1. A medical image display apparatus comprising: a diagnostic image displaying unit configured to display a diagnostic image generated by voxel values in a predefined range formed along a predefined direction in volume data based on a slice image group; a range dividing unit configured to divide a range after changing as the range to an overlapping range that the range after changing overlaps a range before changing, and a non-overlapping range that not includes the overlapping range, when a position of the range is changed; a pixel value after changing setting unit configured to set a pixel value after changing based on a pixel value constituting a diagnostic image before changing and voxel values along the predefined direction in the non-overlapping range according to a predefined condition about one pixel that a position of a voxel value in the volume data corresponding to the pixel value constituting the diagnostic image before changing exists in the overlapping range, and based on voxel values along the predefined direction in the range after changing according to the predefined condition about the other pixel that the position does not exist in the overlapping range, among each pixels constituting a diagnostic image after changing generated based on the voxel values along the predefined direction in the range after changing; and a diagnostic image generating unit configured to generate the diagnostic image after changing based on the pixel value after changing set by the pixel value after changing setting unit.