Line drawings provide an effective means of communication about the geometry of 3-D objects. An understanding of how to duplicate the way humans interpret line drawings is extremely important in enabling man-machine communication with respect to images, diagrams, and spatial constructs. In particular, such an understanding could be used to provide the human with the capability to create a line-drawing sketch of a polyhedral object that the machine can automatically convert into the intended 3-D model. A recently published paper (Marill 1991) presented a simple optimization procedure supposedly able to duplicate human judgment in recovering the 3-D "wire frame" geometry of objects depicted in line drawings. Marill provided some impressive examples, but no theoretical justification for his approach. In this paper we introduce our own work by first critically examining Marill's algorithm. We provide an explanation for why Marill's algorithm was able to perform as well as it did on the exa...

This article describes a method for reducing the shape distortions due to scale-space smoothing that arise in the computation of 3-D shape cues using operators (derivatives) de ned from scale-space representation. More precisely, we are concerned with a general class of methods for deriving 3-D shape cues from 2-D image data based on the estimation of locally linearized deformations of brightness patterns. This class

An extremum principle is developed that determines three-dimensional surface orientation from a two-dimensional contour. The principle maximizes the ratio of the area to the square of the perimeter, a measure of the compactness or symmetry of the three-dimensional surface. I;he principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries. The maximum likelihood method approximates the principle on irregular figures, but we show that it consistently overestimates the slant of an ellipse.

We describe a shape from texture method that constructs a maximum a posteriori estimate of surface coe#cients using only the deformation of individual texture elements. Our method does not need to use either the boundary of the observed surface or any assumption about the overall distribution of elements. The method assumes that texture elements are of a limited number of types of fixed shape. We show that, with this assumption and assuming generic view and texture, each texture element yields the surface gradient unique up to a two-fold ambiguity.

Introduction The idea for this Appendix arose from our perception of a frustrating situation faced by vision researchers. For example, one is interested in some aspect of the theory of perspective image formation such as the epipolar line. The interested party goes to the library to check out a book on projective geometry filled with hope that the necessary mathematical machinery will be directly at hand. These expectations are quickly dashed. Upon opening the book, the expectant reader finds the presentation dominated by endless observations about harmonic relations and a few chapters which explore the minutiae of Pappus' theorem. Finally, as a last cruel twist of irony, the book ends in triumph with a rather exhilarating discourse on the conic pencil. All of the material is presented in the form of theorems defined on points, lines and conics without the use of coordinates, except perhaps for a quick pause to define barycentric coordinates just to taunt the reader. Dejected, the vis

A unified framework for shape from texture and contour is proposed. It is based on the assumption that the surface markings are not systematically compressed, or formally, that they are weakly isotropic. The weak isotropy principle is based on analysis of the directional statistics of the projected surface markings. It builds on several previous theories, in particular by Witkin [25] and Kanatani [15]. It extends these theories in various ways, most notably to perspective projection. The theory also provides an exact solution to an estimation problem earlier solved approximately by Kanatani. The weak isotropy principle leads to a computationally efficient algorithm, WISP, for estimation of surface orientation. WISP uses simple image observables that are shown to be direct correlates of the surface orientation to compute an initial approximate estimate in a single step. In certain simple cases this first estimate is exact, and in experiments with natural images it is typically within 5...

We address the problem of texture segmentation by using a novel affine invariant model. The introduction of affine invariance as a requirement for texture analysis goes beyond what is known of the human performance and also beyond the psychophysical theories. We propose to compute texture features using affine invariant intrinsic neighborhoods and affine invariant intrinsic orientation matrices. We discuss several possibilities for the definition of the channels and give comparative experimental results where an affine invariant Mumford-Shah type energy functional is used to compute the multichannel affine invariant segmentation. We prove that the method is able to retrieve faithfully the texture regions and to recover the shape from texture information in images where several textures are present. The numerical algorithm is multiscale.

Line drawings produced by contours traced on a surface can produce a vivid impression of the surface shape. The stability of this perception is notable considering that the information provided by the surface contours is quite ambiguous. We have studied the stability of line drawing perception from psychophysical and computational standpoints. For a given family of simple line drawings, human observers could perceive the drawings as depicting either an elliptic (egg-shaped) or hyperbolic (saddle-shaped) smooth surface patch. Rotation of the image along the line of sight and change in aspect ratio of the line drawing could bias the observer toward either interpretation. The results were modeled by a simple Bayesian observer that computes the probability to choose either interpretation given the information in the image and prior preferences. The model's decision rule is noncommitting: for a given input image its responses are still probabilistic, reflecting variability in the modeled observers' judgements. A good fit to the data was obtained when three observer assumptions were introduced: a preference for convex surfaces, a preference for surface contours aligned with the principal lines of curvature, and a preference for a surface orientation consistent with an object viewed from above. We discuss how these assumptions might reflect regularities of the visual world. 1998 Elsevier Science Ltd. All rights reserved.

Research on the perception of texture gradients has relied heavily on the subjective reports of observers engaged in free-viewing. We asked whether these findings generalized to speeded performance. Experiment 1 showed that an important aspect of subjective perception—sizeconstancy scaling with perceived distance—also predicted the speed of pop-out visual search for cylinders viewed against a texture gradient. Experiment 2 showed that this finding could not be attributed to the local contrast between search items and the background texture. Experiment 3 assessed the relative contributions of 2 separable dimensions of texture gradients—perspective (radial spreading) and compression (foreshortening)—finding them to be independent in the more rapid search conditions (long target among shorter distractors) but combined in their influence in the slower conditions (short target among longer distractors). When observers view the texture gradient shown in Figure 1A they usually report seeing a flat surface recede into the distance, despite the fact that a two-dimensional (2-D) image alone cannot specify the three-dimensional (3-D) surface that gave rise to the projection. This study asked whether the factors influencing the perceived slant of such texture gradients also influences rapid visual search for objects placed on their surface. Although a large number of previous studies have examined the perception of slant in texture gradients (e.g., Flock,

Recent theoretmal developments in Image Understandmg are surveyed. Among the issues discussed are edge finding, region finding, texture, shape from shading, shape from texture, shape from contour, and the representations of surfaces and objects. Much of the work described was developed in the DARPA Image Understanding project.