1. An image processing apparatus comprising: a processor that: inputs color image data obtained by capturing an image at a given imaging sensitivity, the input color image data includes RGB values having linear gradation characteristics; executes a first conversion to a uniform color and uniform noise space on the input color image data, wherein: in the first conversion, the RGB values are transformed into CIE XYZ values, and the CIE XYZ values having been transformed are converted to L^a^b^ values having non linear characteristics by using a function f(t)=(t+ε) 1/2 where f(t) denotes an output gradation scale, t denotes an input gradation scale and c denotes a positive offset having an increasing function increasing according to a value of the imaging sensitivity, the L^ designating a luminance value and the a^ and b^ designating chrominance values; executes a specific image processing on the color image data having undergone the first conversion, the specific image processing being executed by using the L^a^b^ values having been converted; executes a second conversion reverse to the first conversion on the color image data having undergone the specific image processing; and outputs the color image data having undergone the second conversion.