A quantum Jensen-Shannon graph kernel for unattributed graphs

In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) [27,28] to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.

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.

The role of oscillatory brain activity in object processing and figure-ground segmentation in human vision

The perception of an object as a single entity within a visual scene requires that its features are bound together and segregated from the background and/or other objects. Here, we used magnetoencephalography (MEG) to assess the hypothesis that coherent percepts may arise from the synchronized high frequency (gamma) activity between neurons that code features of the same object. We also assessed the role of low frequency (alpha, beta) activity in object processing. The target stimulus (i.e. object) was a small patch of a concentric grating of 3c/°, viewed eccentrically. The background stimulus was either a blank field or a concentric grating of 3c/° periodicity, viewed centrally. With patterned backgrounds, the target stimulus emerged--through rotation about its own centre--as a circular subsection of the background. Data were acquired using a 275-channel whole-head MEG system and analyzed using Synthetic Aperture Magnetometry (SAM), which allows one to generate images of task-related cortical oscillatory power changes within specific frequency bands. Significant oscillatory activity across a broad range of frequencies was evident at the V1/V2 border, and subsequent analyses were based on a virtual electrode at this location. When the target was presented in isolation, we observed that: (i) contralateral stimulation yielded a sustained power increase in gamma activity; and (ii) both contra- and ipsilateral stimulation yielded near identical transient power changes in alpha (and beta) activity. When the target was presented against a patterned background, we observed that: (i) contralateral stimulation yielded an increase in high-gamma (>55 Hz) power together with a decrease in low-gamma (40-55 Hz) power; and (ii) both contra- and ipsilateral stimulation yielded a transient decrease in alpha (and beta) activity, though the reduction tended to be greatest for contralateral stimulation. The opposing power changes across different regions of the gamma spectrum with 'figure/ground' stimulation suggest a possible dual role for gamma rhythms in visual object coding, and provide general support of the binding-by-synchronization hypothesis. As the power changes in alpha and beta activity were largely independent of the spatial location of the target, however, we conclude that their role in object processing may relate principally to changes in visual attention.

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.