Mark W. Jones

3D distance fields: a survey of techniques and applications

A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the distance field is signed, we may also determine if the point is internal or external to objects within the domain. The distance field has been found to be a useful construction within the areas of computer vision, physics, and computer graphics. This paper serves as an exposition of methods for the production of distance fields, and a review of alternative representations and applications of distance fields. In the course of this paper, we present various methods from all three of the above areas, and we answer pertinent questions such as How accurate are these methods compared to each other? How simple are they to implement?, and What is the complexity and runtime of such methods?.

A New Approach to the Construction of Surfaces from Contour Data

This paper presents a new approach to the construction of a surface from a stack of contour slices. Unlike most existing methods, this new approach handles ambiguous conditions consistently without employing an algorithm to establish a correspondence between vertices on one contour and those on the next. It is easy to implement and fast to compute, requiring only basic geometric properties, namely closedness and simplicity, to be available with contour data. The advantages of this new approach have also been demonstrated with solutions to a few classical problems from the literature and some practical problems in medical imaging. It can also be applied to geographical surveying and keyframe animations.

The Production of Volume Data from Triangular Meshes Using Voxelisation

Voxelisation is the term given to the process of converting data from one source type into a three dimensional volume of data values. The techniques known collectively as volume visualisation can then be applied to the data in order to produce a graphical representation of the object. This paper gives a practical approach to the voxelisation of data in the form of triangular meshes, and demonstrates the use of the method on various datasets. Visualisation is achieved by a method also described in the paper.

Vector-City Vector Distance Transform

This paper will examine the current chamfer and vector distance transforms for encoding objects as distance fields. A new vector distance transform is introduced which uses the city-block chamfer distance transform as a basis. Detailed error analysis using real CT data is presented, demonstrating the improved accuracy of the new approach over existing methods. The production of a subvoxel accurate distance field is also demonstrated by employing an improved classification. Distance fields are shown for skull and chess piece datasets.

MatchPad : Interactive Glyph-Based Visualization for Real-Time Sports Performance Analysis

Today real‐time sports performance analysis is a crucial aspect of matches in many major sports. For example, in soccer and rugby, team analysts may annotate videos during the matches by tagging specific actions and events, which typically result in some summary statistics and a large spreadsheet of recorded actions and events. To a coach, the summary statistics (e.g., the percentage of ball possession) lacks sufficient details, while reading the spreadsheet is time‐consuming and making decisions based on the spreadsheet in real‐time is thereby impossible. In this paper, we present a visualization solution to the current problem in real‐time sports performance analysis. We adopt a glyph‐based visual design to enable coaching staff and analysts to visualize actions and events “at a glance”. We discuss the relative merits of metaphoric glyphs in comparison with other types of glyph designs in this particular application. We describe an algorithm for managing the glyph layout at different spatial scales in interactive visualization. We demonstrate the use of this technical approach through its application in rugby, for which we delivered the visualization software, MatchPad, on a tablet computer. The MatchPad was used by the Welsh Rugby Union during the Rugby World Cup 2011. It successfully helped coaching staff and team analysts to examine actions and events in detail whilst maintaining a clear overview of the match, and assisted in their decision making during the matches. It also allows coaches to convey crucial information back to the players in a visually‐engaging manner to help improve their performance.

Visualisation of sensor data from animal movement

A new area of biological research is identifying and grouping patterns of behaviour in wild animals by analysing data obtained through the attachment of tri‐axial accelerometers. As these recording devices become smaller and less expensive their use has increased. Currently acceleration data are visualised as 2D time series plots, and analyses are based on summary statistics and the application of Fourier transforms. We develop alternate visualisations of this data so as to analyse, explore and present new patterns of animal behaviour. Our visualisations include interactive spherical scatterplots, spherical histograms, clustering methods, and feature‐based state diagrams of the data. We study the application of these visualisation methods to accelerometry data from animal movement. The reaction of biologists to these visualisations is also reported.

Similarity Measures for Enhancing Interactive Streamline Seeding

Streamline seeding rakes are widely used in vector field visualization. We present new approaches for calculating similarity between integral curves (streamlines and pathlines). While others have used similarity distance measures, the computational expense involved with existing techniques is relatively high due to the vast number of euclidean distance tests, restricting interactivity and their use for streamline seeding rakes. We introduce the novel idea of computing streamline signatures based on a set of curve-based attributes. A signature produces a compact representation for describing a streamline. Similarity comparisons are performed by using a popular statistical measure on the derived signatures. We demonstrate that this novel scheme, including a hierarchical variant, produces good clustering results and is computed over two orders of magnitude faster than previous methods. Similarity-based clustering enables filtering of the streamlines to provide a nonuniform seeding distribution along the seeding object. We show that this method preserves the overall flow behavior while using only a small subset of the original streamline set. We apply focus + context rendering using the clusters which allows for faster and easier analysis in cases of high visual complexity and occlusion. The method provides a high level of interactivity and allows the user to easily fine tune the clustering results at runtime while avoiding any time-consuming recomputation. Our method maintains interactive rates even when hundreds of streamlines are used.

Smooth Graphs for Visual Exploration of Higher-Order State Transitions

In this paper, we present a new visual way of exploring state sequences in large observational time-series. A key advantage of our method is that it can directly visualize higher-order state transitions. A standard first order state transition is a sequence of two states that are linked by a transition. A higher-order state transition is a sequence of three or more states where the sequence of participating states are linked together by consecutive first order state transitions. Our method extends the current state-graph exploration methods by employing a two dimensional graph, in which higher-order state transitions are visualized as curved lines. All transitions are bundled into thick splines, so that the thickness of an edge represents the frequency of instances. The bundling between two states takes into account the state transitions before and after the transition. This is done in such a way that it forms a continuous representation in which any subsequence of the timeseries is represented by a continuous smooth line. The edge bundles in these graphs can be explored interactively through our incremental selection algorithm. We demonstrate our method with an application in exploring labeled time-series data from a biological survey, where a clustering has assigned a single label to the data at each time-point. In these sequences, a large number of cyclic patterns occur, which in turn are linked to specific activities. We demonstrate how our method helps to find these cycles, and how the interactive selection process helps to find and investigate activities.

Into the Blue: Better Caustics through Photon Relaxation

The photon mapping method is one of the most popular algorithms employed in computer graphics today. However, obtaining good results is dependent on several variables including kernel shape and bandwidth, as well as the properties of the initial photon distribution. While the photon density estimation problem has been the target of extensive research, most algorithms focus on new methods of optimising the kernel to minimise noise and bias. In this paper we break from convention and propose a new approach that directly redistributes the underlying photons. We show that by relaxing the initial distribution into one with a blue noise spectral signature we can dramatically reduce background noise, particularly in areas of uniform illumination. In addition, we propose an efficient heuristic to detect and preserve features and discontinuities. We then go on to demonstrate how reconfiguration also permits the use of very low bandwidth kernels, greatly improving render times whilst reducing bias.

Shape representation using space filled sub-voxel distance fields

Voxelisation is the process of converting a source object of any data type into a three-dimensional grid of voxel values. This voxel grid should represent the original object as closely as possible, although some inaccuracies will occur due to the discrete nature of the voxel grid representation. In this paper we report our ongoing research into methods for representing objects as voxelised distance fields, in particular we report fast methods for accurate distance field production. A review of current alternative voxelisation methods is also given.