Spatial Uncertainty Analytics for Budget-Limited Inspection of Hyperspectral Scenes

Ritesh Sharma; Yuichi Motai

Scene	GSD (m/px)	Footprint (m)	Area (m 2 )
Indian Pines	$20.0$	$300\times 300$	$90{,}000$
Salinas	$3.7$	$55.5\times 55.5$	$3{,}080$
KSC	$18.0$	$270\times 270$	$72{,}900$
Pavia U.	$1.3$	$19.5\times 19.5$	$380$
LongKou	$0.46$	$6.9\times 6.9$	$48$
HanChuan	$0.11$	$1.6\times 1.6$	$3$

Table 1. Physical size of the fixed

15\times 15

-pixel sensor footprint across scenes, given each scene’s ground sampling distance (GSD). Holding the footprint fixed in pixels controls the planning problem for the cross-scene comparison; absolute coverage is therefore not physically comparable across datasets.

Scene	AUC	AUC (held-out)	AUC (blocked)	AP, held-out (prevalence)	Error rate	Top-10% error	Error where $u>0$
Indian Pines	$0.789\pm 0.006$	$0.742\pm 0.011$	$0.630\pm 0.070$	$0.48$ ( $0.26$ )	$22.8\%$	$59.3\%$	$41.2\%$
Salinas	$0.825\pm 0.004$	$0.747\pm 0.007$	$0.648\pm 0.052$	$0.26$ ( $0.06$ )	$5.8\%$	$38.1\%$	$37.5\%$
KSC	$0.825\pm 0.009$	$0.778\pm 0.011$	$0.692\pm 0.081$	$0.51$ ( $0.25$ )	$22.9\%$	$65.9\%$	$44.8\%$
Pavia U.	$0.827\pm 0.004$	$0.767\pm 0.005$	$0.652\pm 0.045$	$0.32$ ( $0.10$ )	$8.9\%$	$44.1\%$	$37.9\%$
LongKou	$0.870\pm 0.001$	$0.817\pm 0.006$	$0.792\pm 0.021$	$0.31$ ( $0.03$ )	$2.2\%$	$17.3\%$	$35.8\%$
HanChuan	$0.809\pm 0.001$	$0.760\pm 0.002$	$0.740\pm 0.019$	$0.40$ ( $0.14$ )	$12.6\%$	$56.5\%$	$50.4\%$

Table 2. Does disagreement predict error? ROC-AUC of the uncertainty score

u(p)

for ranking misclassified labelled pixels (majority-vote error against ground truth), mean

\pm

std over seeds (Indian Pines: 10, others: 5). “AUC (held-out)” repeats the test with evaluation pixels excluded from every member’s training set (Section 5.1 ) and is the primary measure; “AUC (blocked)” trains on whole

32\times 32

blocks and tests on labelled pixels more than

7

pixels from any of them. “AP, held-out” is the average precision of

u

on held-out pixels, next to the held-out error prevalence, which is the AP of an uninformative score. “Top-10% error” is the error rate among the

10\%

of labelled pixels ranked highest by

u

, with ties at the cut broken at random; “Error where

u>0

” is the error rate among pixels on which at least two members disagree. Both are to be read against the scene’s overall error rate.

	Archival airborne				UAV-borne (WHU-Hi)
Strategy	Indian Pines	Salinas	KSC	Pavia U.	LongKou	HanChuan	HongHu
Peak uncertainty	$32.4\pm 2.7$	$5.6\pm 1.1$	$27.4\pm 3.9$	$7.6\pm 1.4$	$6.7\pm 1.4$	$3.1\pm 0.3$	$2.5\pm 0.3$
Greedy coverage	$42.4\pm 2.5$	$32.5\pm 1.9$	$54.9\pm 2.3$	$23.3\pm 0.8$	$18.8\pm 1.4$	$5.0\pm 0.2$	$3.1\pm 0.2$
Unc.-wt. dispersion	$\mathbf{53.0\pm 1.9}$	$\mathbf{45.7\pm 1.3}$	$\mathbf{56.7\pm 2.3}$	$\mathbf{31.8\pm 1.0}$	$\mathbf{27.2\pm 0.7}$	$\mathbf{6.6\pm 0.1}$	$\mathbf{4.0\pm 0.1}$
Unc.-ranked NMS	$52.9\pm 2.2$	$45.3\pm 1.2$	$56.4\pm 2.5$	$31.6\pm 0.7$	$26.9\pm 0.7$	$\mathbf{6.6\pm 0.1}$	$\mathbf{4.0\pm 0.1}$
Stratified unc.	$43.0\pm 1.5$	$19.0\pm 1.2$	$40.6\pm 2.7$	$13.0\pm 1.0$	$14.6\pm 1.1$	$4.9\pm 0.1$	$3.3\pm 0.1$

