1. An image processing apparatus comprising: an intermediate image generating unit configured to generate a first horizontal intermediate image by extracting a horizontal component in a particular frequency band in an input image and a first vertical intermediate image by extracting a vertical component in a particular frequency band in the input image; an intermediate image processing unit configured to generate a second intermediate image from the first horizontal intermediate image and the first vertical intermediate image; and a first adding unit configured to add the input image and the second intermediate image; wherein the intermediate processing unit includes a horizontal non-linear processing unit with processing content that varies from pixel to pixel in the first horizontal intermediate image, and a vertical non-linear processing unit with processing content that varies from pixel to pixel in the first vertical intermediate image; and wherein the intermediate image processing unit has a second adding unit configured to add the first horizontal intermediate image, the first vertical intermediate image, a second horizontal intermediate image obtained by processing an output of the horizontal non-linear processing unit, and a second vertical intermediate image obtained by processing an output of the vertical non-linear processing unit, and to output a resulting sum as the second intermediate image; and wherein the second adding unit comprises at least one of a first horizontal-vertical combining unit conjured to take a weighted sum of the first horizontal intermediate image and the first vertical intermediate image, and a second horizontal-vertical combining unit conjured to take a weighted sum of the second horizontal intermediate image and the second vertical intermediate image.