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Ultrasonic image segmentation is a difficult problem due to speckle noise, low contrast, and local changes of intensity. Intensity-based methods do not perform particularly well on ultrasound images. However, it has been previously shown that these images respond well to local phase-based methods which are theoretically intensity invariant. Here, we use level set propagation to capture the left ventricle boundaries. The proposed approach uses a new speed term based on local phase and local orientation derived from the monogenic signal, which makes the algorithm robust to attenuation artifact. Furthermore, we use Cauchy kernels, as a better alternative to the commonly used log-Gabor, as pair of quadrature filters for the feature extraction. Results on synthetic and natural data show that the proposed method can robustly handle noise, and captures well the low contrast boundaries.