Color Space Mapping YCbCr to RGB

Question

I am experimenting with JPEG compression using python. I load in a tiff image and store it as numpy uint8 RGB array. I was doing this for color mapping.

def rgb2ycbcr(im):
    cbcr = np.empty_like(im)
    r = im[:,:,0]
    g = im[:,:,1]
    b = im[:,:,2]
    # Y
    cbcr[:,:,0] = .299 * r + .587 * g + .114 * b
    # Cb
    cbcr[:,:,1] = 128 - .169 * r - .331 * g + .5 * b
    # Cr
    cbcr[:,:,2] = 128 + .5 * r - .419 * g - .081 * b
    return np.uint8(cbcr)

def ycbcr2rgb(im):
    rgb = np.empty_like(im)
    y   = im[:,:,0]
    cb  = im[:,:,1] - 128
    cr  = im[:,:,2] - 128
    # R
    rgb[:,:,0] = y + 1.402 * cr
    # G
    rgb[:,:,1] = y - .34414 * cb - .71414 * cr
    # B
    rgb[:,:,2] = y + 1.772 * cb
    return np.uint8(rgb)

I did a simple RGB to YCbCr transformation followed with a inverse transformation.

img = rgb2ycbcr(img)
imshow(img)
img = ycbcr2rgb(img)
imshow(img)

I got these two output image as YCbCr and RGB output after the color space transformation.

It seems that something is wrong with my color conversion and I cannot figure out what is wrong. I was using the JPEG color space conversion provided by Wikipedia. Thanks you for the help.

Answer 1

You have to do your intermediate calculations in floating point. The posterization should tip you off; you have a lot of "hot" (saturated) pixels.

def rgb2ycbcr(im):
    xform = np.array([[.299, .587, .114], [-.1687, -.3313, .5], [.5, -.4187, -.0813]])
    ycbcr = im.dot(xform.T)
    ycbcr[:,:,[1,2]] += 128
    return np.uint8(ycbcr)

def ycbcr2rgb(im):
    xform = np.array([[1, 0, 1.402], [1, -0.34414, -.71414], [1, 1.772, 0]])
    rgb = im.astype(np.float)
    rgb[:,:,[1,2]] -= 128
    rgb = rgb.dot(xform.T)
    np.putmask(rgb, rgb > 255, 255)
    np.putmask(rgb, rgb < 0, 0)
    return np.uint8(rgb)