Table 3. Error coverage (%): the percentage of genuine classifier errors (majority-vote misclassifications against ground truth) that fall within an inspected footprint, with a budget of 15 sites. Mean

\pm

std over seeds (Indian Pines: 10, others: 5). Scene-wide baselines sweep the whole scene; region-matched baselines are restricted to the labelled region (Section 4.3 ); random baselines are averaged over

20

draws per classifier seed. The best policy per scene is bolded. Dispersion and NMS differ by at most

0.4

points (paired comparison in Section 5.2 ).

	Archival airborne				UAV-borne (WHU-Hi)
Strategy	Indian Pines	Salinas	KSC	Pavia U.	LongKou	HanChuan	HongHu
Peak uncertainty	$41.6\pm 4.1$	$8.8\pm 2.4$	$35.5\pm 4.2$	$18.3\pm 3.3$	$12.2\pm 2.1$	$42.1\pm 3.1$	$71.6\pm 7.2$
Greedy coverage	$\mathbf{49.3\pm 2.1}$	$\mathbf{52.4\pm 2.1}$	$\mathbf{45.2\pm 2.8}$	$\mathbf{44.9\pm 3.3}$	$\mathbf{53.3\pm 3.2}$	$\mathbf{69.8\pm 2.1}$	$\mathbf{80.3\pm 2.6}$
Unc.-wt. dispersion	$45.4\pm 1.8$	$44.9\pm 1.5$	$43.4\pm 1.3$	$38.7\pm 1.7$	$39.8\pm 1.7$	$65.0\pm 0.8$	$80.1\pm 1.4$
Unc.-ranked NMS	$45.2\pm 2.1$	$44.2\pm 1.3$	$43.1\pm 1.1$	$38.3\pm 1.3$	$39.2\pm 1.8$	$65.0\pm 0.8$	$80.1\pm 1.4$
Stratified unc.	$37.2\pm 1.7$	$21.8\pm 1.0$	$25.0\pm 1.2$	$22.3\pm 2.1$	$23.2\pm 2.3$	$55.9\pm 1.4$	$69.8\pm 3.3$

Table 4. Inspection precision (%): of the labelled pixels an inspection visits, the fraction that are genuine classifier errors. Mean

\pm

std over seeds. On the finest-resolution scenes (HanChuan, HongHu) the error mass a 15-site budget can cover is small (Table 3 ), yet precision is highest there because errors fragment across a large scene and the uncertainty-driven policies still land mostly on true errors. The best uncertainty-driven policy per scene is bolded. Random baselines are averaged over

20

draws per classifier seed.

Figure 1. Error coverage with a budget of 15 sites. Fraction of genuine classifier errors covered by each policy across the seven scenes (mean

\pm

std). Lawnmower and Random are the scene-wide baselines. Dispersion covers the most errors among the plotted policies; uncertainty-ranked NMS, which is within

0.4

points of it, stratified sampling and the region-matched baselines are in Table 3 . Grouped bar chart of the percentage of classifier errors covered by five policies on seven scenes; dispersion has the tallest bar on every scene.

	Archival airborne				UAV-borne (WHU-Hi)
Strategy	Indian Pines	Salinas	KSC	Pavia U.	LongKou	HanChuan	HongHu
Peak uncertainty	$50.2\pm 5.4$	$12.3\pm 3.2$	$39.8\pm 10.4$	$12.6\pm 4.5$	$13.2\pm 4.9$	$4.0\pm 1.2$	$4.6\pm 0.7$
Greedy coverage	$53.9\pm 7.4$	$23.6\pm 5.0$	$68.1\pm 9.7$	$26.9\pm 7.3$	$25.6\pm 9.2$	$8.8\pm 0.6$	$6.2\pm 0.5$
Unc.-wt. dispersion	$\mathbf{68.0\pm 5.7}$	$33.0\pm 4.8$	$\mathbf{75.6\pm 11.5}$	$34.0\pm 10.9$	$33.3\pm 5.3$	$\mathbf{11.6\pm 1.0}$	$\mathbf{7.8\pm 0.2}$
Unc.-ranked NMS	$67.7\pm 4.6$	$\mathbf{34.1\pm 5.3}$	$74.3\pm 10.1$	$\mathbf{34.1\pm 10.8}$	$\mathbf{33.4\pm 5.4}$	$\mathbf{11.6\pm 1.1}$	$\mathbf{7.8\pm 0.2}$
Stratified unc.	$59.7\pm 5.1$	$17.5\pm 6.7$	$66.3\pm 4.9$	$19.9\pm 3.1$	$20.0\pm 5.0$	$7.8\pm 1.0$	$6.2\pm 0.3$

