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

Junjing Zheng, Zhiyi Zhou, Ningrui Yang, Hongying Meng

arXiv:2609.39366v1cs.CV

TL;DR

Remote sensing counting faces a transfer gap: counters trained on similar domains may not transfer reliably when categories, imaging conditions, or backgrounds change. COBICount separates candidate response generation, acceptance, and background suppression using source-only supervision. On three unseen DOTA targets, it achieves the lowest average MAE among the compared methods.

  • Problem

    Counters developed on similar training and test domains leave open whether their responses remain valid when object categories, imaging conditions, or backgrounds change.

    Source: §I · p. 1

  • Method

    COBICount separates response generation, acceptance of compact centered patterns, and suppression of responses associated with repeated background structures using source supervision.

    Source: §I · p. 2

  • Results

    174.132 MT-MAE: COBICount has the lowest MT-MAE among compared methods and the lowest MAE on each of three unseen target domains.

    Source: D. Main Results · p. 12

  • Takeaways & Limitations

    Source-only counting fixes the model using one annotated source domain and permits application to new domains without further training.

    Source: §I · p. 2

    The setting uses one source domain and withholds target images and information until the model is fixed.

    Source: §I · p. 2

Abstract

from arXiv · show

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.

I. INTRODUCTION

The introduction frames source-only remote sensing counting as transfer from one annotated domain without target information, where object responses can be confused with repeated background structures. It positions COBICount as a three-stage response-selection approach amid prior work on point-supervised counting and cross-domain transfer.

I. INTRODUCTION

  • Source-only counting trains and selects a model using one source domain with point annotations, then evaluates it on a different target domain unavailable during development.The source and target differ in object category or imaging conditions; target information is not used before the final model is fixed.Source: §I · pp. 1–2
  • Repeated roads, roofs, parking patterns, and boundaries can produce responses resembling objects, while total-count metrics may hide missed objects offset by false responses.Response size changes also matter: small target objects may yield weaker evidence than persistent background patterns.Source: §I · p. 2, A. Counting with Point Supervision in… · p. 3
  • COBICount separates candidate generation, local acceptance, and background suppression, using only source point supervision and no target data or target-background labels.The three stages are Candidate Evidence, Candidate Acceptance, and Bias Isolation.Source: §I · p. 2

II. RELATED WORK

  • The related-work review organizes prior research around point-supervised counting, data requirements for cross-domain transfer, and checking whether responses lie on objects or background structures.Its stated questions motivate linking counting design with response-location analysis.Source: §II · p. 2, §I · p. 2

A. Counting with Point Supervision in Remote Sensing Images

  • Prior remote-sensing counters use point-based density estimation and address object-scale or background variation, but do not establish whether responses remain valid after category, sensor, resolution, or background changes.The related work also distinguishes target-image adaptation, multi-source domain generalization, and pretrained models, whose data or outputs differ from this setting.Source: A. Counting with Point Supervision in… · p. 3, B. Learning across Domains under… · pp. 3–4

C. Checking Where Counting Responses Occur

The paper motivates checking response locations because total-count metrics cannot show whether density falls on objects or background. It defines source-only evaluation and describes a counting path that combines candidate responses, acceptance, background retention, and valid image regions.

C. Checking Where Counting Responses Occur

  • MAE and RMSE can conceal offsetting missed objects and false background responses, so response locations provide evidence that total-count errors omit.Responses near annotated points indicate object coverage, while unsupported responses can reveal background responses.Source: C. Checking Where Counting Responses… · p. 4

A. Problem Setting and Model Output

  • Training and model selection use only the source domain; target images are used only after the model is fixed, without target-derived signals selecting or updating it.The model output is a density map whose spatial sum gives the predicted count; its values are local count contributions, not class probabilities.Source: A. Problem Setting and Model Output · p. 4

B. Overall Data Flow

  • The counting path multiplies candidate responses, an acceptance gate, a retention gate, and the valid-region mask; their product forms the density map whose spatial sum is the count.The Audit head is an auxiliary inspection output and does not feed back into the count.Source: Figure 1 · p. 5, B. Overall Data Flow · p. 5

C. Shared Feature and Effective Valid Mask

The shared feature network produces a multiscale representation, while a fixed image-derived mask removes padding without classifying valid pixels. Candidate Evidence (CE) combines routed density branches with bounded response maps to create possible responses for later stages.

