Supervised learning of graph structure

Graph-based representations have been used with considerable success in computer vision in the abstraction and recognition of object shape and scene structure. Despite this, the methodology available for learning structural representations from sets of training examples is relatively limited. In this paper we take a simple yet effective Bayesian approach to attributed graph learning. We present a naïve node-observation model, where we make the important assumption that the observation of each node and each edge is independent of the others, then we propose an EM-like approach to learn a mixture of these models and a Minimum Message Length criterion for components selection. Moreover, in order to avoid the bias that could arise with a single estimation of the node correspondences, we decide to estimate the sampling probability over all the possible matches. Finally we show the utility of the proposed approach on popular computer vision tasks such as 2D and 3D shape recognition. © 2011 Springer-Verlag.

Large-scale data for multiple-view stereopsis

The seminal multiple-view stereo benchmark evaluations from Middlebury and by Strecha et al. have played a major role in propelling the development of multi-view stereopsis (MVS) methodology. The somewhat small size and variability of these data sets, however, limit their scope and the conclusions that can be derived from them. To facilitate further development within MVS, we here present a new and varied data set consisting of 80 scenes, seen from 49 or 64 accurate camera positions. This is accompanied by accurate structured light scans for reference and evaluation. In addition all images are taken under seven different lighting conditions. As a benchmark and to validate the use of our data set for obtaining reasonable and statistically significant findings about MVS, we have applied the three state-of-the-art MVS algorithms by Campbell et al., Furukawa et al., and Tola et al. to the data set. To do this we have extended the evaluation protocol from the Middlebury evaluation, necessitated by the more complex geometry of some of our scenes. The data set and accompanying evaluation framework are made freely available online. Based on this evaluation, we are able to observe several characteristics of state-of-the-art MVS, e.g. that there is a tradeoff between the quality of the reconstructed 3D points (accuracy) and how much of an object’s surface is captured (completeness). Also, several issues that we hypothesized would challenge MVS, such as specularities and changing lighting conditions did not pose serious problems. Our study finds that the two most pressing issues for MVS are lack of texture and meshing (forming 3D points into closed triangulated surfaces).

Shape from photographs:a multi-view stereo pipeline

Acquiring 3D shape from images is a classic problem in Computer Vision occupying researchers for at least 20 years. Only recently however have these ideas matured enough to provide highly accurate results. We present a complete algorithm to reconstruct 3D objects from images using the stereo correspondence cue. The technique can be described as a pipeline of four basic building blocks: camera calibration, image segmentation, photo-consistency estimation from images, and surface extraction from photo-consistency. In this Chapter we will put more emphasis on the latter two: namely how to extract geometric information from a set of photographs without explicit camera visibility, and how to combine different geometry estimates in an optimal way. © 2010 Springer-Verlag Berlin Heidelberg.

Practical 3D reconstruction based on photometric stereo

Photometric Stereo is a powerful image based 3D reconstruction technique that has recently been used to obtain very high quality reconstructions. However, in its classic form, Photometric Stereo suffers from two main limitations: Firstly, one needs to obtain images of the 3D scene under multiple different illuminations. As a result the 3D scene needs to remain static during illumination changes, which prohibits the reconstruction of deforming objects. Secondly, the images obtained must be from a single viewpoint. This leads to depth-map based 2.5 reconstructions, instead of full 3D surfaces. The aim of this Chapter is to show how these limitations can be alleviated, leading to the derivation of two practical 3D acquisition systems: The first one, based on the powerful Coloured Light Photometric Stereo method can be used to reconstruct moving objects such as cloth or human faces. The second, permits the complete 3D reconstruction of challenging objects such as porcelain vases. In addition to algorithmic details, the Chapter pays attention to practical issues such as setup calibration, detection and correction of self and cast shadows. We provide several evaluation experiments as well as reconstruction results. © 2010 Springer-Verlag Berlin Heidelberg.

Edge centrality via the Holevo quantity

In the study of complex networks, vertex centrality measures are used to identify the most important vertices within a graph. A related problem is that of measuring the centrality of an edge. In this paper, we propose a novel edge centrality index rooted in quantum information. More specifically, we measure the importance of an edge in terms of the contribution that it gives to the Von Neumann entropy of the graph. We show that this can be computed in terms of the Holevo quantity, a well known quantum information theoretical measure. While computing the Von Neumann entropy and hence the Holevo quantity requires computing the spectrum of the graph Laplacian, we show how to obtain a simplified measure through a quadratic approximation of the Shannon entropy. This in turns shows that the proposed centrality measure is strongly correlated with the negative degree centrality on the line graph. We evaluate our centrality measure through an extensive set of experiments on real-world as well as synthetic networks, and we compare it against commonly used alternative measures.

