The three-dimensional shape and relative depth of a smoothly curving layered transparent surface may be communicated particularly effectively when the surface is artistically enhanced with sparsely distributed opaque detail. This paper describes how the set of principal directions and principal curvatures specified by local geometric operators can be understood to define a natural "flow " over the surface of an object, and can be used to guide the placement of the lines of a stroke texture that seeks to represent 3D shape information in a perceptually intuitive way. The driving application for this work is the visualization of layered isovalue surfaces in volume data, where the particular identity of an individual surface is not generally known a priori and observers will typically wish to view a variety of different level surfaces from the same distribution, superimposed over underlying opaque structures. By advecting an evenly distributed set of tiny opaque particles, and the empty space between them, via 3D line integral convolution through the vector field defined by the principal directions and principal curvatures of the level surfaces passing through each gridpoint of a 3D volume, it is possible to generate a

This paper presents a new method for using texture and color to visualize multivariate data elements arranged on an underlying height field. We combine simple texture patterns with perceptually uniform colors to increase the number of attribute values we can display simultaneously. Our technique builds multicolored perceptual texture elements (or pexels) to represent each data element. Attribute values encoded in an element are used to vary the appearance of its pexel. Texture and color patterns that form when the pexels are displayed can be used to rapidly and accurately explore the dataset. Our pexels are built by varying three separate texture dimensions: height, density, and regularity. Results from computer graphics, computer vision, and human visual psychophysics have identified these dimensions as important for the formation of perceptual texture patterns. The pexels are colored using a selection technique that controls color distance, linear separation, and color category. Prop...

Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the `texture distortion' from the image, and (b) Interpreting the `texture distortion' to infer the orientation and shape of the surface in the scene. We model the texture distortion for a given point and direction on the image plane as an affine transformation and derive the relationship between the parameters of this transformation and the shape parameters. We have developed a technique for estimating affine transforms between nearby image patches which is based on solving a system of linear constraints derived from a differential analysis. One need not explicitly identify texels or make restrictive assumptions about the nature of the texture such as isotropy. We use non-linear minimization of a least squares error criterion to recover the surface orientation (slant and tilt) and shape (principal curvatures and directions) based on the estimated affine transforms in a number of different directions. A simple linear algorithm based on singular value decomposition of the linear parts of the affine transforms provides the initial guess for the minimization procedure. Experimental results on both planar and curved surfaces under perspective projection demonstrate good estimates for both orientation and shape. A sensitivity analysis yields predictions for both computer vision algorithms and human perception of shape from texture.

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Transparency can be a useful device for depicting multiple overlapping surfaces in a single image. The challenge is to render the transparent surfaces in such a way that their three-dimensional shape can be readily understood and their depth distance from underlying structures clearly perceived. This paper describes our investigations into the use of sparsely-distributed discrete, opaque texture as an "artistic device" for more explicitly indicating the relative depth of a transparent surface and for communicating the essential features of its 3D shape in an intuitively meaningful and minimally occluding way. The driving application for this work is the visualization of layered surfaces in radiation therapy treatment planning data, and the technique is illustrated on transparent isointensity surfaces of radiation dose. We describe the perceptual motivation and artistic inspiration for defining a stroke texture that is locally oriented in the direction of greatest normal curvatu...

Projective distortion of surface texture observed in a perspective image can provide direct information about the shape of the underlying surface. Previous theories have generally concerned planar surfaces; in this paper we present a systematic analysis of first- and second-order texture distortion cues for the case of a smooth curved surface. In particular, we analyze several kinds of texture gradients and relate them to surface orientation and surface curvature. The local estimates obtained from these cues can be integrated to obtain a global surface shape, and we show that the two surfaces resulting from the well-known tilt ambiguity in the local foreshortening cue typically have qualitatively different shapes. As an example of a practical application of the analysis, a shape from texture algorithm based on local orientation-selective filtering is described, and some experimental results are shown. i Figure 1: This image of a slanting plane covered with circles illustrates several...

