Defect Detection on Inclined Textured Planes Using the Shape from Texture Method and the Delaunay Triangulation
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Defect Detection on Inclined Textured Planes Using the Shape from Texture Method and the Delaunay Triangulation Justin Plantier Cognitive Science Department, IMASSA, BP 73, 91223 Br´etigny-sur-Orge, France Email: [email protected]
Laurent Boutte´ CEMIF-LSC, Universit´e d’Evry, 40 rue du Pelvoux, CE 1455 Courcouronnes, 91020 EVRY Cedex, France Email: [email protected]
Sylvie Lelandais CEMIF-LSC, Universit´e d’Evry, 40 rue du Pelvoux, CE 1455 Courcouronnes, 91020 EVRY Cedex, France Email: [email protected] Received 20 July 2001 and in revised form 13 March 2002 We present one method for detecting defects on an inclined textured plane. This method uses a combination of a shape from texture (SFT) method with the Delaunay triangulation technique. The SFT method provides the theoretical equation of the plane orientation in two steps. First, a wavelet decomposition allows us to build an image of the inverse of the local frequency, that is the scale, that we call the local scales map. Then we perform an interpolation of this map using the equation of the theoretical variation of the scales. With the interpolation parameters it is possible to extract the texels by the use of an adaptive thresholding for each pixel of this map. Then we compute the centers of each texel in order to match a mesh on it after processing a Delaunay triangulation. When there is a defect, the regularity of the triangulation is disturbed, so one hole appears in the mesh. Keywords and phrases: defect detection, inclined textured planes, wavelet decomposition, local scales, texels extraction, shape from texture method, Delaunay triangulation.
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INTRODUCTION
It is not easy to detect defects on an inclined plane because the relations between the different points are modified according to the orientation of the plane. In this paper, we present one way to detect defects on an inclined plane which is covered by a regular macrotexture. Two steps are necessary for this method. First, we compute the local scale of each pixel of the image by a wavelet decomposition. An interpolation of the local scales map gives the equation of the plane orientation. Then we threshold the local scales map in order to extract the texels of the original image. With the previous equation it is possible to obtain a threshold value for each pixel. After that, we compute the gravity centers of the texels and map a mesh on it using a Delaunay triangulation. The triangulation is regular when there is no defect. When there is a defect, the regularity of the triangulation is disturbed and it is not possible to build the mesh. Then, to look for defects is the same as looking for holes in the mesh. Some results of
this fully automatic method, obtained on synthetic and real textures, will be shown. Much work has been performed with the aim to analyze textures [1]. Since Haralick’s work with the co-occurrence matrix which allows classification of microtextures [2], several authors have proposed methods for texture segmentation [1, 3, 4, 5]. In our application, we want to
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