## 1 Introduction  
The task of automatic segmentation of coronary arteries in X-ray angiograms can be integrated in a computer-aided diagnosis system (CAD) to support the analysis of coronary heart disease. In cardiology, the X-ray coronary angiogram is the gold standard employed to evaluate and monitor abnormalities of the coronary arteries. However, the detection of blood vessels in coronary angiograms is a challenging task for the current CAD systems. The most common problems that are present in coronary angiograms involve the non-uniform illumination, weak contrast between arterial features and image background, and occlusion caused by different organs or medical devices in the acquired images. In the literature, the challenge of automatic detection of blood vessels has been widely addressed by different methods. A common approach is the use of operators and transformations from the mathematical morphology framework. The most used strategy to enhance vessel-like structures is the Top-hat operator, which was applied by [PERSON] and [PERSON] [1] in coronary angiograms. The Top-hat response is combined with an interactive procedure to segment the main artery using another morphological operator. Later, a multiscale approach composed for the Top-hat filter responses of a number of structuring elements at different size was proposed by [PERSON] et al. [2]. This method allows the automatic detection of vessels with different diameters in a single medical image. Other common methodology is based on the information of the Hessian matrix of the medical image. In this approach, the gradient of an image is defined as the convolution of itself and the first order derivative of a Gaussian curve. Consequently, the Hessian matrix of the image is the second order derivative of a Gaussian curve convolved with the image. [PERSON] et al. [3] proposed the enhancement of tubular structures, such is the case of blood vessels, by using a vesselness measure defined from the eigenvalues of the Hessian matrix. For the particular problem of detection of coronary arteries in X-ray angiograms, multiple vesselness measures have been recently proposed. [PERSON] et al. [4] used the eigenvalues of the Hessian matrix to construct a vessel probability map; in a similar manner, [PERSON] et al. [5] proposed the generation of a vessel feature map also from the Hessian matrix using a different vesselness measure. These two works use the vessel map as starting point for a region growing method to segment the coronary artery tree. On the other hand, methods based on matching templates have considered the shape of a blood vessel in the spatial domain to propose a suitable model. [PERSON] et al. [6] introduced a two dimensional Gaussian Matched Filter (GMF) for the enhancement of blood vessels in retinal fundus images. GMF is founded under the fact that in the spatial domain the cross-section of a blood vessel is Gaussian shaped. In addition, GMF assumes that vessels can be modeled in segments that share the same orientation and diameter. To detect vessel segments at different orientations, a directional filter bank is built by rotating the GMF template into a number of evenly spaced directions in the range \([-\pi/2,\pi/2]\) to be later convolved with the input image. Methods based on the GMF have modified the parameters that govern the shape of the matching template and the number of orientations. Most of them have selected the parameters empirically, such is the case of the method proposed by [PERSON] and [PERSON] [7], where the number of directional templates is increased in order to improve the detection performance. In the method proposed by [PERSON] et al. [8], the parameters were empirically modified to allow the detection of arteries in coronary angiograms. Moreover, some methods have addressed the selection of the parameters by a training step prior to its application. A first approach is the proposed by [PERSON] et al. [9], where a full-search of the parameters was employed.