C. Shared Feature and Effective Valid Mask

  • A residual backbone and FPN fuse features from four strides into four 96-channel tensors, then resize and concatenate them at P2 resolution.Two 3×3 convolution blocks fuse the concatenated tensor.Source: C. Shared Feature and Effective Valid… · p. 5
  • The effective valid mask removes padding but does not distinguish objects from background, and the same fixed rule applies to source and target images.A 9 × 9 pooling operation expands nearly black pixels into a neutral-mask buffer.Source: C. Shared Feature and Effective Valid… · p. 6

D. Candidate Evidence

  • CE’s bounded responses include an edge-reduced map and a wider-support map formed by pooling over a 5 × 5 neighborhood.The Sobel magnitude measures local change in the base response.Source: D. Candidate Evidence · p. 6
  • The scale head routes three nonnegative density heads with location-specific weights, without assigning the branches fixed physical scales.The labels s, m, and l identify branches, not object-size categories.Source: D. Candidate Evidence · p. 6
  • CE combines a routed mixture of three density branches with base, edge-reduced, and wider-neighborhood responses into one candidate map.The branches are routed by location; the resulting map is not treated as a final prediction.Source: D. Candidate Evidence · p. 6

E. Candidate Acceptance

Candidate Acceptance (CA) controls how much of each broad CE response continues to the final density map. Its four learned gates favor responses near source-point centers and reduce them away from the learned support patterns.

E. Candidate Acceptance

  • CA multiplies four learned maps into an acceptance gate that controls how much of each broad CE response continues to the final density map.CE may spread one object response across several locations or produce nearby peaks.Source: E. Candidate Acceptance · p. 7
  • The quality and reliability maps are implementation names, not separately annotated properties, and neither gate alone can remove a response.Each of their factors stays between 0.35 and 1; CA uses learned spatial gates rather than connected-component detection or a hand-written shape rule.Source: E. Candidate Acceptance · p. 7
  • The center and wider-support targets train CA to keep accepted responses near source points and decrease them away from those points.Ac is trained high near a source point center; Ao, Aq, and Ar use wider targets, with Aq and Ar trained using different loss weights.Source: E. Candidate Acceptance · p. 7

F. Bias Isolation

Bias Isolation (BI) estimates continuous response-risk maps from source counting supervision and converts their weighted sum into a retention gate. Audit provides visual descriptions of internal response patterns, with its channel values not intended as reliable probabilities for unseen target classes.

F. Bias Isolation

  • BI estimates four continuous risk maps and converts their weighted sum into a retention gate, without recognizing named background categories in the target domain.The maps may overlap and are not four exclusive classes.Source: F. Bias Isolation · p. 7
  • The learned line, broad, grid, and background maps are not classifiers of named structures; three receive no named-structure labels and are learned through source counting supervision.The background map is the only map in this group with a direct background target; suppression losses penalize mass outside protected source regions.Source: F. Bias Isolation · p. 7

G. Audit Response Maps

  • Audit’s response-channel values should not be read as reliable probabilities of unseen target classes; in the main protocol, only building and background channels receive direct source labels.The other channels receive no vehicle or ship label during training, so Audit is a visual description of internal response patterns.Source: G. Audit Response Maps · p. 8

H. Training with Source Points

Training maps and losses are constructed from source images and their point sets. Source points are projected onto the output grid and used to build density, center, support, and protection targets for training.