Table 5. Spatially blocked evaluation: error coverage of held-out errors (%). Planning and scoring are restricted to the labelled pixels of test blocks (

32\times 32

-pixel blocks, none within

7

pixels of a training block); the surface is renormalized over them. Mean

\pm

std over seeds (Indian Pines: 10, others: 5); random baselines averaged over

20

draws per seed. The best policy per scene is bolded.

Scene	px	m	Test	AUC	Disp.	Best RM	Ratio
Indian Pines	$32$	$640$	$36\%$	$0.630$	$68.0$	$48.7$	$1.4$
	$64$	$1280$	$41\%$	$0.574$	$63.7$	$48.5$	$1.3$
Salinas	$32$	$118$	$40\%$	$0.648$	$33.0$	$12.7$	$2.6$
	$64$	$237$	$49\%$	$0.703$	$21.8$	$10.0$	$2.2$
	$128$	$474$	$42\%$	$0.590$	$15.5$	$12.3$	$1.3$
KSC	$32$	$576$	$46\%$	$0.692$	$75.6$	$48.1$	$1.6$

Table 6. Block-size sweep of the blocked protocol: block side in pixels and metres, test share of the labelled pixels, AUC of

u

on test pixels, error coverage (%) of dispersion and of the best region-matched (RM) baseline inside the test blocks, and their ratio. Mean over seeds (Indian Pines: 10, others: 5). Indian Pines at

128

pixels (test share

3\%

) is omitted.

	Archival airborne				UAV-borne (WHU-Hi)
Strategy	Indian Pines	Salinas	KSC	Pavia U.	LongKou	HanChuan	HongHu
Peak uncertainty	$28.9\pm 1.8$	$8.0\pm 1.0$	$26.0\pm 2.5$	$7.5\pm 1.3$	$6.3\pm 1.3$	$2.9\pm 0.3$	$2.2\pm 0.2$
Greedy coverage	$36.2\pm 2.0$	$20.6\pm 0.8$	$48.1\pm 1.8$	$18.1\pm 1.2$	$10.7\pm 0.7$	$4.9\pm 0.3$	$3.2\pm 0.2$
Unc.-wt. dispersion	$\mathbf{45.4\pm 0.9}$	$\mathbf{30.5\pm 0.7}$	$\mathbf{50.1\pm 1.5}$	$\mathbf{26.0\pm 0.3}$	$\mathbf{17.5\pm 0.2}$	$\mathbf{6.6\pm 0.1}$	$\mathbf{4.0\pm 0.0}$
Unc.-ranked NMS	$45.3\pm 1.0$	$30.3\pm 0.7$	$\mathbf{50.1\pm 1.5}$	$\mathbf{26.0\pm 0.3}$	$17.4\pm 0.2$	$\mathbf{6.6\pm 0.1}$	$\mathbf{4.0\pm 0.0}$
Stratified unc.	$37.5\pm 1.2$	$16.8\pm 0.8$	$40.9\pm 1.6$	$12.7\pm 0.3$	$11.1\pm 0.3$	$4.9\pm 0.2$	$3.2\pm 0.1$

Table 7. Uncertainty covered (%): the share of the scene’s uncertainty mass inside the inspected footprints, objective ( 1 ), with 15 sites. Mean

\pm

std over seeds (Indian Pines: 10; all others: 5). Every uncertainty-driven policy exceeds every baseline on every scene, and dispersion and NMS are the best of them. The scene-wide baselines cover little except on the densely labelled Indian Pines.

