pSnakes: A new radial active contour model and its application in the segmentation of the left ventricle from echocardiographic images

Active contours are image segmentation methods that minimize the total energy of the contour to be segmented. Among the active contour methods, the radial methods have lower computational complexity and can be applied in real time. This work aims to present a new radial active contour technique, called pSnakes, using the 1D Hilbert transform as external energy. The pSnakes method is based on the fact that the beams in ultrasound equipment diverge from a single point of the probe, thus enabling the use of polar coordinates in the segmentation. The control points or nodes of the active contour are obtained in pairs and are called twin nodes. The internal energies as well as the external one, Hilbertian energy, are redefined. The results showed that pSnakes can be used in image segmentation of short-axis echocardiogram images and that they were effective in image segmentation of the left ventricle. The echo-cardiologist's golden standard showed that the pSnakes was the best method when compared with other methods. The main contributions of this work are the use of pSnakes and Hilbertian energy, as the external energy, in image segmentation. The Hilbertian energy is calculated by the 1D Hilbert transform. Compared with traditional methods, the pSnakes method is more suitable for ultrasound images because it is not affected by variations in image contrast, such as noise. The experimental results obtained by the left ventricle segmentation of echocardiographic images demonstrated the advantages of the proposed model. The results presented in this paper are justified due to an improved performance of the Hilbert energy in the presence of speckle noise.