H. Training with Source Points

  • The training procedure constructs source-point maps first, followed by density and count losses, CA and BI losses, and routing and Audit terms.These maps and losses are computed from a source image and its point set.Source: H. Training with Source Points · p. 8

1) Maps constructed from source points:

  • Source point coordinates are divided by the output stride of 4 and rounded to the nearest grid location before target-map construction.The annotated point set supplies the reference count for the source image.Source: 1) Maps constructed from source points · p. 8
  • A unit-sum Gaussian kernel is placed around each projected source point and added to form the density target.A kernel cut by an image boundary is not renormalized; this target is used in training, not when processing target images.Source: 1) Maps constructed from source points · p. 8
  • CA uses separate narrow center and wider support targets, while protection and background masks define regions for support losses and the direct background target.When no point is present, the density and support maps are zero; the protection and background regions serve distinct roles.Source: 1) Maps constructed from source points · pp. 8–9

2) Density and count losses:

The density and count losses combine map-level penalties with per-image comparisons between predicted and reference counts.

2) Density and count losses:

  • The map loss uses smooth L1 and binary cross entropy, with predictions bounded away from zero and one before cross-entropy evaluation.The implementation clips predictions by 10^-4 for numerical stability.Source: 2) Density and count losses · p. 9
  • Dividing by Nnorm prevents object-rich images from dominating map loss, while (1+4Msup) upweights locations near source objects.Source: 2) Density and count losses · p. 9
  • Two per-image losses compare summed predictions with reference counts, then average across the batch.The relative term limits the effect of large reference counts, and the logarithmic term reduces differences across very large numerical ranges.Source: 2) Density and count losses · p. 9

3) Losses for CA and BI:

CA losses supervise where candidate maps remain open and where learned background responses should be high, while BI penalties act on final counting mass.

3) Losses for CA and BI:

  • CA losses use the previously defined center and support targets and specify where CA remains open and learned background response is high.They do not label any named target background structure.Source: 3) Losses for CA and BI · p. 9
  • BI uses four penalties on final counting mass, with detached risk maps serving as weights while their heads still receive gradients through V and final density bS.The background penalty uses wider protection mask Mfg; the other three use Msup.Source: 3) Losses for CA and BI · p. 9
  • Hard negatives are the strongest remaining responses outside Mfg, where source point supervision labels locations as background despite large model responses.The loss selects the Khn largest locations of Q; stop-gradient is used only for selection, while selected bS values remain differentiable.Source: 3) Losses for CA and BI · p. 9

4) Routing, Audit, and total loss:

Routing, Audit, and other weighted penalties are combined in the training objective, with routing regularization discouraging concentrated branch choices.

4) Routing, Audit, and total loss:

  • Routing entropy is largest when three weights are similar and smallest when one dominates; minimizing Lent avoids early concentrated choices outside the support area.The 1.10 reference approximates the maximum entropy, log 3.Source: 4) Routing, Audit, and total loss · pp. 9–10
  • Mean branch use is (0.36, 0.34, 0.30) for the three routing branches.Source: 4) Routing, Audit, and total loss · p. 10
  • Direct Audit supervision begins at epoch 10, using RSOC Building points for the building channel inside Msup and valid outside-Mfg locations for background; vehicle and ship channels lack direct source class labels.Source: 4) Routing, Audit, and total loss · p. 10
  • The total objective combines weighted losses, and CE receives no separate direct loss but is updated through density, count, BI, strong-response, and routing terms computed from source data or fixed source-image transforms.Source: 4) Routing, Audit, and total loss · p. 10

I. Diagnostic Points at Inference

This section defines diagnostic-point extraction and the source-only experiment protocol, then specifies evaluation measures and comparison settings.

I. Diagnostic Points at Inference

  • Diagnostic points are greedy local maxima extracted from bS for spatial analysis, not part of the numerical count.The search removes each selected point's neighborhood, enforces 3.2 output-grid-cell spacing, and uses a budget that does not force extracted-point count to equal predicted count.Source: §I · p. 10

A. Protocol and Data

  • Source and target roles are experiment-specific: source data train and select the model, while a target category or imaging condition remains unavailable until selection.In the main experiment, RSOC Building is the source and DOTA Large Vehicle, Small Vehicle, and Ship are separate unseen targets; targets do not update parameters or select the checkpoint.Source: A. Protocol and Data · p. 10