The average mixing matrix signature

Laplacian-based descriptors, such as the Heat Kernel Signature and the Wave Kernel Signature, allow one to embed the vertices of a graph onto a vectorial space, and have been successfully used to find the optimal matching between a pair of input graphs. While the HKS uses a heat di↵usion process to probe the local structure of a graph, the WKS attempts to do the same through wave propagation. In this paper, we propose an alternative structural descriptor that is based on continuoustime quantum walks. More specifically, we characterise the structure of a graph using its average mixing matrix. The average mixing matrix is a doubly-stochastic matrix that encodes the time-averaged behaviour of a continuous-time quantum walk on the graph. We propose to use the rows of the average mixing matrix for increasing stopping times to develop a novel signature, the Average Mixing Matrix Signature (AMMS). We perform an extensive range of experiments and we show that the proposed signature is robust under structural perturbations of the original graphs and it outperforms both the HKS and WKS when used as a node descriptor in a graph matching task.

Effect of uncorrected astigmatism on vision

PURPOSE: To examine the effect of uncorrected astigmatism in older adults. SETTING: University Vision Clinic METHOD: Twenty-one healthy presbyopes, aged 58.9±2.8 years, had astigmatism of 0.0 to -4.0 x 90?DC and -3.0DC of cylinder at 90?, 180? and 45? induced with spectacle lenses, with the mean spherical equivalent compensated to plano, in random order. Visual acuity was assessed binocularly using a computerised test chart at 95%, 50% and 10% contrast. Near acuity and reading speed were measured using standardised reading texts. Light scatter was quantified with the cQuant and driving reaction times with a computer simulator. Finally visual clarity of a mobile phone and computer screen was subjectively rated. RESULTS: Distance visual acuity decreased with increasing uncorrected astigmatic power (F=174.50, p<0.001) and was reduced at lower contrasts (F=170.77, p<0.001). Near visual acuity and reading speed also decreased with increasing uncorrected astigmatism power (p<0.001). Light scatter was not significantly affected by uncorrected astigmatism (p>0.05), but the reliability and variability of measurements decreased with increasing uncorrected astigmatic power (p<0.05). Driving simulator performance was also unaffected by uncorrected astigmatism (p>0.05), but subjective rating of clarity decreased with increasing uncorrected astigmatic power (p<0.001). Uncorrected astigmatism at 45? or 180? orientation resulted in a worse distance and near visual acuity, and subjective rated clarity than 90? orientation (p<0.05). CONCLUSION: Uncorrected astigmatism, even as low as 1.0DC, causes a significant burden on a patient’s vision. If left uncorrected, this could impact significantly on their independence, quality of life and wellbeing.

Edge coding in human vision: a psychophysical and computational investigation

This thesis presents a study of how edges are detected and encoded by the human visual system. The study begins with theoretical work on the development of a model of edge processing, and includes psychophysical experiments on humans, and computer simulations of these experiments, using the model. The first chapter reviews the literature on edge processing in biological and machine vision, and introduces the mathematical foundations of this area of research. The second chapter gives a formal presentation of a model of edge perception that detects edges and characterizes their blur, contrast and orientation, using Gaussian derivative templates. This model has previously been shown to accurately predict human performance in blur matching tasks with several different types of edge profile. The model provides veridical estimates of the blur and contrast of edges that have a Gaussian integral profile. Since blur and contrast are independent parameters of Gaussian edges, the model predicts that varying one parameter should not affect perception of the other. Psychophysical experiments showed that this prediction is incorrect: reducing the contrast makes an edge look sharper; increasing the blur reduces the perceived contrast. Both of these effects can be explained by introducing a smoothed threshold to one of the processing stages of the model. It is shown that, with this modification,the model can predict the perceived contrast and blur of a number of edge profiles that differ markedly from the ideal Gaussian edge profiles on which the templates are based. With only a few exceptions, the results from all the experiments on blur and contrast perception can be explained reasonably well using one set of parameters for each subject. In the few cases where the model fails, possible extensions to the model are discussed.

The vision strategy of golf putting

Golfers, coaches and researchers alike, have all keyed in on golf putting as an important aspect of overall golf performance. Of the three principle putting tasks (green reading, alignment and the putting action phase), the putting action phase has attracted the most attention from coaches, players and researchers alike. This phase includes the alignment of the club with the ball, the swing, and ball contact. A significant amount of research in this area has focused on measuring golfer’s vision strategies with eye tracking equipment. Unfortunately this research suffers from a number of shortcomings, which limit its usefulness. The purpose of this thesis was to address some of these shortcomings. The primary objective of this thesis was to re-evaluate golfer’s putting vision strategies using binocular eye tracking equipment and to define a new, optimal putting vision strategy which was associated with both higher skill and success. In order to facilitate this research, bespoke computer software was developed and validated, and new gaze behaviour criteria were defined. Additionally, the effects of training (habitual) and competition conditions on the putting vision strategy were examined, as was the effect of ocular dominance. Finally, methods for improving golfer’s binocular vision strategies are discussed, and a clinical plan for the optometric management of the golfer’s vision is presented. The clinical management plan includes the correction of fundamental aspects of golfers’ vision, including monocular refractive errors and binocular vision defects, as well as enhancement of their putting vision strategy, with the overall aim of improving performance on the golf course. This research has been undertaken in order to gain a better understanding of the human visual system and how it relates to the sport performance of golfers specifically. Ultimately, the analysis techniques and methods developed are applicable to the assessment of visual performance in all sports.