A video encoding apparatus, video encoding method, and computer program, which are capable of employing an adaptive filter that provides improved encoding performance while reducing the processing cost required for calculation. A video encoding apparatus estimates interpolation filter coefficients by means of an image frequency characteristic analysis. When a loop continuation condition is satisfied, the video encoding apparatus performs re-estimation of the interpolation filter coefficients. As the loop continuation condition, a first condition can be used, in which the number of times the re-estimation has been consecutively performed for the current frame to be processed is smaller than a predetermined number, for example.