Abstract
This paper presents a new method based on Estimation of Distribution Algorithms (EDAs) to detect parabolic shapes in synthetic and medical images. The method computes a virtual parabola using three random boundary pixels to calculate the constant values of the generic parabola equation. The resulting parabola is evaluated by matching it with the parabolic shape in the input image by using the Hadamard product as fitness function. This proposed method is evaluated in terms of computational time and compared with two implementations of the generalized Hough transform and RANSAC method for parabola detection. Experimental results show that the proposed method outperforms the comparative methods in terms of execution time about 93.61% on synthetic images and 89% on retinal fundus and human plantar arch images. In addition, experimental results have also shown that the proposed method can be highly suitable for different medical applications.
Highlights
In the pattern recognition field, detection of curves in natural or medical images is a significant and challenging problem since relevant information about an object is highly related to the shape of its boundary
In order to assess the proposed method, it is compared with the Hough transform by applying the algorithm of Sanchez found in the MATLAB central [25] and by running the Hough transform for parabolic shapes algorithm provided by the MIPAV [26] software, that can be downloaded from the website [37]
Considering that MIPAV and MATLAB parabola detection implementations are based on Hough transform, Randomized Sampled Consensus (RANSAC) algorithm [21] was implemented to analyze the performance of the proposed algorithm
Summary
In the pattern recognition field, detection of curves in natural or medical images is a significant and challenging problem since relevant information about an object is highly related to the shape of its boundary. The CHT is able to detect suitable approximation to circles in different type of images, the computational time to detect a single curve is high This disadvantage is due to the fact that each single pixel represents a potential center (x0, y0), and a range of possible radii have to be tested for each particular pixel. AyalaRamirez et al [6] optimize the computational time of the CHT, by applying a strategy consisting in selecting three random pixels from the edge image as the chromosomes for the genetic algorithm These three points are used to calculate a center and radius of a circle, and the fitness function evaluates how many pixels of a virtual circle are present in the real edge image
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