Figure 2. Uncertainty covered as inspection sites are added, for four representative scenes (seed 0). The dispersion policy leads or ties at every budget on each scene shown and is still rising at the 15th site; the scene-wide lawnmower and random baselines stay far below it. Note the differing vertical scales: attainable coverage is far larger on the coarser-resolution scenes (Indian Pines, KSC) than on the fine-grained UAV scenes. Four line plots of percent uncertainty covered against the number of sites, 1 to 15, for five policies on Indian Pines, KSC, LongKou and HanChuan; dispersion is highest or tied at every budget.

	Archival airborne				UAV-borne (WHU-Hi)
Strategy	Indian Pines	Salinas	KSC	Pavia U.	LongKou	HanChuan	HongHu
Peak uncertainty	$26.0\pm 1.3$	$\mathbf{24.1\pm 4.0}$	$27.1\pm 1.2$	$\mathbf{20.8\pm 2.4}$	$10.9\pm 1.3$	$3.2\pm 0.3$	$2.0\pm 0.1$
Greedy coverage	$30.0\pm 2.2$	$6.5\pm 1.7$	$38.9\pm 0.5$	$4.1\pm 1.9$	$4.2\pm 0.8$	$4.0\pm 0.1$	$2.3\pm 0.3$
Unc.-wt. dispersion	$\mathbf{40.0\pm 1.5}$	$14.0\pm 2.8$	$\mathbf{41.5\pm 1.3}$	$7.3\pm 1.3$	$12.6\pm 0.6$	$\mathbf{5.7\pm 0.2}$	$\mathbf{2.9\pm 0.2}$
Unc.-ranked NMS	$39.7\pm 1.5$	$14.2\pm 2.9$	$41.4\pm 1.3$	$7.3\pm 1.3$	$\mathbf{13.0\pm 1.0}$	$\mathbf{5.7\pm 0.2}$	$\mathbf{2.9\pm 0.2}$
Stratified unc.	$34.8\pm 3.0$	$22.2\pm 3.1$	$36.6\pm 1.3$	$14.5\pm 2.4$	$11.9\pm 1.5$	$4.8\pm 0.5$	$2.5\pm 0.2$

Table 8. Connected-anomaly coverage (%), mean

\pm

std over seeds (Indian Pines: 10; all others: 5). The best uncertainty-driven policy per scene is bolded; unlike Table 7 , it is not the same policy on every scene. Dispersion or NMS leads on five scenes and peak uncertainty on Salinas and Pavia University. Components are the 4-connected regions of

U\geq 0.7

.

Figure 3. Representative ensemble-disagreement uncertainty surfaces (seed 0, shared colour scale clipped at 0.8; unlabelled background masked to zero; (a) Indian Pines, (b) Salinas, (c) LongKou, (d) HongHu; Salinas, LongKou and HongHu are rotated by

90^{\circ}

to fit the page). The arrangement differs between scenes: in Indian Pines and HongHu high uncertainty is speckled across many fields; in Salinas most of it lies in one or two fields, and in LongKou in thin strips along field edges. These arrangements shape connected-anomaly coverage (Table 8 ). Four heatmaps of normalized classifier uncertainty on a shared colour scale for Indian Pines, Salinas, LongKou and HongHu, showing speckled, field-concentrated and edge-strip patterns.

Figure 4. Two policies on the same Pavia University uncertainty surface (seed 0). Dispersion (right) places most of its footprints on the one dense high-uncertainty patch, which holds most of the mass, while peak-uncertainty selection (left) centres each footprint on an isolated maximum and spreads across the scene. On Pavia University the spread-out policy covers more connected anomalies (Table 8 ), while dispersion covers more uncertainty mass and more errors (Tables 7 and 3 ). Squares mark the sensor field of view; the scene is rotated by

90^{\circ}

to fit the page, and lines join the sites in the order each policy selected them. Two side-by-side heatmap panels of the same uncertainty surface with overlaid inspection paths: the dispersion policy clusters its waypoints on a dense patch, the peak policy spreads them across the scene.

	Margin at threshold			Components at $0.7$
Scene	$0.6$	$0.7$	$0.8$	$n$	$C$
Indian Pines	$+11.6$	$+14.1$	$+15.4$	$550$	$0.0088$
Salinas	$+17.9$	$-10.1$	$-15.2$	$192$	$0.0099$
KSC	$+15.8$	$+14.4$	$+18.3$	$355$	$0.0071$
Pavia U.	$+12.7$	$-13.5$	$-17.9$	$259$	$0.0049$
LongKou	$+6.8$	$+1.6$	$-0.4$	$616$	$0.0024$

Table 9. Connected-anomaly margin (dispersion minus peak uncertainty, percentage points; mean over seeds) with components defined at three thresholds, and two descriptors of the

0.7

components: their number

n

and the concentration index

C

. A negative margin means peak uncertainty covers more components.

