3D shape from focus using LULU operators and discrete pulse transform in the presence of noise

3D shape recovery is an interesting and challenging area of research. Recovering the depth information of an object from a sequence of 2D images with varying focus is known as shape from focus. Focus value of an image carries information about the object and shape from focus is a method which depends on different focused value images. It reconstructs the shape/surface/depth of an object based on the different focused values of the object. These different focused valued images should be captured from the same angle. Calculating the shape of the object from different images with different focused values can be done by applying sharpness detection methods to maximize and detect the focused values. In this paper, we propose new 3D shape recovery techniques based on LULU operators and discrete pulse transform. LULU operators are nonlinear rank selector operators that are efficient with low complexity. They hold consistent separation, total variation and shape preservation properties. Discrete pulse transform is a transform that decomposes image into pulses. Therefore selection of right pulses, give sharpest focus values. The proposed techniques provide better result than traditional techniques in a noisy environment.