscopic images of specular surfaces in which the disparity information can be varied parametrically and independently of monocular appearance. Using the generated surfaces and images, we explain how stereo correspondence can be established with known and unknown surface geometry. We show that even with known geometry, stereo matching for specular surfaces is nontrivial because points in one eye may have zero, one, or multiple matches in the other eye. Matching features typically yield skew (nonintersecting) rays, leading to substantial ortho-epipolar components to the disparities, which makes deriving depth values from matches nontrivial. We suggest that the human visual system may base its depth estimates solely on the epipolar components of disparities while treating the ortho-epipolar components as a measure of the underlying reliability of the disparity signals. Reconstructing virtual surfaces according to these principles reveals that they are piece-wise smooth with very large discontinuities close to inflection points on the physical surface. Together, these distinctive characteristics lead to cues that the visual system could use to diagnose specular reflections from binocular information.The work was funded by the Wellcome Trust (grants 08459/Z/07/Z & 095183/Z/10/Z) and the EU Marie Curie Initial Training Network “PRISM” (FP7-PEOPLE-2012-ITN, Agreement: 316746).This is the author accepted manuscript. The final version is available from ARVO via http://dx.doi.org/10.1167/14.14.1