Perspective (geometry)

About: Perspective (geometry) is a research topic. Over the lifetime, 277 publications have been published within this topic receiving 5795 citations. The topic is also known as: perspective (geometry).

Are size illusions in simple line drawings affected by shading

Abstract: In a number of simple line drawings, such as the Muller-Lyer or Judd figures, we can experience strong distortions of perceived space-geometric illusions. One way of explaining these effects is based on the perspective information that can be read from the line drawings. For instance, the 'inappropriate constancy scaling' theory advocates that the inferred three-dimensional structure of the pictured object is used by the perceptual system to adjust the size of line-drawing components. Such a theory would predict that additional depth cues, for instance shading added to line drawings, should affect these illusions because they influence the three-dimensional appearance. We present here systematic measurements of the magnitude of length misjudgments in horizontal Muller-Lyer and Judd figures for three configurations: (i) pure line drawings, and with shading attached to (ii) the top, and (iii) the bottom of the figures. The latter two configurations are unambiguously interpreted as 'folded' structures with a horizontal edge behind the image plane or protruding from it, respectively. While we could not find any effect of shading in our experimental data, we did observe a length misjudgment in Judd figures that corresponds precisely to the asymmetry that can be observed in the Muller-Lyer illusion for inward and outward fins. This pattern of results is not consistent with notions of inappropriate constancy scaling but is fully coherent with the view that neural filtering mechanisms, which are affecting the perceived position of line intersections, are responsible for this type of geometrical illusions.

Projective area-invariants as an extension of the cross-ratio

Abstract: Projective invariants provide a framework for computer vision where the image of an object is described by its intrinsic properties, independently of the particular view. It is advantageous if these intrinsic properties are defined in terms of computationally simple features. An area-measurement provides a good candidate that is easy to reliably compute from a particular image of the object. The main contributions of this paper are the definition and justification of area-invariants in projective geometry and the indication of its relevance in image analysis. A framework that covers one-dimensional intervals and two-dimensional figures has been developed. In the linear case, the invariants are linear only in two cases. The first case is the well known cross-ratio, and the second case is called the polar case. The generalization to the plane can be done in different directions. One can use either points (on the line or in the plane) or the geometric figures (intervals, triangles, circles) as the basic entities involved. The first view was adopted already by Mobius, who generalized the cross-ratio in various directions. The second view used here leads to another generalization of the cross-ratio, where the invariants are relations between the areas of a class of geometric figures, related to each other in a certain manner. Remarkably enough, these invariants turn out to be linear if the figures involved are related in a pole/ polar configuration

On Pencils of Tangent Planes and the Recognition of Smooth 3D Shapes from Silhouettes

Abstract: This paper presents a geometric approach to recognizing smooth objects from their outlines We define a signature function that associates feature vectors with objects and baselines connecting pairs of possible viewpoints Feature vectors, which can be projective, affine, or Euclidean, are computed using the planes that pass through a fixed baseline and are also tangent to the object's surface In the proposed framework, matching a test outline to a set of training outlines is equivalent to finding intersections in feature space between the images of the training and the test signature functions The paper presents experimental results for the case of internally calibrated perspective cameras, where the feature vectors are angles between epipolar tangent planes

Three Dimensions in Fine Structure

Abstract: With some knowledge of perspective and by use of a perspective chart it is possible to construct an accurate three-dimensional illustration depicting the interrelation of tissue components from electron micrographs of serial sections of biological materials. Tracings of pertinent structures from electron micrographs are overlaid with a grid plane and subsequently redrawn on a perspective grid plane. The new tracings are then connected to one another in the most logical manner to form an illustration in perspective.