Informational Aesthetics Measures

The Birkhoff aesthetic measure of an object is the ratio between order and complexity. Informational aesthetics describes the interpretation of this measure from an information-theoretic perspective. From these ideas, the authors define a set of ratios based on information theory and Kolmogorov complexity that can help to quantify the aesthetic experience

Random walk radiosity with generalized absorption probabilities

The author studies random walk estimators for radiosity with generalized absorption probabilities. That is, a path will either die or survive on a patch according to an arbitrary probability. The estimators studied so far, the infinite path length estimator and finite path length one, can be considered as particular cases. Practical applications of the random walks with generalized probabilities are given. A necessary and sufficient condition for the existence of the variance is given, together with heuristics to be used in practical cases. The optimal probabilities are also found for the case when one is interested in the whole scene, and are equal to the reflectivities

Error and complexity of random walk Monte Carlo radiosity

The author studies the error and complexity of the discrete random walk Monte Carlo technique for radiosity, using both the shooting and gathering methods. The author shows that the shooting method exhibits a lower complexity than the gathering one, and under some constraints, it has a linear complexity. This is an improvement over a previous result that pointed to an O(n log n) complexity. The author gives and compares three unbiased estimators for each method, and obtains closed forms and bounds for their variances. The author also bounds the expected value of the mean square error (MSE). Some of the results obtained are also shown

Reuse of paths in light source animation

In this paper we extend the reuse of paths to the shot from a moving light source. In the classical algorithm new paths have to be cast from each new position of a light source. We show that we can reuse all paths for all positions, obtaining in this way a theoretical maximum speed-up equal to the average length of the shooting path

New medical registration and segmentation techniques using information-theoretic tools

El processament d'imatges mèdiques és una important àrea de recerca. El desenvolupament de noves tècniques que assisteixin i millorin la interpretació visual de les imatges de manera ràpida i precisa és fonamental en entorns clínics reals. La majoria de contribucions d'aquesta tesi són basades en Teoria de la Informació. Aquesta teoria tracta de la transmissió, l'emmagatzemament i el processament d'informació i és usada en camps tals com física, informàtica, matemàtica, estadística, biologia, gràfics per computador, etc. En aquesta tesi, es presenten nombroses eines basades en la Teoria de la Informació que milloren els mètodes existents en l'àrea del processament d'imatges, en particular en els camps del registre i la segmentació d'imatges. Finalment es presenten dues aplicacions especialitzades per l'assessorament mèdic que han estat desenvolupades en el marc d'aquesta tesi.

Optimization of inverse reflector design

Aquesta tesi presenta un nou mètode pel disseny invers de reflectors. Ens hem centrat en tres temes principals: l’ús de fonts de llum reals i complexes, la definició d’un algoritme ràpid pel càlcul de la il•luminació del reflector, i la definició d’un algoritme d’optimització per trobar més eficientment el reflector desitjat. Les fonts de llum estan representades per models near-field, que es comprimeixen amb un error molt petit, fins i tot per fonts de llum amb milions de raigs i objectes a il•luminar molt propers. Llavors proposem un mètode ràpid per obtenir la distribució de la il•luminació d’un reflector i la seva comparació amb la il•luminació desitjada, i que treballa completament en la GPU. Finalment, proposem un nou mètode d’optimització global que permet trobar la solució en menys passos que molts altres mètodes d’optimització clàssics, i alhora evitant mínims locals.

An automated calibration method for non-see-through head mounted displays

Accurate calibration of a head mounted display (HMD) is essential both for research on the visual system and for realistic interaction with virtual objects. Yet, existing calibration methods are time consuming and depend on human judgements, making them error prone. The methods are also limited to optical see-through HMDs. Building on our existing HMD calibration method [1], we show here how it is possible to calibrate a non-see-through HMD. A camera is placed inside an HMD displaying an image of a regular grid, which is captured by the camera. The HMD is then removed and the camera, which remains fixed in position, is used to capture images of a tracked calibration object in various positions. The locations of image features on the calibration object are then re-expressed in relation to the HMD grid. This allows established camera calibration techniques to be used to recover estimates of the display’s intrinsic parameters (width, height, focal length) and extrinsic parameters (optic centre and orientation of the principal ray). We calibrated a HMD in this manner in both see-through and in non-see-through modes and report the magnitude of the errors between real image features and reprojected features. Our calibration method produces low reprojection errors and involves no error-prone human measurements.

Canonical description of the perspective projections

A unique parameterization of the perspective projections in all whole-numbered dimensions is reported. The algorithm for generating a perspective transformation from parameters and for recovering parameters from a transformation is a modification of the Givens orthogonalization algorithm. The algorithm for recovering a perspective transformation from a perspective projection is a modification of Roberts' classical algorithm. Both algorithms have been implemented in Pop-11 with call-out to the NAG Fortran libraries. Preliminary monte-carlo tests show that the transformation algorithm is highly accurate, but that the projection algorithm cannot recover magnitude and shear parameters accurately. However, there is reason to believe that the projection algorithm might improve significantly with the use of many corresponding points, or with multiple perspective views of an object. Previous parameterizations of the perspective transformations in the computer graphics and computer vision literature are discussed.

