Zhang et al

Zhang et al. · DCT-domain JND with parabolic luminance adaptation and block-classified contrast masking

Lineage: Subband refinement Domain: Transform (DCT) Reference: Zhang, X. H., Lin, W. S., and Xue, P., "Improved estimation for just-noticeable visual distortion," Signal Processing, vol. 85, no. 4, pp. 795–808, 2005.

This directory contains the OpenJND implementation of Zhang et al.'s DCT-domain JND model. Building directly on the Ahumada–Peterson spatial-CSF model and Watson's DCTune, it sharpens two specific weaknesses of those estimators: an inaccurate luminance-adaptation base threshold at dark and bright extremes, and an over-estimated contrast-masking elevation factor around edges.

What the model does

For each 8×8 block, the JND of each DCT coefficient is expressed, as in DCTune, as the product of a base threshold t_b (spatial CSF × luminance adaptation) and an elevation factor a_CM (contrast masking), with a final global scale tfac:

t_JND(n1, n2, i, j) = tfac · t_ij(i, j) · a_lum(n1, n2) · a_CM(n1, n2, i, j),    tfac = 0.3

The four building blocks:

1. Spatial CSF. Per-coefficient base thresholds t_ij(i, j) are computed from spatial frequency, orientation, and an assumed mean display luminance LB. The CSF parameters used by the reference implementation are the standard Ahumada–Peterson fit:

   LT = 13.45,  S0 = 94.7,  aT = 0.649,        % threshold lifting
   f0 = 6.78,   af = 0.182, Lf = 300,           % peak-frequency curve
   K0 = 3.125,  aK = 0.0706, LK = 300,          % bandwidth
   s  = 0.25,   r  = 0.6,    LB = 65 cd/m²      % overall scale & orientation

An orientation correction 1 / (r + (1 − r) · cos²(θ)) (r = 0.6) is applied to off-axis DCT frequencies. The DC threshold is set to min(t_ij(0,1), t_ij(1,0)) to avoid a singular value at zero frequency.

2. Parabolic luminance adaptation. Driven by the block DC coefficient C(n1, n2, 0, 0), the LA factor is a two-branch function around C00 = 1024:

   a_lum = { k_T · (1 − C/C00)^a_T + 1     if C ≤ C00
           { k_Q · (C/C00 − 1)^a_Q + 1     otherwise

with k_T = 2, a_T = 3, k_Q = 0.8, a_Q = 2. This is higher in very dark and very bright regions, lowest around mid-grey — the parabolic correction that mainly improves accuracy below gray level 128 where DCTune is least faithful.

3. Block classification. Every 8×8 block is assigned to PLAIN / EDGE / TEXTURE from sums of absolute DCT coefficients in the low-frequency lowf, edge-frequency edg and high-frequency highf groups, with the empirical thresholds from the paper:

   Symbol	Value	Role
   u1, u2	125, 900	Cutoffs on edg + highf for PLAIN / mixed / TEXTURE
   k1	290	Secondary PLAIN-vs-TEXTURE cutoff in the mixed range
   a1, b1	6.9, 4.8	High-energy edge ratios (a1 = 2.3·3, b1 = 1.6·3)
   a2, b2	1, 1.6	Low-energy edge ratios
   y1, y	2.0, 16	Cutoffs on (lowf + edg) / highf

4. Contrast masking with block-class-dependent elevation. Inside TEXTURE blocks, each AC coefficient picks up an intra-band masking factor max(1, |C / t_b|^0.36) further multiplied by a texture-amplification TexMask:

   TEXTURE :  TexMask = 1 + (F_maxT − 1) · (TexE − 290) / (1800 − 290),     F_maxT = 2.5
   EDGE    :  TexMask = 1.125  if EdgE ≤ 400 else 1.25
   PLAIN   :  TexMask = 1

Crucially, for EDGE blocks the LF and MF coefficients are excluded from intra-band masking — their a_CM is held at the per-block TexMask value only — which is exactly what prevents the JND over-estimation that DCTune produces around edges. The DC coefficient has a_CM = 1 in all blocks.

Behaviour of the JND map

• The map is per-coefficient in the DCT domain and carries the imprint of the 8×8 block grid by construction — appropriate for block-based codecs.
• EDGE blocks receive lower budgets than TEXTURE blocks of comparable energy, because their LF/MF bands are kept out of the masking elevation.
• Better matched to subjective scores than DCTune, especially in dark regions and around object boundaries (validated by subjective tests on Actor and Lena, and in JPEG-style compression).

Directory layout

Zhang et al/
├── MATLAB/          # reference implementation (main.m)
├── Python/          # ported implementation (main.py)
└── paper.pdf        # original paper

Unified calling convention

INPUT  : grayscale image  (uint8 / float, H × W; H and W are auto-cropped to multiples of 8)
OUTPUT : JND map  (float, H' × W' where H', W' are the post-crop dimensions)

Internally the input is partitioned into non-overlapping 8×8 blocks, each block is DCT-transformed and classified (PLAIN / EDGE / TEXTURE), and a per-coefficient threshold is derived from the base threshold and elevation factor. The output is the spatial-domain assembly of the per-coefficient thresholds (one threshold value per pixel position).

Minimal usage example

MATLAB

addpath('MATLAB');
img = imread('../test_data/lena.png');
if size(img, 3) == 3, img = rgb2gray(img); end
jnd = JND_dct(img);
imagesc(jnd); colormap gray; colorbar;

Python

cd Python
pip install numpy scipy imageio matplotlib
python main.py

Programmatic call:

from main import JND_dct
import imageio.v2 as imageio
img = imageio.imread('../test_data/lena.png', mode='L')
jnd = JND_dct(img)

Default parameters

Parameter	Default	Meaning
bsize	8	DCT block side length
wx, wy	0.0298, 0.0298	Horizontal / vertical pixel size in degrees of visual angle
tfac	0.3	Global JND scaler applied at the very end
Lmax, Lmin, M	130, 0, 256	Display luminance range and gray-level resolution
LB	65 cd/m²	Assumed mean display luminance
r (orientation)	0.6	Orientation-correction shape constant
s (CSF scale)	0.25	Spatial-CSF overall scale
LT, S0, aT	13.45, 94.7, 0.649	CSF threshold-lifting parameters
f0, af, Lf	6.78, 0.182, 300	CSF peak-frequency parameters
K0, aK, LK	3.125, 0.0706, 300	CSF bandwidth parameters
k_T, a_T, k_Q, a_Q, C00	2, 3, 0.8, 2, 1024	Parabolic luminance-adaptation parameters
u1, u2, k1	125, 900, 290	Block-classification thresholds on edg + highf
a1, b1	6.9, 4.8	High-energy edge ratios in block classification
a2, b2, y1, y	1, 1.6, 2.0, 16	Low-energy edge ratios in block classification
F_maxT	2.5	Maximum texture-masking factor (TEXTURE blocks)
EDGE-block factor	1.125 / 1.25	Below / above 400 in edge energy EdgE = edg + lowf
Intra-band exponent	0.36	`max(1,

All defaults reproduce the configuration used in the reference implementation.

Citation

@article{zhang2005improved,
  title   = {Improved estimation for just-noticeable visual distortion},
  author  = {Zhang, X. H. and Lin, W. S. and Xue, P.},
  journal = {Signal Processing},
  volume  = {85}, number = {4}, pages = {795--808}, year = {2005}
}