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The Local Character of Luminance Transitions

The purpose is to identify the computational requirements for accurate characterization of luminance transitions caused by defocused edges, shadow penumbrae and high-curvature shading. Results have shown that attempts to understand human sensitivity to spatial luminance modulations in terms of scene structure have typically distinguished the problems of edge detection and shading interpretation. We show that this distinction is artificial, in that the luminance variations produced by defocused step edges, the penumbrae of cast shadows, and shading over high-curvature surfaces are mathematically equivalent. We therefore propose that the goal of early visual processing of luminance transitions is not to distinguish but rather to reliably detect, localize and characterize these stimuli. This observation motivates a computational theory which rests on two key findings. First, we show that while 1st derivative (2-lobe, odd-phase) filters are by themselves inadequate, the conjunction of first- and second-order (3-lobe, even-phase) derivative estimates are sufficient to accurately localize and estimate the blur and contrast of luminance edges. Second, while previous considerations of the problem of scale in edge detection have led to global solutions over a complete scale space, we show that in fact this problem has a local solution. This solution relies on the notion of a minimum reliable scale which can be related to the parameters of the luminance transition, blurring processes, and receptor uncertainty. This result is relevant to the puzzle of how responses of filters of different sizes are arbitrated to produce a unique characterization of the local luminance pattern. We demonstrate the effectiveness of this theory by experiments on images with small depth of field and shadows cast by extended light sources. We show that edges over a wide range of blur and contrasts can be reliably recovered, and that the accurate estimation of blur allows the inference of complete space curves from the image. These space curves provide continuous estimates of depth from the focal plane in the case of defocus and of the distance between objects in the scene in the case of cast shadows. The conclusions show that

  1. The characterization of generalized luminance transitions is a second order differential problem.
  2. The problem of scale in edge detection has a local solution in the form of a minimum reliable scale defined by the contrast and blur of the luminance transition and the statistics of the receptor noise.

J. Elder, S.W. Zucker



next up previous contents
Next: Independence of Texture Up: Computer Vision Previous: Scale Space Surfaces



Thierry Baron
Mon Nov 13 10:43:02 EST 1995