Region-Local Copula Evidence Fusion for Heterogeneous Remote Sensing Change Detection
Authors: Zhiyuan Ji, Junjun Yin, Jian Yang
Organizations: Department of Electronic Engineering, Tsinghua University, Beijing 100084, P.R. China · School of Computer and Communication Engineering, University of Science and Technology Beijing, P.R. China
Superpixel copula models provide stable regional evidence for heterogeneous remote sensing change detection, but a single label per region limits localization within mixed superpixels. This letter develops a region-local copula evidence fusion method that retains the regional decision structure while introducing spatially varying local dependence anomalies. Independently fitted local models characterize departures from unchanged cross-image relationships. Reference ranking and an upper-tail gate transform these anomalies for fusion with continuous regional confidence. We derive the resulting regiondependent local decision threshold and identify a condition under which gating is equivalent to reparameterizing ungated fusion. On Lake and UK, whole-image optimized configurations achieve kappa coefficients of 0.78136 and 0.90817 and improve mixedregion and boundary decisions. Four-fold retrospective spatial validation over ten training subsets confirms complementary local information, with ungated reference fusion increasing mean kappa by 0.00693 and 0.01793. Fixed gating yields a larger UK gain of 0.03353 but only 0.00041 on Lake. These results support regional-local dependence interaction, while showing that calibration and gating have scene-dependent benefits.
Figures & tables
Fig. 2: Whole-image optimized A2 results on Lake (top) and UK (bottom). Columns show the image pair, GT, regional confidence (cool to warm: low to high), and A2 error map. White, black, green, and red denote true positives, true negatives, false positives, and false negatives, respectively. These are the established reference runs, not out-of-fold predictions.
Lake
UK
Method
KC
F1
ACC
KC
F1
ACC
M3CD
.669
.689
.963
.588
.636
.915
FPMS
.552
.588
.925
.816
.837
.962
NPSG
.559
.587
.947
.608
.663
.902
IRG-McS.dist
.739
.754
.971
.714
.749
.939
IRG-McS.sim
.733
.749
.971
.735
.768
.942
TABLE I: Whole-image comparison. Baselines are published values quoted through SCOPS; A2 is the optimized reference run.
Scene
Subset
Pixels
S ACC
A2 ACC
Net gain
Lake
Mixed
14357
.78422
.80685
325
Lake
Boundary
9195
.69897
.71452
143
UK
Mixed
89811
.84197
.89535
4794
UK
Boundary
40416
.73013
.81173
3298
TABLE II: Internal paired localization analysis. S denotes matched SCOPS, used here only for spatial mechanism assessment.
Local evidence / mapping
Lake
UK
Region only
.76853±.00675
.85911±.00672
Copula / min–max
.77363±.00374
.89366±.00762
Copula / reference CDF
.77546±.00735
.87704±.00811
Copula / CDF + gate .97
.76895±.00250
.89265±.00752
Pixel diff. / CDF + gate .97
.76832±.00712
.85702±.00710
Mean diff. / CDF + gate .97
.76786±.00702
.85677±.00710
TABLE III: Retrospective blocked validation: out-of-fold KC mean ± sample standard deviation over ten training subsets. All variants use regional distance confidence.
Local mapping
Lake KC
UK KC
Min–max
.77649±.00384
.89617±.00661
Reference CDF
.76755±.00361
.88870±.00641
Reference CDF + gate .97
.77313±.00423
.89769±.00717
TABLE IV: Whole-image calibration ablation with established regional mappings and a common full threshold grid. Parameters maximize ten-subset mean KC (oracle selection).