	Archival airborne				UAV-borne (WHU-Hi)
Strategy	Indian Pines	Salinas	KSC	Pavia U.	LongKou	HanChuan	HongHu
Peak uncertainty	$26.7\pm 1.6$	$7.2\pm 0.9$	$25.0\pm 2.5$	$7.1\pm 1.2$	$5.8\pm 1.2$	$2.7\pm 0.3$	$2.0\pm 0.2$
Greedy coverage	$33.8\pm 1.9$	$20.4\pm 0.7$	$47.1\pm 1.5$	$17.7\pm 1.1$	$10.7\pm 0.7$	$4.3\pm 0.2$	$2.8\pm 0.2$
Unc.-wt. dispersion	$\mathbf{43.1\pm 0.9}$	$\mathbf{30.0\pm 0.8}$	$\mathbf{49.3\pm 1.3}$	$\mathbf{25.7\pm 0.3}$	$\mathbf{17.2\pm 0.3}$	$\mathbf{6.0\pm 0.0}$	$\mathbf{3.5\pm 0.0}$
Unc.-ranked NMS	$43.0\pm 0.9$	$29.9\pm 0.8$	$\mathbf{49.3\pm 1.3}$	$25.6\pm 0.3$	$17.1\pm 0.3$	$\mathbf{6.0\pm 0.0}$	$\mathbf{3.5\pm 0.0}$
Stratified unc.	$36.5\pm 1.1$	$16.4\pm 0.8$	$40.7\pm 1.6$	$12.4\pm 0.3$	$10.8\pm 0.3$	$4.6\pm 0.2$	$2.9\pm 0.1$

Table 10. High-uncertainty coverage (%), the fraction of labelled pixels with

U>0

(the above-median pixels; the median is zero) falling within an inspected footprint, mean

\pm

std over seeds (Indian Pines: 10; all others: 5). Higher is better. Dispersion and NMS are best on every scene.

	Archival airborne				UAV-borne (WHU-Hi)
Strategy	Indian Pines	Salinas	KSC	Pavia U.	LongKou	HanChuan	HongHu
Peak uncertainty	$61\pm 4$	$151\pm 19$	$179\pm 17$	$208\pm 40$	$169\pm 22$	$217\pm 48$	$120\pm 18$
Greedy coverage	$54\pm 6$	$66\pm 2$	$185\pm 9$	$36\pm 10$	$66\pm 19$	$160\pm 28$	$330\pm 62$
Unc.-wt. dispersion	$60\pm 3$	$102\pm 7$	$185\pm 11$	$60\pm 5$	$151\pm 2$	$294\pm 27$	$369\pm 33$
Unc.-ranked NMS	$60\pm 3$	$102\pm 8$	$184\pm 12$	$60\pm 5$	$151\pm 2$	$294\pm 27$	$369\pm 33$
Stratified unc.	$68\pm 1$	$193\pm 3$	$243\pm 1$	$265\pm 2$	$241\pm 6$	$444\pm 7$	$403\pm 4$

Table 11. Waypoint dispersion (mean pairwise distance between waypoints, in pixels), mean

\pm

std over seeds. This is a descriptive measure of how each policy distributes its waypoints, not a quality score: the most dispersed policy on every scene is a sampling design (random, systematic or stratified), and none of them covers the most errors. The lawnmower sweep is fixed by its grid.

