LAMBERTIAN REFLECTANCE AND LINEAR SUBSPACES PDF

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: ICCV We prove that the set of all reflectance functions the mapping from surface normals to intensities produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that the images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately with a low-dimensional linear subspace, explaining prior empirical results.

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A method for choosing an image from a plurality of three-dimensional models which is most similar to an input image is provided. Step d is preferably repeated for each of a red, green, and blue color component for each three-dimensional model. The linear subspace is preferably either four-dimensional or nine-dimensional. Share Patent Tools. The method of claim 1 wherein the candidate image constructed from the harmonic images is restricted to a subset of the linear subspace that corresponds to physically realizable lighting conditions.

The method of claim 1 wherein the linear subspace is spanned by a first four harmonic images. The method of claim 1 wherein the linear subspace is spanned by a first nine harmonic images. The method of claim 1 wherein the linear subspace is spanned by a first eighteen harmonic images.

The method of claim 1 wherein the candidate object is one of a plurality of candidate objects and wherein a candidate object with a three-dimensional model that generates a candidate image that is closest to the input image is selected. US B1. US A.

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US6853745B1 - Lambertian reflectance and linear subspaces - Google Patents

The present invention relates generally to computer vision and, more particularly, to image recognition and model reconstructions systems. One of the most basic problems in vision is to understand how variability in lighting affects the images that an object can produce. Even when lights are isotropic and relatively far from an object, it has been shown that smooth Lambertian objects can produce infinite-dimensional sets of images. It has been very popular in object recognition to represent the set of images that an object can produce using low dimensional linear subspaces of the space of all images.

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A method for choosing an image from a plurality of three-dimensional models which is most similar to an input image is provided. Step d is preferably repeated for each of a red, green, and blue color component for each three-dimensional model. The linear subspace is preferably either four-dimensional or nine-dimensional. Share Patent Tools. The method of claim 1 wherein the candidate image constructed from the harmonic images is restricted to a subset of the linear subspace that corresponds to physically realizable lighting conditions. The method of claim 1 wherein the linear subspace is spanned by a first four harmonic images.

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Lambertian reflectance and linear subspaces

Abstract—We prove that the set of all Lambertian reflectance functions the mapping from surface normals to intensities obtained with arbitrary distant light sources lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution.

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