3D Surface Orientation from Texture Gradient

3D Surface Orientation from Texture Gradient computed in a single image of a homogeneously textured surface.

In an image containing texture elements at a range of scales, detect all elements, their relative locations and mutual containment relationships.

Given a slanted view of a planar, homogeneously textured surface, estimate the surface slant from the image texture gradient.

(1) Identification of image texture elements (texels) that correspond to surface texture elements is itself a significant problem since the scale at which surface detail is captured varies continuously with the three-dimensional distance, and therefore across the image texture. The image texels may exhibit a systematic variation in a priori unknown properties, e. g., size, density or contrast. All regions are potential texels. Consequently, all regions, of all sizes and contrasts, are detected at each location and treated as candidate texels.

(2) The estimation of surface slope (slant and tilt) is integrated with the process of selecting texels from among the large number of detected regions. For any given slant and tilt, only those regions across the image are interpreted as texels whose properties, e. g., area distribution, match the spatial distribution predicted by the hypothesized slant and tilt, and which occupy the largest fraction of the image. The image area is used as a measure of  the extent of support for the particular slant-tilt pair.

(3) All possible slant-tilt values are considered as hypotheses, and a search is conducted to find the hypothesis with most support. This is the estimated surface orientation.

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