Scene	Label mask	No mask	Novelty $q=0.90$	Novelty $q=0.95$	Novelty $q=0.99$	Unlab. kept	On labels
Indian Pines	$53.0$	$27.2$	$42.9$	$41.8$	$31.2$	$63\%$	$63\%$
Salinas	$45.7$	$0.0$	$0.0$	$0.0$	$0.0$	$57\%$	$0\%$
KSC	$56.7$	$0.0$	$10.0$	$8.4$	$4.3$	$64\%$	$7\%$
Pavia U.	$31.8$	$2.7$	$12.4$	$8.6$	$6.3$	$79\%$	$31\%$
LongKou	$27.2$	$18.9$	$23.4$	$22.6$	$21.7$	$61\%$	$77\%$
HanChuan	$6.6$	$5.2$	$4.1$	$5.0$	$5.3$	$94\%$	$54\%$

Table 12. Label-free novelty mask: error coverage (%) of the dispersion policy when the surface is restricted by the labelled region (as in the main results), by nothing (Table 13 ), or by a novelty mask that drops pixels whose spectra are far from the training spectra (threshold at the

q

-quantile of in-distribution scores). “Unlab. kept” is the share of unlabelled pixels the mask keeps at

q=0.90

; “On labels” the share of inspected pixels that are labelled at

q=0.90

. Mean over seeds.

	Indian P.	Salinas	KSC	Pavia U.	LongKou	HanChuan	HongHu
Uncertainty covered
Peak uncertainty	$16.0$	$3.5$	$1.3$	$2.2$	$6.2$	$1.6$	$1.5$
Greedy coverage	$20.8$	$7.4$	$2.0$	$3.3$	$9.6$	$2.5$	$2.6$
Dispersion	$\mathbf{26.2}$	$\mathbf{10.6}$	$\mathbf{2.9}$	$\mathbf{3.9}$	$\mathbf{12.4}$	$\mathbf{3.4}$	$\mathbf{3.1}$
Lawnmower	$22.2$	$3.4$	$1.1$	$1.4$	$1.2$	$0.3$	$0.5$
Random	$14.7$	$2.8$	$1.1$	$1.6$	$1.5$	$0.9$	$0.7$

Table 13. Unmasked control: the uncertainty surface is computed over the whole scene and every policy may select anywhere. Uncertainty covered over the whole scene (%) and error coverage on labelled pixels (%), mean over seeds (Indian Pines: 10, others: 5).

Strategy	Covered (%)	Path, selection order (km)	Path, 2-opt (km)	Covered per km
Peak uncertainty	$6.3\pm 1.3$	$0.85\pm 0.04$	$0.44\pm 0.05$	$14.7\pm 4.1$
Greedy coverage	$10.7\pm 0.7$	$0.38\pm 0.10$	$0.13\pm 0.00$	$\mathbf{82.7\pm 3.7}$
Unc.-wt. dispersion	$\mathbf{17.5\pm 0.2}$	$0.88\pm 0.19$	$0.24\pm 0.01$	$72.8\pm 2.8$
Lawnmower, scene-wide	$0.5\pm 0.0$	$0.10\pm 0.00$	$0.10\pm 0.00$	$5.3\pm 0.3$
Random, scene-wide	$1.5\pm 0.5$	$1.54\pm 0.14$	$0.73\pm 0.08$	$2.0\pm 0.8$

Table 14. Flight-cost analysis on the LongKou UAV scene (15 sites, 5 seeds, mean

\pm

std,

0.463

m/pixel). Path lengths are for the sites flown in selection order and after nearest-neighbour and 2-opt ordering. “Covered” is the share of the uncertainty mass inside the footprints; coverage per km uses the 2-opt route.

Figure 5. Uncertainty covered by the five policies versus cumulative flight distance along the nearest-neighbour and 2-opt route on the LongKou UAV scene, mean over five seeds with

\pm

standard-deviation bands. Line plot of percent uncertainty covered against cumulative flight distance in kilometres for five policies, with shaded standard deviation bands.

Figure 6. Single-seed sensitivity of uncertainty covered to the training fraction

\tau

on Indian Pines and KSC (seed 0). Across

\tau\in\{0.05,0.1,0.2,0.3,0.5\}

the dispersion policy remains the strongest on both scenes and all three uncertainty-driven policies stay above the baselines. Absolute magnitudes are not comparable across

\tau

because the surface is renormalized at each setting. Two line plots of percent uncertainty covered versus the training fraction tau for Indian Pines and KSC; the dispersion policy is highest at every tau and all three targeted policies stay above the baselines.

Figure 7. The planner is agnostic to the uncertainty estimator (Indian Pines). The dispersion policy is applied unchanged to surfaces from four estimators, the tree ensemble, MC dropout, a deep ensemble and softmax entropy (mean

\pm

std over five seeds; Indian Pines only). Left: error-ranking AUC, with chance at

0.5

. Right: uncertainty covered by dispersion and by random sites on the same surface. Two bar charts for four uncertainty estimators on Indian Pines: error-ranking AUC of 0.73 to 0.79 above the 0.5 chance line, and uncertainty covered by dispersion (37 to 47 percent) against random sites (about 14 percent).

