Digital Image Representation and Color Spaces

Module: Computer Vision | Difficulty: Premium

Image as a Matrix

A grayscale image is a 2D function sampled on a discrete grid:

A color image adds a channel dimension:

RGB to HSV Conversion

Given normalized RGB values :

CIE XYZ Color Space

The CIE 1931 XYZ color matching functions map spectral power distributions to perceptual color:

import numpy as np

def rgb_to_hsv(rgb):
    rgb = rgb / 255.0
    r, g, b = rgb[..., 0], rgb[..., 1], rgb[..., 2]
    max_c = np.max(rgb, axis=-1)
    min_c = np.min(rgb, axis=-1)
    diff = max_c - min_c
    v = max_c
    s = np.where(max_c == 0, 0, diff / max_c)
    h = np.zeros_like(max_c)
    mask = diff > 0
    rm = mask & (max_c == r)
    gm = mask & (max_c == g)
    bm = mask & (max_c == b)
    h[rm] = 60 * ((g[rm] - b[rm]) / diff[rm] % 6)
    h[gm] = 60 * ((b[gm] - r[gm]) / diff[gm] + 2)
    h[bm] = 60 * ((r[bm] - g[bm]) / diff[bm] + 4)
    return np.stack([h / 360, s, v], axis=-1)

def compute_histogram(img, bins=256):
    hist, _ = np.histogram(img.ravel(), bins=bins, range=(0, 256))
    return hist / hist.sum()

Research Insight: The choice of color space profoundly affects downstream tasks. HSV and HSL decouple luminance from chrominance, making them robust to illumination changes in tasks like object tracking. CIELAB provides perceptual uniformity, which is critical for color constancy algorithms and image quality assessment. Modern deep networks typically learn their own color representations directly from raw RGB, but preprocessing with color space normalization can accelerate convergence.