In natural vision, information overspecifies the relative distances between objects and their layout in three dimensions. Directed perception applies (Cutting, 1986), rather than direct or indirect perception, because any single source of information (or cue) might be adequate to reveal relative depth (or local depth order), but many are present and useful to observers. Such overspecification presents the theoretical problem of how perceivers use this multiplicity of information to arrive at a unitary appreciation of distance between objects in the environment. This article examines three models of directed perception: selection, in which only one source of information is used; addition, in which all sources are used in simple combination; and multiplication, in which interactions among sources can occur. To establish perceptual overspecification, we created stimuli with four possible sources of monocular spatial information, using all combinations of the presence or absence of relative size, height in the projection plane, occlusion, and motion parallax. Visual stimuli were computer generated and consisted of three untextured parallel planes arranged in depth. Three tasks were used: one of magnitude estimation of exocentric

In theoretical analyses of visual form perception, it is often assumed that the 3-dimensional structures of smoothly curved surfaces are perceptually represented as point-by-point mappings of metric depth and/or orientation relative to the observer. This article describes an alternative theory in which it is argued that our visual knowledge of smoothly curved surfaces can also be denned in terms of local, nonmetric order relations. A fundamental prediction of this analysis is that relative depth judgments between any two surface regions should be dramatically influenced by the monotonicity of depth change (or lack of it) along the intervening portions of the surface through which they are separated. This prediction is confirmed in a series of experiments using surfaces depicted with either shading or texture. Additional experiments are reported, moreover, that demonstrate that smooth occlusion contours are a primary source of information about the ordinal structure of a surface and that the depth extrema in between contours can be optically specified by differences in luminance at the points of occlusion. For many higher organisms, including humans, a primary source of knowledge about objects and events in the surrounding environment is provided by vision. Because of the ecological

We examined how depth information from two different cue types (object motion and texture gradient) is integrated into a single estimate in human vision. Two critical assumptions of a recent model of depth cue combination (termed modified weak fusion) were tested. The first assumption is that the overall depth estimate is a weighted linear combination of the estimates derived from the individual cues, after initial processing needed to bring them to a common format. The second assumption is that the weight assigned to a cue reflects the apparent reliability of that cue in a particular scene. By this account, the depth combination rule is linear and dynamic, changing in a predictable fashion in response to the particular scene and viewing conditions. A novel procedure was used to measure the weights assigned to the texture and motion cues across experimental conditions. This procedure uses a type of perturbation analysis. The results are consistent with the weighted linear combination rule. In addition, when either cue is corrupted by added noise, the weighted linear combination rule shifts in favor of the uncontaminated cue.

Previous investigators have shown that observers' visual cue combination strategies are remarkably flexible in the sense that these strategies adapt on the basis of the estimated reliabilities of the visual cues. However, these researchers have not addressed how observers' acquire these estimated reliabilities. This article studies observers' abilities to learn cue combination strategies. Subjects made depth judgments about simulated cylinders whose shapes were indicated by motion and texture cues. Because the two cues could indicate different shapes, it was possible to design tasks in which one cue provided useful information for making depth judgments, whereas the other cue was irrelevant. The results of experiment 1 suggest that observers' cue combination strategies are adaptable as a function of training; subjects adjusted their cue combination rules to use a cue more heavily when the cue was informative on a task versus when the cue was irrelevant. Experiment 2 demonstrated that experience-dependent adaptation of cue combination rules is context-sensitive. On trials with presentations of short cylinders, one cue was informative, whereas on trials with presentations of tall cylinders, the other cue was informative. The results suggest that observers can learn multiple cue combination rules, and can learn to apply each rule in the appropriate context. Experiment 3 demonstrated a possible limitation on the context-sensitivity of adaptation of cue combination rules. One cue was informative on trials with presentations of cylinders at a left oblique orientation, whereas the other cue was informative on trials with presentations of cylinders at a right oblique orientation. The results indicate that observers did not learn to use different cue combination rules in differe...