B. Evaluation Measures and Comparison Settings

  • Mean target MAE summarizes the three unseen DOTA domains and excludes the RSOC Building source result.MAE and RMSE measure count error, with RMSE weighting large errors more heavily; lower values are better for both.Source: B. Evaluation Measures and Comparison… · p. 11
  • All methods use the same preprocessing and frozen RSOC-selected checkpoint for each main result, with no target labels or statistics used for input-size selection.The comparison includes density-map, point-prediction, transformer, compact, feature-pyramid, generic domain-generalization, and remote-sensing counters; none receives target data for adaptation or checkpoint selection.Source: B. Evaluation Measures and Comparison… · p. 11

C. Implementation Details

COBICount is trained and selected using a single source domain, with target data excluded from adaptation and checkpoint selection. In the main comparison, it leads the compared methods on average target error, though transfer remains difficult for some domains and objects.

C. Implementation Details

  • COBICount training uses 512 × 512 source crops, AdamW for 80 epochs, and an EMA model for source validation and final evaluation.The implementation also uses point-centered crop sampling, flips, and occasional brightness, contrast, and saturation changes.Source: C. Implementation Details · p. 11

D. Main Results

  • Training and checkpoint selection use only RSOC Building; architecture, thresholds, loss weights, extraction settings, and input sizes are fixed without target information.The same selected checkpoint is evaluated across all three target domains.Source: C. Implementation Details · p. 12, Table I · p. 12
  • Low source MAE does not guarantee transfer: P2PNet scores 7.460 on RSOC Building but 249.435 MT-MAE across targets.The target columns evaluate the same checkpoint selected using source validation.Source: D. Main Results · p. 12
  • 174.132 MT-MAE gives COBICount the lowest average target MAE among compared methods, with the lowest MAE on each unseen target domain.The closest baseline, CAN, has MT-MAE 243.722; MT-MAE averages MAE over the three target domains and excludes the source result.Source: D. Main Results · p. 12, Table I · p. 12
  • BDRNet is smaller and more accurate than MPCount under this protocol, but differing objectives and learning-rate schedules prevent isolating architecture as the cause.BDRNet uses 17.09 million parameters and 91.64 GFLOPs; MPCount uses 33.23 million parameters and 143.79 GFLOPs.Source: D. Main Results · p. 12
  • COBICount remains imperfect, with MAE/RMSE of 327.045/941.040 on DOTA Small Vehicle and 165.478/266.511 on DOTA Ship.After resizing, small vehicles occupy fewer output cells than source buildings while several background structures remain visually strong.Source: D. Main Results · p. 13

E. Tests with Different Source Domains

Changing the training source changes transfer accuracy: COBICount is not restricted to RSOC Building, but performance depends on how closely source patterns match the unseen domain. Ablations distinguish the effects of BI, its constituent terms, and CE/CA cues, while prediction-bias analysis shows that residual over- and under-counting remains.

E. Tests with Different Source Domains

  • 17.389/19.496 MAE/RMSE for DIOR Airplane to RSOC Building contrasted with 220.378/317.497 for DIOR Airplane to DOTA Ship; transfer depends on source choice.COBICount is not restricted to RSOC Building, but its accuracy depends on how closely source patterns match the unseen domain. Table II varies the single annotated source and evaluates fixed checkpoints; DIOR Airplane uses box centers only.Source: E. Tests with Different Source Domains · p. 13

A. Ablation of Model Parts

  • DOTA Proxy crops favor regions containing targets and omit empty images, so their MAE and RMSE are not comparable with complete-image DOTA results.Proxy metrics are used only for ablation analysis, not for loss or checkpoint selection; checkpoints are selected using RSOC Building validation data.Source: A. Ablation of Model Parts · p. 13, Table III · p. 14
  • 610.964 RSOC Building MAE and 655.634 DOTA Proxy MAE for “w/o BI” show that neutralizing BI can raise error, unlike the numerically stable “Density only” variant.“Density only” also removes bounded CE cues and CA, whereas “w/o BI” retains broader CE and CA; the DOTA Proxy is used only for ablation analysis.Source: A. Ablation of Model Parts · pp. 13–14
  • 283.996 DOTA Proxy MAE without BG versus 484.697 without Line/Broad/Grid indicates that the learned background response and structure risks have distinct effects.Figure 5 illustrates responses on parking lines, road boundaries, shadows, and repeated structures; both BI components are needed in the current formulation.Source: Figure 5 · p. 13, A. Ablation of Model Parts · p. 14
  • Removing CE support raises DOTA Proxy MAE from 16.937 to 27.835, while removing the CA center gate raises RSOC Building MAE from 6.574 to 7.043 and DOTA Proxy MAE from 16.937 to 18.865.Removing Audit causes a more moderate change; the full model has the lowest MAE on both sets.Source: A. Ablation of Model Parts · p. 14

