Chou and Li

Chou & Li · Foundational pixel-domain JND model

Lineage: Foundational Domain: Pixel Reference: Chou, C.-H. and Li, Y.-C., "A perceptually tuned subband image coder based on the measure of just-noticeable-distortion profile," IEEE Transactions on Circuits and Systems for Video Technology, vol. 5, no. 6, pp. 467–476, December 1995.

This directory contains the OpenJND implementation of the foundational pixel-domain JND model proposed by Chou and Li. It is the cornerstone model around which the rest of the OpenJND catalogue is organised.

What the model does

Chou & Li estimate a per-pixel visibility threshold from two HVS factors:

1. Background luminance adaptation JNDl. The HVS is more tolerant to distortion in very dark and very bright regions and most sensitive around mid-grey (≈127). The luminance term is modelled as a piecewise function — a square-root rise in dark regions and a linear ramp in bright regions:

   JNDl(x,y) = { T₀ · (1 − √(bg/127)) + 3      if bg ≤ 127
               { γ · (bg − 127) + 3              if bg > 127

with T₀ = 17 and γ = 3/128, where bg(x,y) is the local mean luminance computed with the 5×5 weighted lowpass operator from the original paper (centre pixel excluded; weights summing to 32).

2. Texture / spatial masking JNDt. The maximum weighted gradient Gm(x,y) over a 5×5 neighbourhood is computed in four directions using the operators G1, G2, G3, G4 from the paper (normalised by 16). The masking term scales linearly with Gm through luminance-dependent slope α and intercept β:

   JNDt(x,y) = Gm(x,y) · α(bg)  +  β(bg)
   α(bg) = 0.0001 · bg + 0.115
   β(bg) = λ − 0.01 · bg,    λ = 0.5

The two terms are combined into the final pixel-wise JND as

JND(x,y) = JNDl(x,y) + JNDt(x,y) − C_TG · min{ JNDl(x,y), JNDt(x,y) },    C_TG = 0.3

The companion paper also introduces PSPNR (Peak Signal-to-Perceptible-Noise Ratio), a fidelity metric that counts only the distortion above the JND threshold.

Behaviour of the JND map

• Large budgets on dark and on busy regions.
• Relatively conservative near isolated edges.
• The estimator is image-plane and grayscale by construction — it serves as the spatial baseline reused by Yang et al., Wu et al., and Liu et al.

Directory layout

Chou and Li/
├── MATLAB/          # reference implementation (main.m)
├── Python/          # ported implementation (main.py)
└── paper.pdf        # original paper

Unified calling convention

INPUT  : grayscale image       (uint8 / float, H × W)
         mode flag
OUTPUT : JND map of the same H × W shape (float)

Minimal usage example

MATLAB

addpath('MATLAB');
img = imread('../test_data/lena.png');
jnd = JND_pixel(img, 'Chou');
imshow(mat2gray(jnd));

Python

cd Python
pip install numpy scipy opencv-python matplotlib
python main.py

Programmatic call:

from main import jnd_pixel
import cv2
img = cv2.imread('../test_data/lena.png', cv2.IMREAD_GRAYSCALE)
jnd = jnd_pixel(img, 'Chou')

Default parameters

Parameter	Default	Meaning
T₀	17	Base threshold at zero background luminance (JNDl at bg = 0)
γ	3/128	Slope of the bright branch of JNDl
λ	0.5	Constant term of β(bg) in JNDt
C_TG	0.3	Combiner factor when merging JNDl and JNDt

All defaults reproduce the numbers reported in the original publication.

Citation

@article{chou1995perceptually,
  title   = {A perceptually tuned subband image coder based on the measure of just-noticeable-distortion profile},
  author  = {Chou, Chun-Hsien and Li, Yun-Chin},
  journal = {IEEE Transactions on Circuits and Systems for Video Technology},
  volume  = {5}, number = {6}, pages = {467--476}, year = {1995}
}