Accurate reconstruction of three-dimensional shape and focused image from a sequence of noisy defocused images

A new approach is proposed for highly accurate reconstruction of 3D shape and focused image of an object from a sequence of noisy defocused images. This approach unifies the two approaches- image focus analysis and image defocus analysis, which have been treated separately in the research literature so far. In the new unified approach, high accuracy is attained at the cost of increased data acquisition and computation. This approach is based on modeling the sensing of defocused images in a camera system. A number of images are acquired at different levels of defocus. The resulting data is treated as a function sampled in the 3D space where x and y are the image spatial coordinates and d is a parameter representing the level off defocus. The concept of a "Three-Dimensional Point Spread Function" (3D PSF) in the (x, y, d) space is introduced. The problem of 3D shape and focused image reconstruction is formulated as an optimization problem where the difference between the observed image data and the estimated image data is minimized. The estimated image data is obtained from the image sensing model and the current best known solutions to the 3D shape and focused image. An initial estimation to the solutions is obtained through traditional shape-from-focus methods. This solution is improved iteratively by a gradient descent approach. This approach reduces the errors in shape and focused image introduced by the image-overlap problem and the non- smoothness of the object's 3D shape. Experimental results are presented to show that the new method yields improved accuracy.