Edge and Depth from Focus

This paper proposes a novel method to obtain the reliable edge and depth information by integrating a set of multi-focus images, i.e., a sequence of images taken by systematically varying a camera parameter focus. In previous work on depth measurement using focusing or defocusing, the accuracy depends upon the size and location of local windows where the amount of blur is measured. In contrast, no windowing is needed in our method; the blur is evaluated from the intensity change along corresponding pixels in the multi-focus images. Such a blur analysis enables us not only to detect the edge points without using spatial differentiation but also to estimate the depth with high accuracy. In addition, the analysis result is stable because the proposed method involves integral computations such as summation and least-square model fitting. This paper first discusses the fundamental properties of multi-focus images based on a step edge model. Then, two algorithms are presented: edge detection using an accumulated defocus image which represents the spatial distribution of blur, and depth estimation using a spatio-focal image which represents the intensity distribution along focus axis. The experimental results demonstrate that the highly precise measurement has been achieved: 0.5 pixel position fluctuation in edge detection and 0.2% error at 2.4 m in depth estimation.