Skip to content

README.md

Latest commit

 

History

History
135 lines (102 loc) · 6.74 KB

README.md

File metadata and controls

135 lines (102 loc) · 6.74 KB
Raw

Liu et al. · TV-based decomposition for edge / texture separation

Lineage: Decomposition era Domain: Pixel Reference: Liu, A., Lin, W., Paul, M., Deng, C., and Zhang, F., "Just noticeable difference for images with decomposition model for separating edge and textured regions," IEEE Transactions on Circuits and Systems for Video Technology, vol. 20, no. 11, pp. 1648–1652, November 2010.

This directory contains the OpenJND implementation of Liu et al.'s pixel-domain JND model, which addresses a long-standing misclassification problem in earlier contrast-masking estimators by separating the image into structural and textural components before computing the masking budget.

What the model does

Earlier pixel-domain estimators lump strong gradients into a single "high-frequency" bucket and apply one contrast-masking gain to both edges and textures. This systematically underestimates the JND budget of texture regions — which the HVS in fact tolerates much more than edges, because textures carry higher entropy masking.

Liu et al. fix this by:

  1. Image decomposition. The input image I is split into a structural component I_s (cartoon-like, piecewise smooth with sharp edges) and a textural component I_t = I − I_s via total-variation (TV-L¹) decomposition with regularisation λ = 0.8. The reference implementation uses Wotao Yin's ParaMaxFlow code (Rice CAAM TR07-09) — a parametric max-flow solver for TV-L¹ — with 4-connected neighbours.

  2. Background-luminance branch JNDl. Chou-style luminance adaptation on the 5×5-averaged background luminance:

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

with T₀ = 17 and γ = 3/128.

  1. Edge-masking and texture-masking branches. The same four-direction gradient operator from Chou & Li gives Gm_e on the structural component and Gm_t on the textural component. Both masking thresholds use the Chou-style luminance-dependent slope and intercept (after Chou & Chen 1996):
   JNDt_e = clip( Gm_e · α(bg) + β(bg),  0, 10 )
   JNDt_t = clip( Gm_t · α(bg) + β(bg),  0, 10 )
   α(bg) = 0.0001 · bg + 0.115
   β(bg) = 0.5 − 0.01 · bg

The two branches are then combined with weights that reflect the higher tolerance of textures:

   JNDt = W_e · JNDt_e + W_t · JNDt_t,    W_e = 0.7,  W_t = 1.4
  1. NAMM combiner. Following Yang et al. 2005, the luminance and masking branches are merged via the nonlinear-additive masking model:
   JND = JNDl + JNDt − C_TG · min(JNDl, JNDt),   C_TG = 0.3

Behaviour of the JND map

  • Textures recover a noticeably larger JND budget than they get from undecomposed contrast-masking models.
  • Edges remain protected — the structural component preserves them sharply, and the W_e < W_t weighting keeps their masking contribution conservative.
  • Reports an average of ≈1.15 dB additional PSNR redundancy over earlier pixel-domain estimators at matched perceived quality.

Directory layout

Liu et al/
├── MATLAB/                          # reference implementation
│   ├── main.m                       # entry-point script
│   ├── JND_ID.m                     # core algorithm
│   ├── Graph_anisoTV_L1_v2.m        # wrapper for the TV-L¹ solver
│   └── mt_TV_L1_8bit.mexw64         # precompiled MEX (Windows-only)
├── Python/                          # ported implementation (main.py)
└── paper.pdf                        # original paper

Platform note (MATLAB). The MATLAB port depends on Wotao Yin's ParaMaxFlow MEX library (mt_TV_L1_8bit.mexw64), which is provided here pre-compiled for 64-bit Windows. Linux / macOS users need to obtain the corresponding .mexa64 / .mexmaci64 builds from http://www.caam.rice.edu/~wy1/ParaMaxFlow/ or rebuild the library from the original source.

Port note (Python). The Python port substitutes a Gaussian-blur surrogate for the TV-L¹ decomposition: I_s = GaussianBlur(I, kernel=7×7, σ = λ). This is a deliberate simplification — the TV-L¹ solver carries a non-trivial dependency and is not straightforward to wrap from Python. Gaussian blur gives a qualitatively similar structural / textural split (low frequencies stay in I_s, high-frequency texture goes to I_t) but does not preserve sharp edges the way TV-L¹ does, so the two ports produce visually similar but numerically different JND maps. The runtime trade-off is what we report in the top-level Runtime Analysis.

Unified calling convention

INPUT  : grayscale image  (uint8 / float, H × W)
         optional lambda  (default 0.8) — TV-L¹ regularisation (MATLAB)
                                          / Gaussian σ for the structural-component surrogate (Python)
OUTPUT : JND map of the same H × W shape  (float)

Minimal usage example

MATLAB

addpath('MATLAB');
img = imread('../test_data/barbara.png');
if size(img, 3) == 3, img = rgb2gray(img); end
jnd = JND_ID(img);                % default lambda = 0.8
imshow(jnd, []);

Python

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

Programmatic call:

from main import jnd_id
import cv2
img = cv2.imread('../test_data/barbara.png', cv2.IMREAD_GRAYSCALE)
jnd = jnd_id(img, lambda_=0.8)

Default parameters

Parameter Default Meaning
λ (TV-L¹) 0.8 MATLAB: regularisation weight of the TV-L¹ structural extraction. Python: Gaussian σ for the surrogate.
nNeighbors 4 MATLAB only: 4-connected neighbourhood in the TV-L¹ solver
biThread 2 MATLAB only: ParaMaxFlow solver thread mode (UP-thread)
T₀ 17 Base luminance-adaptation threshold
γ 3/128 Bright-branch slope of JNDl
λ_β 0.5 Constant term of β(bg)
JNDt clip [0, 10] Edge / texture masking thresholds are clipped before weighting
W_e 0.7 Weight on the edge-masking branch
W_t 1.4 Weight on the texture-masking branch
C_TG 0.3 NAMM overlap-reduction factor

All defaults reproduce the configuration used in the reference implementation.

Citation

@article{liu2010just,
  title   = {Just noticeable difference for images with decomposition model for separating edge and textured regions},
  author  = {Liu, Anmin and Lin, Weisi and Paul, Manoranjan and Deng, Chenwei and Zhang, Fan},
  journal = {IEEE Transactions on Circuits and Systems for Video Technology},
  volume  = {20}, number = {11}, pages = {1648--1652}, year = {2010}
}

If you use the TV-L¹ decomposition step, please also acknowledge:

W. Yin, ParaMaxFlow toolbox, http://www.caam.rice.edu/~wy1/ParaMaxFlow/, Rice University CAAM TR07-09.