Determining the Disparity-Blur Equation and Deriving its Concurrent Algorithm

This paper derives the disparity-blur equation, which describes an explicit relationship between stereo disparity and blur and thereby suggests a method for depth estimation by combining the two quantities. Because disparity and blur are two different aspects of the same 3D point, a direct geometric relationship in the image plane exists between them. Ordinary methods usually separately compute disparity from stereo image pairs, and a blur circle from a defocused image, and then to combine them to achieve depth estimation. Instead, the disparity-blur equation can be used as a constraint for computing disparity and blur together. We confirmed the validity of this concept by experiments both with synthetic and natural images.