Utilização de equações diferenciais parciais para eliminação de ruídos e detecção de bordas

Abstract

The edge detection of digital images is a research field that has attracted great interest from the scientific community. Their applications go from the automatic inspection and quality control of industrial piece to the diagnosis of malignancy of cancerous tumors. However, many existing edge detectors have problems related to false edge detection. In this context, the great challenge is to find methods which minimizes the detection of false edges, usually originating from noise, illumination lack, hair, grass, foliage, etc. It is for this reason that in this work we propose two methods for edge detection that are based on the partial differential equations. The first, inspired in the works proposed in [Grigorescu et al. 2003, Grigorescu et al. 2004, Galvanin et al. 2006], consists in the combining of two techniques of existent edge detection: the nonlinear diffusion model proposed by [Barcelos et al. 2003] and the Canny edge detector with anisotropic surround suppression. The goal is to use the nonlinear diffusion model to smoothen the image of interest, to remove noises and at the same time to preserve edges. Soon afterwards the Canny edge detector with anisotropic surround suppression is applied on the smoothed image to remove textures and obtain the final edge map. The second method consists of the modification of the Canny detector where we substituted the smoothing technique used by Canny by another more efficient one, based on the nonlinear diffusion equation proposed by [Barcelos et al. 2003]. To evaluate the performance of the proposed methods, several experiments were accomplished in a collection of natural images and corrupted images with gaussian noise. The obtained results were compared with the results obtained with the other three detectors: the Canny edge detector [Canny 1986], the Canny edge detector with anisotropic surround suppression [Grigorescu et al. 2004] and edge detector proposed in [Papari et al. 2006b]. In all accomplished experiments, we verified that the proposed edge detectors have the best performance in terms of false edge reduction. We also verified that the second method outperforms the first. To show the efficiency of the proposed detectors in real problems, we applied the second proposal in images of skin cancer. In this case, the goal is to help dermatologists in the clinical diagnosis of skin lesions, since they have difficulties in finding the lesion edges, mainly when the variation between the lesion and the skin is smooth. The results showed that the proposed strategy is efficient.