COBICount: Separating Object and Background Responses for Remote Sensing Object Counting Without Training on Target Data

Junjing Zheng; Zhiyi Zhou; Ningrui Yang; Hongying Meng

cs.CVSep 30, 2026

COBICount: Separating Object and Background Responses for Remote Sensing Object Counting Without Training on Target Data

Authors: Junjing Zheng, Zhiyi Zhou, Ningrui Yang, Hongying Meng

Organizations: School of International Studies, Chongqing University of Posts and Telecommunications, Chongqing 400065, China · Brunel University London, Uxbridge UB8 3PH, U.K. · Department of Electronic and Electrical Engineering, College of Engineering, Design and Physical Sciences, Brunel University of London, Uxbridge UB8 3PH, U.K.

Abstract

Remote sensing object counting estimates how many buildings, vehicles, or ships appear in overhead images. Most supervised counters predict a density map, whose sum gives the object count, and assume similar categories, sizes, and backgrounds. Applying them across regions, sensors, or categories often requires target data or further training, which may be costly or unavailable. We study source-only counting. Training for the counting task and model selection use one group of images that shares an object category and similar imaging conditions, with one point marking each object. Target images and information remain unavailable until the model is fixed. This reduces data preparation but makes transfer harder. A model trained on one source may place high density values, called responses, on real objects and repeated background structures. Road edges, parking grids, roof boundaries, and water boundaries may then be counted as objects, creating candidate origin ambiguity. COBICount separates response generation, acceptance, and background suppression. Candidate Evidence (CE) generates possible responses. Candidate Acceptance (CA) keeps compact responses centered on objects. Bias Isolation (BI) reduces responses associated with repeated background structures. Their outputs form the final density map. Trained on RSOC Building and evaluated directly on DOTA Large Vehicle, Small Vehicle, and Ship, COBICount achieves the lowest mean absolute error (MAE) averaged over the target domains among the compared methods, 174.132. It uses 5.07 million parameters and 17.41 billion floating point operations for a 512x512 input. COBICount improves transfer without target data or training for each target. The code will be available at: https://github.com/yixuxi22/COBICount.

Figures & tables

Fig. 1: Overall data flow of COBICount. The input image produces the shared feature tensor $\mathbf{F}$ and the effective valid mask $\mathbf{M}^{eff}$ . CE, CA, and BI produce $\mathbf{C}^{all}$ , $\mathbf{A}$ , and $\mathbf{V}$ . These four maps enter one elementwise multiplication node to form $\widehat{\mathbf{S}}$ . Its spatial sum gives $\widehat{N}$ , while $\mathcal{U}_{mp}$ produces the density map at image resolution used for display. The Audit head is an auxiliary output and does not return to the counting path.

Fig. 2: Candidate Evidence. The shared feature tensor first produces $\mathbf{E}_{p}$ . Its Sobel response $\mathbf{G}$ enters the computation of $\mathbf{E}_{b}$ , and $\mathbf{E}_{p}$ enters the computation of $\mathbf{E}_{h}$ . The scale head supplies $\pi_{s}$ , $\pi_{m}$ , and $\pi_{l}$ , which multiply the matching density head outputs. The weighted sum in Eq. ( 22 ) combines $\mathbf{D}^{ms}$ , $\mathbf{E}_{p}$ , $\mathbf{E}_{b}$ , and $\mathbf{E}_{h}$ into $\mathbf{C}^{all}$ .

Fig. 3: Candidate Acceptance. Four heads produce $\mathbf{A}_{c}$ , $\mathbf{A}_{o}$ , $\mathbf{A}_{q}$ , and $\mathbf{A}_{r}$ . The last two maps form $0.35+0.65\mathbf{A}_{q}$ and $0.35+0.65\mathbf{A}_{r}$ , respectively, before the four factors enter one multiplication node. The output is the acceptance gate $\mathbf{A}$ .

Fig. 4: Bias Isolation. The exact inputs are $\mathbf{F}$ , $\mathbf{E}_{p}$ , $\mathbf{A}_{c}$ , and $\mathbf{M}^{neu}$ . Fixed filters applied to $\mathbf{E}_{p}$ produce $\mathbf{G}$ , $\mathbf{L}$ , and $\mathbf{P}$ . These maps combine with four learned maps to form $\mathbf{R}_{line}$ , $\mathbf{R}_{broad}$ , $\mathbf{R}_{grid}$ , and $\mathbf{R}_{bg}$ . The weighted sum in Eq. ( 32 ) produces $\mathbf{R}^{bi}$ , followed by $\operatorname{clip}(1-\mathbf{R}^{bi},0,1)$ to obtain $\mathbf{V}$ .

