1. An ultrasound apparatus comprising: an ultrasonic probe for capturing three-dimensional echo data; a computer configured to process the captured three-dimensional echo data, wherein the computer operates in accordance with executable instructions, that, when executed, cause the computer to be configured as a rendering processor which sets a plurality of rays with respect to volume data acquired from a three-dimensional space within a living organism and executes a rendering operation along each ray, to thereby generate an original image in the form of a three-dimensional image; and a directional interpolation processor which generates a display image based on the original image, the directional interpolation processor applying directional interpolation processing on the basis of the original image to each of noted pixels forming the display image to generate an interpolated pixel value for the noted pixel, wherein in the directional interpolation processing, a pixel reference direction for computing the interpolated pixel value is determined in a direction along a contour of a tissue which is three-dimensionally represented in the original image, and the directional interpolation processor generates, as the display image, a first display image having a first resolution based on the original image in a first display mode, the first display image being a three-dimensional image in a four view display, and generates a second display image having a second resolution different from the first resolution based on the original image in a second display mode, the second display image being an enlarged or magnified image formed by the directional interpolation processing, and by changing the magnification of the directional interpolation processing based on the number of views in the four view display, the first display image and the second display image are generated without changing the number of rays which are set with respect to the volume data beyond the number of rays used to generate the first display image.