1. An image processing apparatus which processes image data and outputs the processed image data, comprising: a maximum/minimum density detecting unit detecting whether a center pixel of a matrix of N×N pixels in the image data has a maximum or minimum density among the pixels of the matrix; a center pixel selecting unit selecting one of neighboring pixels of the matrix adjacent to the center pixel as being an active center pixel; a diagonal pixel selecting unit selecting one of pairs of diagonal pixels of the matrix at positions symmetrical with respect to the center pixel as being active diagonal pixels; a determination unit determining whether the absolute value of a difference between an average of densities of all the pairs of diagonal pixels selected by the diagonal pixel selecting unit and a density of the center pixel selected by the center pixel selecting unit is larger than a predetermined threshold value; a peak pixel detecting unit detecting peak pixels of the matrix, each peak pixel being the center pixel detected as having the maximum or minimum density by the maximum/minimum density detecting unit, and the absolute value of the difference with respect to the center pixel determined as being larger than the threshold value by the determination unit; and a dot region detecting unit detecting one of the neighboring pixels including the peak pixels as being a dot region based on a relationship between the number of the peak pixels in a two-dimensional target region and the number of the peak pixels in each of two-dimensional neighboring regions of the target region.