Shape from regular patterns

doi:10.1016/0004-3702(84)90025-0

Artificial Intelligence

Volume 22, Issue 1, January 1984, Pages 49-75

https://doi.org/10.1016/0004-3702(84)90025-0 Get rights and content

Abstract

This paper describes an algorithm to obtain local surface orientation from the apparent surface-pattern distortion in an image.

We propose a spherical projection to model perspective imaging. A mapping is defined based on the measurement of the local distortions of a repeated known texture pattern due to the image projection. This mapping maps an apparent shape on the image sphere to a locus of possible surface orientations on the Gaussian sphere.

An iterative constraint propagation algorithm with the orientations at occluding boundaries reduces possible surface orientations to a unique orientation. This algorithm can recover local surface orientation as well as interpolate surface orientations where no information is available. This algorithm is applied to a real image to demonstrate its performance.

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Cited by (56)

A neural model of 3D shape-from-texture: Multiple-scale filtering, boundary grouping, and surface filling-in
2007, Vision Research
A neural model is presented of how cortical areas V1, V2, and V4 interact to convert a textured 2D image into a representation of curved 3D shape. Two basic problems are solved to achieve this: (1) Patterns of spatially discrete 2D texture elements are transformed into a spatially smooth surface representation of 3D shape. (2) Changes in the statistical properties of texture elements across space induce the perceived 3D shape of this surface representation. This is achieved in the model through multiple-scale filtering of a 2D image, followed by a cooperative-competitive grouping network that coherently binds texture elements into boundary webs at the appropriate depths using a scale-to-depth map and a subsequent depth competition stage. These boundary webs then gate filling-in of surface lightness signals in order to form a smooth 3D surface percept. The model quantitatively simulates challenging psychophysical data about perception of prolate ellipsoids [Todd, J., & Akerstrom, R. (1987). Perception of three-dimensional form from patterns of optical texture. Journal of Experimental Psychology: Human Perception and Performance, 13(2), 242–255]. In particular, the model represents a high degree of 3D curvature for a certain class of images, all of whose texture elements have the same degree of optical compression, in accordance with percepts of human observers. Simulations of 3D percepts of an elliptical cylinder, a slanted plane, and a photo of a golf ball are also presented.
Estimating the perspective pose of texture planes using spectral analysis on the unit sphere
2002, Pattern Recognition
Citation Excerpt :
The main advantage is that unlike the image plane, the unit sphere is a closed space parametrised by the two angles of azimuth, and, zenith or elevation. Spherical projections of the image plane have been exploited by several authors [15,28]. However, they have employed structural representations of texture.
Multiple vanishing point detection provides the key to recovering the perspective pose of textured planes. If vanishing points are to be detected from spectral information then there are two computational problems that need to be solved. Firstly, the search of the extended image plane is unbounded, and hence the location of vanishing points at or near infinity is difficult. Secondly, correspondences between local spectra need to be established so that vanishing points can be triangulated. In this paper, we offer a way of overcoming these two difficulties. We overcome the problem of unbounded search by mapping the information provided by local spectral moments onto the unit sphere. According to our representation, the position and direction of each local spectrum maps onto a great circle on the unit sphere. The need for correspondences is overcome by accumulating the great circle intercepts. Vanishing points occur at local accumulator maxima on the unit sphere. To improve the accuracy of the recovered perspective pose parameters for highly slanted planes, we use an adaptive spectral window. This selects the window so as to reduce spectral defocusing by minimising the determinant of the spectral covariance matrix. We experiment with the new shape-from-texture technique on both synthetic and real world data. Here it proves to be an accurate and robust means of estimating perspective pose.
Detecting multiple texture planes using local spectral distortion
2002, Image and Vision Computing
This paper presents a spectral method for identifying multiple texture planes. We commence by showing how pairs of spectral peaks can be used to make direct estimates of the slant and tilt angles. Our method commences by computing the affine distortion matrices for pairs of corresponding spectral peaks. We show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local planar pose. The leading eigenvector points in the tilt direction and the direction of the second eigenvector can be used to estimate the slant direction. By searching for clusters in the computed slant and tilt angles, we locate multiple texture planes. We apply the method to a variety of real-world and synthetic imagery.
Estimating the 3D orientation of texture planes using local spectral analysis
2000, Image and Vision Computing
Citation Excerpt :
By contrast, the spectral method attempts to infer shape from distortions in the frequency representation of texture. Structural methods use the geometry of edges, lines or arcs to identify perspective distortion using shape cues [4–6]. Unfortunately, the segmentation of the texture primitives is a process of extreme fragility, and in most cases the techniques have only been demonstrated on synthetic or highly contrived data.
This paper describes a new method for recovering the perspective geometry of textured planes from local spectral analysis. The novel contribution of the work is to use the angular distribution of texture moments to locate the vanishing point of textured planes viewed under perspective geometry. Our key observation is that lines of uniform spectral orientation radiate from the vanishing point. We exploit this property to develop a simple algorithm for estimating the slant and tilt of textured planes. This is a two-step process. It commences by computing the Fourier power spectrum at each of a series of local neighbourhoods and identifying contours which connect the local spectral moments of equal power. As noted by Sevens (1981), these contours are perpendicular to the tilt direction. The second step is to triangulate the vanishing point. We do this by using a correlation method to identify lines of uniform spectral orientation that originate from the vanishing point. This second property represents the novel contribution of the paper. We evaluate the new algorithm on both synthetic imagery with known ground-truth and on real-world data.
Planar surface orientation from texture spatial frequencies
1995, Pattern Recognition
This paper presents a computational model and a practical algorithm for determining the three-dimensional orientation of a planar surface from visual texture information. The model consists of three parts: (1) a local spatial frequency based texture representation; (2) a model describing the projection of surface texture to image texture; and (3) a solution of the texture projection model for the surface orientation under an assumption of surface texture homogeneity. The algorithm first measures the dominant frequency at each image point using three wavelet-like transforms, and then finds the surface orientation that minimizes the variance of the image frequencies' backprojections. The algorithm is tested on photographs of real-world surfaces, exhibiting an average accuracy of better than 3° in slant and 4° in tilt. The current model and algorithm are more accurate, yet substantially simpler, than earlier versions of this approach.
Improved orientation estimation for texture planes using multiple vanishing points
2000, Pattern Recognition
Vanishing point locations play a critical role in determining the perspective orientation of textured planes. However, if only a single vanishing point is available then the problem is undetermined. The tilt direction must be computed using supplementary information such as the texture gradient. In this paper we describe a method for multiple vanishing point and, hence complete perspective pose estimation, which obviates the need to compute the texture gradient. The method is based on local spectral analysis. It exploits the fact that spectral orientation is uniform along lines that radiate from vanishing points on the image plane. We experiment with the new method on both synthetic and real-world imagery. This demonstrates that the method provides accurate pose angle estimates, even when the slant angle is large.

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View full text

Shape from regular patterns

Abstract

Computer Graphics and Image Processing

Artificial Intelligence

Artificial Intelligence

Artificial Intelligence

Understanding line drawing of scenes with shadows

Representing visual information—a computational approach

Recovering intrinsic scene characteristics from images

SEQUINS and QUILLS: representation for surface topography

Shape from texture: a computational paradigm

Recovery of the three-dimensional shape of an object from a single view