B. Prediction Bias

  • COBICount’s Pred/GT is 1.78 on DOTA Large Vehicle, 0.92 on DOTA Ship, and 0.52 on DOTA Small Vehicle, showing residual over- and under-counting.Other compared methods also show domain-specific over- or under-counting; Pred/GT is the ratio of mean predicted count to mean reference count.Source: B. Prediction Bias · pp. 14–15, Table IV · p. 14

C. Locations of Diagnostic Points

The diagnostic analysis separates count totals from response locations, showing that diagnostic-point volume alone does not ensure object-aligned responses; DOTA Small Vehicle remains the method’s main boundary.

C. Locations of Diagnostic Points

  • Diagnostic points are extracted after the numerical count and assess response locations, while the predicted count remains the sum of the complete density map.Recall@32 measures reference-object coverage and Precision@32 measures diagnostic-point support within 32 pixels; these independent nearest-point tests allow many-to-one matches.Source: C. Locations of Diagnostic Points · p. 15, Table V · p. 16
  • Location inspection covers CAN, DM-Count, MLDG-Count, and COBICount, not every numerical baseline; their diagnostic extraction procedures differ, so this is not a controlled ranking.The diagnostic analysis also uses nonoverlapping 512 × 512 tiles for large images, distinct from the numerical-count settings.Source: C. Locations of Diagnostic Points · p. 15
  • 3.408 Diag/GT for CAN on DOTA Large Vehicle coincided with Recall@32 of 0.279 and Precision@32 of 0.079; on Small Vehicle, CAN and MLDG-Count had poor location agreement despite different point totals.DM-Count on Small Vehicle had Diag/GT 0.323, Recall@32 0.036, and Precision@32 0.068; MLDG-Count had 1.623, 0.060, and 0.071, respectively.Source: C. Locations of Diagnostic Points · p. 15
  • COBICount’s Recall@32 and Precision@32 were 0.809 and 0.680 on RSOC Building, 0.742 and 0.542 on DOTA Large Vehicle, and 0.614 and 0.394 on DOTA Ship.DOTA Small Vehicle remained harder: COBICount and CAN had similar Diag/GT values, 0.703 and 0.714, but COBICount had higher Recall@32 and Precision@32, 0.238 and 0.301 versus 0.193 and 0.186.Source: C. Locations of Diagnostic Points · p. 15, Table V · p. 16

D. Boundary Analysis on DOTA Small Vehicle

  • On DOTA Small Vehicle, resized vehicles may occupy few output cells while parking lines and road boundaries remain strong; this problem is less severe for larger vehicles.The observed errors include responses on parking marks, roadside structures, and enclosed empty regions.Source: D. Boundary Analysis on DOTA Small… · p. 17, Figure 7 · p. 17
  • CE, CA, and BI reduce but do not eliminate these errors: weak vehicles may lack evidence, compact empty-region responses may survive, and background patterns may remain hard to separate.Future work should strengthen responses for objects occupying few cells and suppress repeated background patterns more effectively.Source: D. Boundary Analysis on DOTA Small… · p. 17

VI. CONCLUSION

  • 174.132 MT-MAE was the lowest among 12 compared baselines; versus CAN at 243.722, COBICount reduced MT-MAE by 28.553%.The comparison uses RSOC Building as source and DOTA Large Vehicle, Small Vehicle, and Ship as unseen targets.Source: §VI · p. 17
  • COBICount uses source-only supervision and combines broad response generation, compact-response acceptance, and suppression of responses associated with learned background structures.A separate Audit output inspects response patterns without changing the final density map or predicting named target categories.Source: §VI · p. 17

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