Suresh K. Lodha

APPROACHES TO UNCERTAINTY VISUALIZATION

Visualized data often have dubious origins and quality. Different forms of uncertainty and errors are also introduced as the data are derived, transformed, interpolated, and finally rendered. In the absence of integrated presentation of data and uncertainty, the analysis of the visualization is incomplete at best and often leads to inaccurate or incorrect conclusions. This paper surveys techniques for presenting data together with uncertainty. These uncertainty visualization techniques present data in such a manner that users are made aware of the locations and degree of uncertainties in their data so as to make more informed analyses and decisions. The techniques include adding glyphs, adding geometry, modifying geometry, modifying attributes, animation, sonification, and psycho-visual approaches. We present our results in uncertainty visualization for environmental visualization, surface interpolation, global illumination with radiosity, flow visualization, and figure animation. We also present a classification of the possibilities in uncertainty visualization, and locate our contributions within this classification.

Glyphs for visualizing uncertainty in vector fields

Environmental data have inherent uncertainty which is often ignored in visualization. Meteorological stations and doppler radars, including their time series averages, have a wealth of uncertainty information that traditional vector visualization methods such as meteorological wind barbs and arrow glyphs simply ignore. We have developed a new vector glyph to visualize uncertainty in winds and ocean currents. Our approach is to include uncertainty in direction and magnitude, as well as the mean direction and length, in vector glyph plots. Our glyph shows the variation in uncertainty, and provides fair comparisons of data from instruments, models, and time averages of varying certainty. We also define visualizations that incorporate uncertainty in an unambiguous manner as verity visualization. We use both quantitative and qualitative methods to compare our glyphs to traditional ones. Subjective comparison tests with experts are provided, as well as objective tests, where the information density of our new glyphs and traditional glyphs are compared. The design of the glyph and numerous examples using environmental data are given. We show enhanced visualizations, data together with their uncertainty information, that may improve understanding of environmental vector field data quality.

Supervised Parametric Classification of Aerial LiDAR Data

In this work, we classify 3D aerial LiDAR height data into roads, grass, buildings, and trees using a supervised parametric classification algorithm. Since the terrain is highly undulating, we subtract the terrain elevations using digital elevation models (DEMs, easily available from the United States Geological Survey (USGS)) to obtain the height of objects from a flat level. In addition to this height information, we use height texture (variation in height), intensity (amplitude of lidar response), and multiple (two) returns from lidar to classify the data. Furthermore, we have used luminance (measured in the visible spectrum) from aerial imagery as the fifth feature for classification. We have used mixture of Gaussian models for modeling the training data. Model parameters and the posterior probabilities are estimated using Expectation-Maximization (EM) algorithm. We have experimented with different number of components per model and found that four components per model yield satisfactory results. We have tested the results using leave-one-out as well as random \frac{n}{2} test. Classification results are in the range of 66%-84% depending upon the combination of features used that compares very favorably with. train-all-test-all results of 85%. Further improvement is achieved using spatial coherence.

UFLOW: visualizing uncertainty in fluid flow

Uncertainty or errors are introduced in fluid flow data as the data is acquired, transformed and rendered. Although researchers are aware of these uncertainties, little has been done to incorporate them in the existing visualization systems for fluid flow. In the absence of integrated presentation of data and its associated uncertainty, the analysis of the visualization is incomplete at best and may lead to inaccurate or incorrect conclusions. The article presents UFLOW-a system for visualizing uncertainty in fluid flow. Although there are several sources of uncertainties in fluid flow data, in this work, we focus on uncertainty arising from the use of different numerical algorithms for computing particle traces in a fluid flow. The techniques that we have employed to visualize uncertainty in fluid flow include uncertainty glyphs, flow envelopes, animations, priority sequences, twirling batons of trace viewpoints, and rakes. These techniques are effective in making the users aware of the effects of different integration methods and their sensitivity, especially near critical points in the flow field.

