This paper presents a photometric stereo method for determining an object's shape from its appearance manifold by estimating the similarity of appearances observed at points under varying illumination. Assuming no cast shadows on the object's surface, we show that for a pair of surface points, the similarity of their observed intensities under varying illumination is closely related to the similarity of their corresponding surface normals. However, if the object is concave, there are cast shadows on the surface which alter the observed intensity of surface points and result in incorrect similarity estimation. After using a similarity measure, we find and combine similar vectors to interpolate in areas of cast shadow to create new observation values, which means that we remove cast shadows in input images. Then the object's surface normals can be estimated from the observation vector space using a dimensionality reduction technique. Unlike most previous shape reconstruction methods, our method does not require any particular reflectance model which makes it applicable to a wide variety of object materials.
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