Computer aided diagnostics of the breast cancer is one of the most challenging problems of the contemporary medical image processing. Computerized detection of the breast tumors from ultrasound (US) images provides the way which helps the physicians to decide whether a certain solid tumor is benign or malignant. However, it is one of the most difficult types of images to assess. We propose a new method to improve the accuracy of the tumor detection based on phase portrait analysis (PPA) applied at the preprocessing stage. The PPA works on the image gradient vector field. The algorithm detects patterns resembling standard linear flow configurations and classifies them as the noise, the boundary of the tumor or the regular point (background). The PPA is followed by the generalized gradient vector flow procedure (GGVF) and segmentation by active contours (snakes). Standard methods such as conventional filters and clustering are also included in the preprocessing scheme. We present and compare several versions of the method. The first version is a combination of PPA and multiresolution analysis (MRA). The second version called sparse phase portrait analysis (SPPA) includes clustering and subsampling. The PPA has been tested with a rule based, linear and exponential classifier. The preprocessing sequence includes the Gaussian, median and despeckling filters, fuzzy C mean clustering (FCM) and region growing (RG). The approach has been tested with a series of real US breast tumor images. The results are compared with the ground truth hand-drawn by the radiologists. The numerical experiments show that GGVF endowed with MRA and PPA over performs the conventional GGVF snakes. The SPPA is faster and easier to implement. However, it needs to be combined with a clustering procedure such as FCM. In this case its efficiency is comparable with GGVF-MRA. The both procedures benefit from additional preprocessing and the continuous linear or exponential classifier.