Granulometry is the process of measuring 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 a entirely new approach for the granulometry using the cross correlations with circles of different sizes. This technique is primarily adequate for detecting circular-shaped objects, but it can be extended to other shapes using other correlation kernels. Experiments show that the new algorithm is greatly robust to noise and can detect even faint objects. This paper also reports the quantitative structural characteristics of the porous silicon layer based on the proposed algorithm applied to Scanning Electron Microscopy (SEM) images. The new algorithm computes the size distribution of pores and classifies the pores in circular or square ones. We relate these quantitative results to the fabrication process and discuss the square porous silicon formation mechanism. The new algorithm shows to be reliable in SEM images processing and is a promising tool to control the pores formation process. IntroductionGranulometry is the process of measuring sizes of different objects/grains in an image of granular material. The granulometric curve or pattern spectrum of an image is the histogram of objects as the function of radius. The objective of the granulometry is, given an image, to obtain its pattern spectrum. There are two main groups of image-based granulometry algorithms: Mathematical morphology-based algorithms;  Edge detection-based algorithms.Mathematical morphology-based granulometry obtains the pattern spectrum of an image without explicitly segmenting it. Dougherty et al. present a popular morphologybased granulometry for binary images (1). Raimundo et al. used this algorithm to characterize porous material (2). Unfortunately, this algorithm cannot be directly applied to grayscale images. If the original image is grayscale, the algorithm must somehow convert it into a binary image and any binarization discards many important information. Vincent presents a morphology-based granulometry for grayscale images (3). A demonstration program of this algorithm with source code is available at (4). This algorithm seems to be scarcely used in practice. Indeed, the output of this algorithm is highly non-intuitive, difficult to be used in practice. It represents the pattern spectrum as the "sum of pixel values in opened image as a function of radius." Ordinaly, the user wants to obtain simply the "quantity of objects as a function of radius." Moreover, in many applications the spatial localization of each grain is important, and this information is not provided by grayscale morphology granulometry. Edge detection-based granulometry detects the edges of the image using conventional gradient operators and thresholding (5). Then, it delimitates the objects using the edges. Edge-detection is a noise-sensible operation and may not be reliable, especially in blurred low-contrast images. This paper presents a entirely ne...

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.

, meu orientador, pelo incentivo e compreensão no desenvolvimento deste trabalho. Ao Prof. Dr. Hae Yong Kim cuja perseverança e apoio permitiram o desenvolvimento do programa Granul. A minha esposa Conceição (in memorium) e filhos Fabrício, Fábio e Priscilla pelo esforço, incentivo e compreensão nos momentos de fraqueza durante o desenvolvimento deste trabalho. Aos meus pais, Akemi e Nobuiti (in memorium), e irmãos Élcio (in memorium), Márcio, Cláudia e Celso pela possibilidade do desenvolvimento educacional e profissional ao longo de minha vida. Ao meu amigo Guillermo Angel Perez Lopez cujas discussões e reflexões permitiram a elaboração deste trabalho. Ao grupo de microeletrônica, especialmente a Danilo Roque Huanca, que com paciência, alegria e compreensão possibilitou a realização deste trabalho em conjunto. Ao Laboratório de Microscopia Eletrônica da Escola Politécnica, especialmente a Adir José Moreira, pela obtenção das imagens utilizadas no trabalho, material técnico para o conhecimento do equipamento e momentos de descontração no laboratório. Ao Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq-pela bolsa de estudos concedida.