Complex-Valued Disparity: Unified Depth Model of Depth from Stereo, Depth from Focus, and Depth from Defocus Based on the Light Field Gradient.

This paper proposes a unified depth model based on the light field gradient, in which estimated disparity is represented by the complex number. The complex-valued disparity by the proposed depth model can be represented in both the Cartesian and polar coordinates. In the Cartesian representation, the proposed depth model is represented by real and imaginary parts of the disparity. The real part can be used for disparity estimation with respect to the in-focus plane, whereas the imaginary part represents the non-Lambertian-ness. In the polar representation, the proposed depth model is expressed by the disparity magnitude and disparity angle. The disparity magnitude shows the relationship among depth from stereo, depth from focus, and depth from defocus, whereas the disparity angle shows whether or not the bundles of rays are flipped with respect to the in-focus plane. For disparity analysis, we present the real response, imaginary response, magnitude response, and angle response, which are represented by the three-dimensional volume. Experimental results on synthetic and real light field images show that the real and magnitude responses of the proposed depth model are valid for local disparity estimation.