1. An image processing device determining a depth of a target object in real space by performing image processing, the image processing device comprising: a generator generating an X-axis histogram for a designated color and a Y-axis histogram for the designated color, the X-axis histogram indicating a pixel count at each of a plurality of coordinates along an X-axis, the Y-axis histogram indicating a pixel count at each of a plurality of coordinates along a Y-axis, the X-axis and the Y-axis being axes of a screen, a pixel count at a given coordinate indicating the number of pixels having the designated color at the given coordinate in frame image data obtained by filming the real space; a smoother performing smoothing of the X-axis histogram and the Y-axis histogram to acquire a smoothed X-axis histogram and a smoothed Y-axis histogram, respectively; and a depth determiner determining three-dimensional coordinates of the target object using the smoothed X-axis histogram and the smoothed Y-axis histogram, wherein the three-dimensional coordinates are expressed as (Xu, Yu, f(h1(Xu), h2(Yu))) when Xu is an X coordinate in the smoothed X-axis histogram, h1(Xu) is a pixel count at the coordinate Xu, Yu is a Y coordinate in the smoothed Y-axis histogram, h2(Yu) is a pixel count at the coordinate Yu, and f(h1(Xu), h2(Yu)) is a function for determining a Z coordinate from the pixel count h1(Xu) and the pixel count h2(Yu), the pixel count h1(Xu) and the pixel count h2(Yu) determine a centroid intersecting at a center of the target object, the function f(h1(Xu), h2(Yu)) determines the Z coordinate of the target object based on a length of the centroid determined by the X-axis histogram and the Y-axis histogram, the smoothing for the smoothed X-axis histogram and the smoothed Y-axis histogram involves applying an impulse response convolution to pixel counts at the coordinates in the X-axis histogram and pixel counts at the coordinates in the Y-axis histogram, the smoothed X-axis histogram includes a peak pixel count at the center along the X-axis and pixel counts approaching zero at edges along the X-axis, and the smoothed Y-axis histogram includes a peak pixel count at the center along the Y-axis and pixel counts approaching zero at edges along the Y-axis, an impulse response I[n] used in the impulse response convolution is obtained by converting a frequency response H(w), the impulse response I[n] is obtained by: (Math 1) 
 I [ n ]=DTFT −1 [ H ( w )] where DTFT denotes a discrete-time Fourier transform, and the impulse response continues from 0 to M in terms of the X coordinates and an output I[n]*x[n] of the impulse response convolution applied to an nth X coordinate x[n] among coordinates 0 through M is calculated as: (Math 2) I ⁡ [ n ] * x ⁡ [ n ] = ∑ m = 0 M ⁢ ⁢ I ⁡ [ m ] ⁢ x ⁡ [ n - m ] , ( Math ⁢ ⁢ 2 ) and I[n] is defined as: (Math 3) I ⁡ [ n ] = { I n , n ≥ 0 0 , otherwise. ( Math ⁢ ⁢ 3 )