HiPP: A Novel Hierarchical Point Placement Strategy and its Application to the Exploration of Document Collections

Point placement strategies aim at mapping data points represented in higher dimensions to bi-dimensional spaces and are frequently used to visualize relationships amongst data instances. They have been valuable tools for analysis and exploration of data sets of various kinds. Many conventional techniques, however, do not behave well when the number of dimensions is high, such as in the case of documents collections. Later approaches handle that shortcoming, but may cause too much clutter to allow flexible exploration to take place. In this work we present a novel hierarchical point placement technique that is capable of dealing with these problems. While good grouping and separation of data with high similarity is maintained without increasing computation cost, its hierarchical structure lends itself both to exploration in various levels of detail and to handling data in subsets, improving analysis capability and also allowing manipulation of larger data sets.

Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

PedVis: A Structured, Space-Efficient Technique for Pedigree Visualization

Public genealogical databases are becoming increasingly populated with historical data and records of the current population`s ancestors. As this increasing amount of available information is used to link individuals to their ancestors, the resulting trees become deeper and more dense, which justifies the need for using organized, space-efficient layouts to display the data. Existing layouts are often only able to show a small subset of the data at a time. As a result, it is easy to become lost when navigating through the data or to lose sight of the overall tree structure. On the contrary, leaving space for unknown ancestors allows one to better understand the tree`s structure, but leaving this space becomes expensive and allows fewer generations to be displayed at a time. In this work, we propose that the H-tree based layout be used in genealogical software to display ancestral trees. We will show that this layout presents an increase in the number of displayable generations, provides a nicely arranged, symmetrical, intuitive and organized fractal structure, increases the user`s ability to understand and navigate through the data, and accounts for the visualization requirements necessary for displaying such trees. Finally, user-study results indicate potential for user acceptance of the new layout.

Two-Phase Mapping for Projecting Massive Data Sets

Most multidimensional projection techniques rely on distance (dissimilarity) information between data instances to embed high-dimensional data into a visual space. When data are endowed with Cartesian coordinates, an extra computational effort is necessary to compute the needed distances, making multidimensional projection prohibitive in applications dealing with interactivity and massive data. The novel multidimensional projection technique proposed in this work, called Part-Linear Multidimensional Projection (PLMP), has been tailored to handle multivariate data represented in Cartesian high-dimensional spaces, requiring only distance information between pairs of representative samples. This characteristic renders PLMP faster than previous methods when processing large data sets while still being competitive in terms of precision. Moreover, knowing the range of variation for data instances in the high-dimensional space, we can make PLMP a truly streaming data projection technique, a trait absent in previous methods.

Interactive Vector Field Feature Identification

We introduce a flexible technique for interactive exploration of vector field data through classification derived from user-specified feature templates. Our method is founded on the observation that, while similar features within the vector field may be spatially disparate, they share similar neighborhood characteristics. Users generate feature-based visualizations by interactively highlighting well-accepted and domain specific representative feature points. Feature exploration begins with the computation of attributes that describe the neighborhood of each sample within the input vector field. Compilation of these attributes forms a representation of the vector field samples in the attribute space. We project the attribute points onto the canonical 2D plane to enable interactive exploration of the vector field using a painting interface. The projection encodes the similarities between vector field points within the distances computed between their associated attribute points. The proposed method is performed at interactive rates for enhanced user experience and is completely flexible as showcased by the simultaneous identification of diverse feature types.

Resampling Strategies for Deforming MLS Surfaces

Moving-least-squares (MLS) surfaces undergoing large deformations need periodic regeneration of the point set (point-set resampling) so as to keep the point-set density quasi-uniform. Previous work by the authors dealt with algebraic MLS surfaces, and proposed a resampling strategy based on defining the new points at the intersections of the MLS surface with a suitable set of rays. That strategy has very low memory requirements and is easy to parallelize. In this article new resampling strategies with reduced CPU-time cost are explored. The basic idea is to choose as set of rays the lines of a regular, Cartesian grid, and to fully exploit this grid: as data structure for search queries, as spatial structure for traversing the surface in a continuation-like algorithm, and also as approximation grid for an interpolated version of the MLS surface. It is shown that in this way a very simple and compact resampling technique is obtained, which cuts the resampling cost by half with affordable memory requirements.

Verifiable Visualization for Isosurface Extraction

Visual representations of isosurfaces are ubiquitous in the scientific and engineering literature. In this paper, we present techniques to assess the behavior of isosurface extraction codes. Where applicable, these techniques allow us to distinguish whether anomalies in isosurface features can be attributed to the underlying physical process or to artifacts from the extraction process. Such scientific scrutiny is at the heart of verifiable visualization - subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. More concretely, we derive formulas for the expected order of accuracy (or convergence rate) of several isosurface features, and compare them to experimentally observed results in the selected codes. This technique is practical: in two cases, it exposed actual problems in implementations. We provide the reader with the range of responses they can expect to encounter with isosurface techniques, both under ""normal operating conditions"" and also under adverse conditions. Armed with this information - the results of the verification process - practitioners can judiciously select the isosurface extraction technique appropriate for their problem of interest, and have confidence in its behavior.