A generative focus measure with application to omnifocus imaging

Given a stack of registered images acquired using a range of focus settings (focal stack images), we propose a new focus measure to identify the most focused image. Although, most of the paper is concerned with the new focus measure, for evaluation purposes, we will present it in the context of an application to generating omnifocus images. An omnifocus image is the composite image in which each pixel is selected form the frame in the stack in which it appears to be in best focus. Conventional focus measures usually maximize some measure of image gradient in a window. They tend to fail when one of the edges of the window lies near the boundary of an intensity edge, or the pixel is near other complex edge patterns. This leads to the misidentification of the focused frame and formation of artifacts in omnifocused image. Our proposed measure does not attempt to identify the focused frame by calculating the degree of defocus, like the gradient based methods. Rather, it hypothesizes that a specific frame is in focus and then validates or rejects this hypothesis by recreating the defocused frames in the vicinity, and comparing them with the observed de-focused frames. This forward generative process leads to correct focus frame selection in regions where typical measures fail. This is because the conventional measures try to identify the focused frame from its distorted version which is the result of a complex convolution process. This involves a backward estimation for a many-to-one transformation. On the other hand, the generation of defocused frames from a hypothesized focused frame is more accurate since it involves applying an operator in the forward direction. We analytically show that under ideal imaging conditions, the proposed focus measure is unimodal in nature. This makes the search for the best focused image unambiguous. We evaluate our focus measure by generating omnifocus images from real focal stack images, and show that it performs better than all the existing focus measures.