Towards complete generic camera calibration

We consider the problem of calibrating a highly generic imaging model, that consists of a non-parametric association of a projection ray in 3D to every pixel in an image. Previous calibration approaches for this model do not seem to be directly applicable for cameras with large fields of view and non-central cameras. In this paper, we describe a complete calibration approach that should in principle be able to handle any camera that can be described by the generic imaging model. Initial calibration is performed using multiple-images of overlapping calibration grids simultaneously. This is then improved using pose estimation and bundle adjustment-type algorithms. The approach has been applied on a wide variety of central and non-central cameras including fisheye lens, catadioptric cameras with spherical and hyperbolic mirrors, and multi-camera setups. We also consider the question if non-central models are more appropriate for certain cameras than central models.

LISTEN: sounding uncertainty visualization

Integrated presentation of data with uncertainty is a worthy goal in scientific visualization. It allows researchers to make informed decisions based on imperfect data. It also allows users to visually compare and contrast different algorithms for performing the same task or different models for representing the same physical phenomenon. We present LISTEN-a data sonification system that has been incorporated into two visualization systems: a system for visualizing geometric uncertainty of surface interpolants; and a system for visualizing uncertainty in fluid flow. LISTEN is written in C++ for the SGI platform. It works with the SGI internal audio chip or a MIDI device or both. LISTEN is an object-oriented system that is modular, flexible, adaptable, portable, interactive and extensible. We demonstrate that sonification is very effective as an additional tool in visualizing geometric and fluid flow uncertainty.

Topology preserving compression of 2D vector fields

We present an algorithm for compressing 2D vector fields that preserves topology. Our approach is to simplify the given data set using constrained clustering. We employ different types of global and local error metrics including the earth movers distance metric to measure the degradation in topology as well as weighted magnitude and angular errors. As a result, we obtain precise error bounds in the compressed vector fields. Experiments with both analytic and simulated data sets are presented. Results indicate that one can obtain significant compression with low errors without losing topology information.

Aerial Lidar Data Classification using AdaBoost

We use the AdaBoost algorithm to classify 3D aerial lidar scattered height data into four categories: road, grass, buildings, and trees. To do so we use five features: height, height variation, normal variation, lidar return intensity, and image intensity. We also use only lidar-derived features to organize the data into three classes (the road and grass classes are merged). We apply and test our results using ten regions taken from lidar data collected over an area of approximately eight square miles, obtaining higher than 92% accuracy. We also apply our classifier to our entire dataset, and present visual classification results both with and without uncertainty. We implement and experiment with several variations within the AdaBoost family of algorithms. We observe that our results are robust and stable over all the various tests and algorithmic variations. We also investigate features and values that are most critical in distinguishing between the classes. This insight is important in extending the results from one geographic region to another.

A generic structure-from-motion framework

We introduce a generic structure-from-motion approach based on a previously introduced, highly general imaging model, where cameras are modeled as possibly unconstrained sets of projection rays. This allows to describe most existing camera types including pinhole cameras, sensors with radial or more general distortions, catadioptric cameras (central or non-central), etc. We introduce a structure-from-motion approach for this general imaging model, that allows to reconstruct scenes from calibrated images, possibly taken by cameras of different types (cross-camera scenarios). Structure-from-motion is naturally handled via camera independent ray intersection problems, solved via linear or simple polynomial equations. We also propose two approaches for obtaining optimal solutions using bundle adjustment, where camera motion, calibration and 3D point coordinates are refined simultaneously. The proposed methods are evaluated via experiments on two cross-camera scenarios--a pinhole used together with an omni-directional camera and a stereo system used with an omni-directional camera.

Aerial LiDAR Data Classification Using Support Vector Machines (SVM)

We classify 3D aerial LiDAR scattered height data into buildings, trees, roads, and grass using the support vector machine (SVM) algorithm. To do so we use five features: height, height variation, normal variation, LiDAR return intensity, and image intensity. We also use only LiDAR- derived features to organize the data into three classes (the road and grass classes are merged). We have implemented and experimented with several variations of the SVM algorithm with soft-margin classification to allow for the noise in the data. We have applied our results to classify aerial LiDAR data collected over approximately 8 square miles. We visualize the classification results along with the associated confidence using a variation of the SVM algorithm producing probabilistic classifications. We observe that the results are stable and robust. We compare the results against the ground truth and obtain higher than 90% accuracy and convincing visual results.