Eigenspace models are a convenient way to represent sets of observations with widespread applications, including classification. In this paper we describe a new constructive method for incrementally adding observations to an eigenspace model. Our contribution is to explicitly account for a change in origin as well as a change in the number of eigenvectors needed in the basis set. No other method we have seen considers change of origin, yet both are needed if an eigenspace model is to be used for classification purposes. We empirically compare our incremental method with two alternatives from the literature and show our method is the more useful for classification because it computes the smaller eigenspace model representing the observations.
Bas-reliefs are a form of flattened artwork, part-way between 3D sculpture and 2D painting. Recent research has considered automatic bas-relief generation from 3D scenes. However, little work has addressed the generation of bas-reliefs from 2D images. In this paper, we propose a method to automatically generate bas-relief surfaces from frontal photographs of human faces, with potential applications to e.g. coinage and commemorative medals.Our method has two steps. Starting from a photograph of a human face, we first generate a plausible image of a bas-relief of the same face. Secondly, we apply shape-from-shading to this generated bas-relief image to determine the 3D shape of the final bas-relief. To model the mapping from an input photograph to the image of a corresponding bas-relief, we use a feedforward network. The training data comprises images generated from an input 3D model of a face, and images generated from a corresponding bas-relief; the latter is produced by an existing 3D model-to-bas-relief algorithm. A saliency map of the face controls both model building, and bas-relief generation.Our experimental results demonstrate that the generated bas-relief surfaces are smooth and plausible, with correct global geometric nature, the latter giving them a stable appearance under changes of viewing direction and illumination.
The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. B-rep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitable for purposes such as redesign because expected regularities and constraints are not present. This information is lost because each face of the model is determined independently. A global approach is required, in particular one that is capable of finding symmetries originally present. This paper describes a practical algorithm for finding global symmetries in suitable B-rep models built from planes, spheres, cylinders, cones and tori. It has been implemented and used to determine approximate symmetries of models with up to about 200 vertices in reasonable time. The time performance of the algorithm in the worst case is bounded by O (n s'5 log 4 n), and a justification is given that on corn-2 mon engineering objects it takes about O(n log n), making it a practical tool for use in a reverse engineering package. Details of the algorithm are given, along with some results from a number of illustrative test runs.
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