Correlation-based multi-shape granulometry with application in porous silicon nanomaterial characterization

Image-based granulometry measures the size distribution of objects in an image of granular material. Usually, algorithms based on mathematical morphology or edge detection are used for this task. We propose an entirely new approach, using cross correlations with kernels of different shapes and sizes. We use pyramidal structure to accelerate the multi-scale searching. The local maxima of cross correlations are the primary candidates for the centers of the objects. These candidate objects are filtered using criteria based on their correlations and intersection areas with other objects. Our technique spatially localizes each object with its shape, size and rotation angle. This allows us to measure many different statistics (besides the traditional objects size distribution) e.g. the shape and spatial distribution of the objects. Experiments show that the new algorithm is greatly robust to noise and can detect even very faint and noisy objects. We use the new algorithm to extract quantitative structural characteristics of Scanning Electron Microscopy (SEM) images of porous silicon layer. The new algorithm computes the size, shape and spatial distribution of the pores. We relate these quantitative results to the fabrication process and discuss the rectangle porous silicon formation mechanism. The new algorithm is a reliable tool for the SEM image processing.