Sampling-Noise Modeling & Removal in Shape From Focus Systems Through Kalman Filter

Shape from Focus (SFF) is one of the passive techniques to recover the shape of an object under consideration. It utilizes the focus cue present in the stack of images, obtained by a single camera. In SFF when the images are acquired, the inter-frame distance, also known as the sampling step size, is assumed to be constant. However, in practice, due to mechanical constraints, sampling step size cannot remain constant. The inconsistency in the sampling step size causes the problem of jitter, and produces Jitter noise in focus curves. This Jitter noise is not visible in images, because each pixel in an image (of the stack) will be subjected to the same error in focus. Thus, traditional image denoising techniques will not work. This paper formulates a model of the Jitter noise, followed by the design of system and measurement models for Kalman filter. Then, the jittering problem for SFF systems is solved using the proposed filtering technique. Experiments are performed on simulated and real objects. Ten noise levels are considered for simulated, and four for real objects. RMSE and Correlation are used to measure the reconstructed shape. The results show the effectiveness of the proposed scheme.