1. An ultrasonic image processing apparatus, comprising: a contour tracking part configured to receive ultrasonic image data acquired at each time phase by scanning a subject with ultrasonic waves, further receive designation of a contour of a specific tissue shown in an ultrasonic image based on ultrasonic image data acquired at an arbitrary time phase, and obtain a position of each of points composing the contour of the specific tissue in the ultrasonic image data acquired at the each time phase by pattern matching at each time phase based on the ultrasonic image data acquired at the each time phase; a computing part configured to obtain motion information of each of parts composing the specific tissue at each time phase based on the position of each of the points composing the contour, obtain a differential value of the motion information of each of the parts at each time phase by differentiating the motion information of each of the parts with respect to time, divide the differential value of the motion information at each of the parts by a maximum value of an absolute value of the motion information at each of the parts to obtain a normalized differential value of the motion information at each of the parts at each time phase, and assign a color corresponding to a magnitude of the normalized differential value of the motion information to each of the parts; and a display controller configured to control a display device to display an ultrasonic image based on the ultrasonic image data acquired at the each time phase, and further control to display each of the parts of the specific tissue shown in the ultrasonic image of the each time phase in a color assigned to each of the parts.