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:

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).

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}
}

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