Type	Method	Year	Adapt.	Params (M)	GFLOPs	RSOC Building		DOTA LV		DOTA SV		DOTA Ship		MT-MAE
Type	Method	Year	Adapt.	Params (M)	GFLOPs	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MT-MAE
Standard / larger	ResNet50 FPN Counter [ 44 , 45 ]	2017	$\times$	27.15	66.86	10.023	14.794	292.845	668.910	605.817	1322.535	590.810	882.637	496.491
	CSRNet [ 4 ]	2018	$\times$	16.26	27.07	7.180	10.530	225.165	504.559	491.337	1118.768	494.861	687.234	403.788
	CAN [ 6 ]	2019	$\times$	18.18	–	9.120	13.380	76.182	96.163	415.150	1244.760	239.832	372.497	243.722
	Bayesian Loss [ 7 ]	2019	$\times$	21.50	26.99	28.950	32.930	583.585	826.571	872.199	1695.127	925.775	1316.316	793.853
	P2PNet [ 9 ]	2021	$\times$	19.20	23.29	7.460	10.340	124.993	158.005	411.526	1236.752	211.785	329.987	249.435

TABLE I: Main comparison when RSOC Building is the source domain and DOTA Large Vehicle, DOTA Small Vehicle, and DOTA Ship are three unseen target domains. All training for the counting task and checkpoint selection use only RSOC Building. No target data are used for adaptation or checkpoint selection. MT-MAE is the average MAE over the three target domains and excludes the RSOC Building source result.

Source domain	Adapt.	RSOC Building		DIOR Airplane		DOTA Ship
Source domain	Adapt.	MAE	RMSE	MAE	RMSE	MAE	RMSE
RSOC Building	$\times$	6.574	9.753	15.206	21.957	165.478	266.511
DIOR Airplane	$\times$	17.389	19.496	0.885	1.579	220.378	317.497
DOTA Ship	$\times$	11.278	16.373	49.170	50.339	81.980	141.044

TABLE II: Evaluation with three choices of source domain. Each row gives the single domain used for training and checkpoint selection. Each column gives the domain used for evaluation. Entries outside the matching source column measure transfer to an unseen domain without target adaptation.

Variant	Bias Isolation		Candidate Evidence	Candidate Acceptance	Audit	RSOC Building		DOTA Proxy
Variant	BG	Line/Broad/Grid	Support	Center	Audit	MAE	RMSE	MAE	RMSE
Density only	–	–	–	–	–	9.334	14.342	25.841	54.013
w/o BI	–	–	$\checkmark$	$\checkmark$	$\checkmark$	610.964	625.417	655.634	665.124
w/o BG	–	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	261.307	268.222	283.996	292.246
w/o Line/Broad/Grid	$\checkmark$	–	$\checkmark$	$\checkmark$	$\checkmark$	447.158	457.968	484.697	492.678
w/o Support	$\checkmark$	$\checkmark$	–	$\checkmark$	$\checkmark$	10.657	15.300	27.835	54.651

TABLE III: Ablation of COBICount on RSOC Building and DOTA Proxy. Each row removes one model part or one related group. The reported checkpoint is selected by RSOC Building validation MAE. DOTA Proxy is used only to analyze the selected variants and does not select a reported checkpoint.

Fig. 5: Examples from the ablation study when RSOC Building is the source and DOTA is unseen. The panels compare the input, reference points, the full model, and selected variants. They show how removing response generation, local acceptance, or structure suppression changes the final density map. Strong values on roads, parking structures, shadows, and repeated textures are responses without object support.

Method	RSOC	DOTA LV	DOTA SV	DOTA Ship
Bayesian Loss [ 7 ]	0.89	10.30	1.81	4.02
P2PNet [ 9 ]	0.96	2.96	0.44	0.88
CSRNet [ 4 ]	0.96	4.50	1.21	2.29
CAN [ 6 ]	0.90	2.06	0.38	0.70
DM-Count [ 8 ]	0.95	4.21	0.80	1.21
TransCrowd [ 10 ]	0.95	3.05	0.46	0.93

TABLE IV: Pred/GT for selected methods when RSOC Building is the source and the three DOTA categories are unseen targets.

Method	Evaluation domain	Recall@32	Precision@32	Diag/GT
CAN [ 6 ]	DOTA LV	0.279	0.079	3.408
CAN [ 6 ]	DOTA SV	0.193	0.186	0.714
DM-Count [ 8 ]	DOTA SV	0.036	0.068	0.323
MLDG-Count [ 16 ]	DOTA SV	0.060	0.071	1.623
COBICount	RSOC Building	0.809	0.680	1.085
COBICount	DIOR Airplane	0.358	0.214	1.879

TABLE V: Location analysis for selected combinations of methods and domains using a matching radius of 32 pixels. All compared outputs are density maps. Recall@32 measures the coverage of reference objects, Precision@32 measures the fraction of diagnostic points supported by reference objects, and Diag/GT compares the numbers of diagnostic and reference points.

Fig. 6: Response location examples on unseen DOTA and DIOR images. Each row contains an input crop, the reference points, and results from CAN, DM-Count, MLDG-Count, and COBICount. Green marks are reference points, and cyan marks are diagnostic points. The cyan marks are used only for visualization and location analysis; they are not native point predictions and do not produce the numerical count. As explained in Section V-C , COBICount and the baselines use fixed procedures suited to their respective output grids rather than one identical extraction rule. The displayed “Pred” value is the sum of the density map for the shown crop and is independent of the number of cyan marks.

Fig. 7: Representative errors on DOTA Small Vehicle. Manual inspection compares the input image, reference points, final density map, and diagnostic points. Strong responses occur on parking marks, roadside structures, and enclosed empty regions. These descriptions are made by the evaluator; they are not semantic classes predicted by Audit.

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