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Fourier cues to 3-D shape


Fleming,  RW
Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;

Bülthoff,  HH
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Fleming, R., & Bülthoff, H. (2005). Fourier cues to 3-D shape. Talk presented at 28th European Conference on Visual Perception. A Coruña, Spain.

If you pick up a typical vision text, you'll learn there are many cues to 3-D shape, such as shading, linear perspective, and texture gradients. Much work has been done to study each cue in isolation and also how the various cues can be combined optimally. However, relatively little work has been devoted to finding commonalities between cues. Here, we present theoretical work that demonstrates how shape from shading, texture, highlights, perspective, and possibly even stereopsis could share some common processing strategies. The key insight is that the projection of a 3-D object into a 2-D image introduces dramatic distortions into the local image statistics. It does not matter much whether the patterns on a surface are due to shading, specular reflections, or texture: when projected into the image, the resulting distortions reliably cause anisotropies in the local Fourier spectrum. Globally, these anisotropies are organised into smooth, coherent patterns, which we call 'orientation fields'. We have argued recently [Fleming et al, 2004 Journal of Vision 4(9) 798 - 820] that orientation fields can be used to recover shape from specularities. Here we show how orientation fields could play a role in a wider range of cues. For example, although diffuse shading looks completely unlike mirror reflections, in both cases image intensity depends on 3-D surface orientation. Consequently, derivatives of surface orientation (curvature) are related to derivatives of image intensity (intensity gradients). This means that both shading and specularities lead to similar orientation fields. The mapping from orientation fields to 3-D shape is different for other cues, and we exploit this to create powerful illusions. We also show how some simple image-processing tricks could allow the visual system to 'translate' between cues. Finally, we outline the remaining problems that have to be solved to develop a 'unified theory' of 3-D shape recovery.