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Proceedings Paper

Considering shape from shading as an estimation problem
Author(s): Zweitze Houkes; Maarten J. Korsten
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Paper Abstract

This paper presents a method combining shape and shading models in order to obtain estimations of 3D shape parameters directly from image grey values. The problem is considered as an application of optimal parameter estimation theory, according to Liebelt 8 This theory has been applied previously, where the emphasis was laid on time-delay 2, and motion estimation 3, 5, 9. It is applied here to provide an environment in which somewhat more complicated models can be designed with relative ease and to indicate how the behaviour of the parameters can be investigated. A shading model is added, offering explicit prediction of image grey values. We consider the problem for a single image and for an image pair, showing the shade of the object at two consecutive points of time. The last problem requiresalso a model for the motion of the body. The resulting non-linear estimation problem is linearized about a last parameter guess 8,so that a linear estimator can be applied to compute a new estimate. The various stages of the modelling process are separated by introducing several coordinate systems. Coordinate transformations will show the object from other points of view, and perform an orthographic projection of the 3D scene into the 2D image plane. The explicit grey value prediction yields a template, having a definite extent in the image. Because of the shading model this method requires no gradient images, as in the case of motion estimation 6 or stereo 5. The gradients can be computed analytically. To demonstrate the usefulness and the flexibility of our method, we consider a solid cylinder, irradiated with X-rays. The image is a shadow image originating from the absorption of radiation by the cylinder. In section 2 some background is given about the theory of parameter estimation from digital images. In section 3 the various models for the shape and motion of the body and the imaging process are given. In section 4 and 5 we investigate the properties of the estimator. In section 4 identifiability and uniqueness of the parameters are considered, yielding the parameters, that can be estimated uniquely from the image data. In section 5 some examples are given, elucidating the stabilty properties of the algorithm. To conclude we mention the possibility to replace the motion model with a model connecting images taken from two different positions. Thus this method is also suited to handle a stereo configuration.

Paper Details

Date Published: 1 June 1990
PDF: 12 pages
Proc. SPIE 1244, Image Processing Algorithms and Techniques, (1 June 1990); doi: 10.1117/12.19495
Show Author Affiliations
Zweitze Houkes, Univ. of Twente (Netherlands)
Maarten J. Korsten, Univ. of Twente (Netherlands)

Published in SPIE Proceedings Vol. 1244:
Image Processing Algorithms and Techniques
Robert J. Moorhead II; Keith S. Pennington, Editor(s)

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