		Main protocol				Blocked
Scene	Features	Acc.	AUC	Disp.	Ratio	Acc.	AUC	Disp.	Ratio
Indian Pines	pixel	$77.2$	$0.788$	$54.3$	$1.8$	$34.1$	$0.643$	$69.6$	$1.3$
	spatial	$92.6$	$0.869$	$54.8$	$2.0$	$40.3$	$0.656$	$69.7$	$1.2$
Salinas	pixel	$94.2$	$0.825$	$45.7$	$6.0$	$80.9$	$0.648$	$33.0$	$2.6$
	spatial	$99.1$	$0.859$	$81.4$	$6.7$	$87.5$	$0.645$	$31.8$	$2.5$
Pavia U.	pixel	$91.1$	$0.827$	$31.8$	$6.6$	$79.0$	$0.652$	$34.0$	$3.1$

Table 15. Pixel-wise against spectral-spatial features: accuracy (%), AUC of

u

, error coverage of dispersion (%) and its ratio to the best region-matched baseline, under the main and the blocked protocol (

32

-pixel blocks). Mean over seeds 0 to 4.

Figure 8. Cost-aware trade-off on LongKou. Uncertainty covered versus flight-path length as the travel weight

\lambda

varies from

0

(dispersion) to

3

(mean over 5 seeds), with the sites flown in selection order and after nearest-neighbour and 2-opt ordering. Labels mark

\lambda

on the selection-order curve. The penalty acts on distance, not energy. Line plot of percent uncertainty covered against flight path length in kilometres as the travel weight increases from 0 to 3, for sites flown in selection order and after 2-opt ordering.

Scene	Dispersion (ours)	GP-MI	GP-UCB	Random
Indian Pines	$\mathbf{45.4\pm 0.9}$	$16.8\pm 3.1$	$43.4\pm 1.0$	$13.4\pm 2.9$
Salinas	$\mathbf{30.5\pm 0.7}$	$3.3\pm 1.0$	$22.6\pm 1.4$	$2.2\pm 1.0$
KSC	$\mathbf{50.1\pm 1.5}$	$0.8\pm 0.8$	$12.6\pm 2.3$	$1.0\pm 1.0$
Pavia U.	$\mathbf{26.0\pm 0.3}$	$1.0\pm 0.9$	$15.0\pm 1.1$	$1.9\pm 0.7$
LongKou	$\mathbf{17.5\pm 0.2}$	$1.5\pm 0.8$	$10.5\pm 1.5$	$1.5\pm 0.5$
HanChuan	$\mathbf{6.6\pm 0.1}$	$1.1\pm 0.4$	$4.1\pm 0.6$	$0.9\pm 0.2$

Table 16. Comparison to Gaussian-process selection: uncertainty covered (%), mean

\pm

std over seeds,

K=15

sites with no travel limit for every policy.

Figure 9. Comparison to Gaussian-process selection. Uncertainty covered by the dispersion policy (ours), GP mutual information ( Singh et al., 2009 ) , GP-UCB and random sites, each with 15 sites and no travel limit, on all seven scenes (mean

\pm

std over seeds). Grouped bar chart of percent uncertainty covered on seven scenes by dispersion, GP-UCB, GP mutual information and random sites; dispersion is highest on every scene.

Spatial Uncertainty Analytics for Budget-Limited Inspection of Hyperspectral Scenes

Abstract

Figures & tables

Uncertainty Sampling

HyperImageNet: A Large-Scale High-Spatial Resolution Hyperspectral Imagery Classification Benchmark

Adaptive Band Selection for Hyperspectral Classification with Spatially Disjoint Evaluation

Ten Architectures, One Error: Shared Failure Modes in Hyperspectral Classification under Spatially Disjoint Evaluation

Abstract

Uncertainty Sampling

Explore similar work

HyperImageNet: A Large-Scale High-Spatial Resolution Hyperspectral Imagery Classification Benchmark

Adaptive Band Selection for Hyperspectral Classification with Spatially Disjoint Evaluation

Ten Architectures, One Error: Shared Failure Modes in Hyperspectral Classification under Spatially Disjoint Evaluation