Automated Counting of Stacked Objects in Industrial Inspection

Corentin Dumery; Noa Etté; Aoxiang Fan; Ren Li; Jingyi Xu; Hieu Le; Pascal Fua

cs.CVMar 16, 2026

Automated Counting of Stacked Objects in Industrial Inspection

Authors: Corentin Dumery, Noa Etté, Aoxiang Fan, Ren Li, Jingyi Xu, Hieu Le, Pascal Fua

Organizations: EPFL, Lausanne, Switzerland. · MBZUAI, Abu Dhabi, United Arab Emirates. · Southern University of Science and Technology, Shenzhen, China. · Stony Brook University, Stony Brook, New York, USA. ·

Abstract

Visual object counting is a fundamental computer vision task in industrial inspection, where accurate, high-throughput inventory tracking and quality assurance are critical. Moreover, manufactured parts are often too light to reliably deduce their count from their weight, or too heavy to move the stack on a scale safely and practically, making automated visual counting the more robust solution in many scenarios. However, existing methods struggle with stacked 3D items in containers, pallets, or bins, where most objects are heavily occluded and only a few are directly visible. To address this important yet underexplored challenge, we propose a novel 3D counting approach that decomposes the task into two complementary subproblems: estimating the 3D geometry of the stack and its occupancy ratio from multi-view images. By combining geometric reconstruction with deep learning-based depth analysis, our method can accurately count identical manufactured parts inside containers, even when they are irregularly stacked and partially hidden. We validate our 3D counting pipeline on large-scale synthetic and diverse real-world data with manually verified total counts, demonstrating robust performance under realistic inspection conditions.

Figures & tables

Figure 1: 3D Counting (3DC). We estimate both the total volume occupied by the stack and the fraction of this volume taken up by the objects from multiple views of objects to be counted. Combining these estimates yields the total number of objects.

Figure 2: 3DC pipeline. We decompose the counting task into estimating the volume of the objects to be counted and then estimating the occupancy ratio within that volume. The first is done on the basis of geometry reconstructed from segmentations in multiple images.The second uses as input a depth-map computed by a monocular depth estimator and regresses an occupancy ratio from it.

Panel of Figure 3 — Figure 3: Shape-dependent volume occupancy. We show a slice of the stacked objects for varying shapes. Different shapes yield different configurations and the fraction of space occupied by the gaps between objects varies. This is reflected in the images, where deeper layers remain visible for low $\gamma$ values.

Panel of Figure 4 — Figure 4: Dataset samples. We visualize generated scenes in ascending order of occupancy ratio, with ground-truth depth maps.

Panel of Figure 5 — Figure 5: Reducing the domain gap. Instead of estimating the occupancy ratio $\gamma$ from synthetic (top) and real images (bottom) (a), we identify a key view (b) and train a network to predict $\gamma$ from their depth maps (c), which are indistinguishable. Top row: synthetic, $\gamma_{gt}=62.4\%$ . Bottom row: chocolates , $\gamma_{est}=53.5\%$ , $\mathcal{N}_{est}=119$ , $\mathcal{N}_{gt}=131$ .

Panel of Figure 6 — Figure 6: Multi-view images. We generate 30 views from arbitrary angles for each of the scenes in our large-scale synthetic dataset.

	NAE $\scriptscriptstyle\downarrow$	SRE $\scriptscriptstyle\downarrow$	MAE $\scriptscriptstyle\downarrow$	sMAPE $\scriptscriptstyle\downarrow$
BMNet+ Shi et al. (2022)	0.91	0.87	320.50	158.87
SAM+CLIP Kirillov et al. (2023) ; Radford et al. (2021)	0.73	0.61	259.22	102.77
CNN	0.66	0.48	235.74	98.44
ViT+H	0.42	0.24	149.90	47.36
Ours	0.22	0.09	79.48	27.65

Table 1: Counting evaluation on 100 synthetic scenes.

Panel of Figure 7 — Figure 7: Additional qualitative results.

Panel of Figure 9 — Figure 9: Intermediate results. From images (a), we find the key viewpoint and compute its depth (b) to estimate the occupancy ratio $\gamma$ . Using the unit shape previously reconstructed from images of a template (c), and the overall reconstruction (d), we deduce the final count. ( Pasta : $\gamma_{est}=30.5\%$ , $N_{est}=509$ , $N_{gt}=588$ . Bricks : $\gamma_{est}=31.8\%$ , $N_{est}=73$ , $N_{gt}=100$ . Crosses : $\gamma_{est}=29.6\%$ , $N_{est}=88$ , $N_{gt}=116$ )

	MAE $\downarrow$	RMSE $\downarrow$	sMAPE $\downarrow$
Convex hull	0.1847	0.2121	23.58
$\alpha$ -concave hull	0.4134	0.6724	54.07
Ours	0.0455	0.0690	9.33

Table 4: Evaluation of volume estimation.

	NAE $\downarrow$	SRE $\downarrow$	MAE $\downarrow$	sMAPE $\downarrow$
( $\mathcal{T}-$ , $\mathcal{D}-$ )	0.22	0.09	79.48	27.65
( $\mathcal{T}+$ , $\mathcal{D}-$ )	0.28	0.11	100.12	30.93
( $\mathcal{T}+$ , $\mathcal{D}+$ )	0.31	0.12	111.04	35.92

Table 5: Ablation study on 3D counting. If ground-truth depth maps are used during training, it is indicated as

\mathcal{T}+

, and

\mathcal{T}-

otherwise. Similarly, for evaluation purposes if ground-truth depth-maps are used during validation, we indicate it as

\mathcal{D}+

Figure 10: Counting approximation. In an ideal setting where $\gamma$ , $v$ and $V$ are know, comparing the estimated counts with Equation 4 and ground-truth values demonstrates that this equation is a good approximation of the real count of objects in our released dataset, with a slight tendency to overestimate at larger counts.

Figure 11: Border effects. Measuring the ground-truth $\gamma$ over the complete box or over only a smaller section makes little difference, indicating that our assumption of uniform $\gamma$ across the volume is justified.

Figure 12: Complexity Analysis. Each point represents the $\gamma$ occupancy ratio error for a shape in the validation set.

Panel of Figure 13 — Figure 13: Instance localization. Previous methods also produce interpretable results, representing a promising direction for future work.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 14 — Figure 14: Localization of visible objects. Left: $\mathcal{N}_{vis}=168$ , Right: $\mathcal{N}_{vis}=96$

	NAE $\scriptscriptstyle\downarrow$	SRE $\scriptscriptstyle\downarrow$	sMAPE $\scriptscriptstyle\downarrow$
Visible objects only
BMNet+ [21]	0.51	0.65	51.28
SAM+CLIP [7,16]	0.57	0.81	50.84
All objects
BMNet+ [21]	0.93	0.98	131.44
SAM+CLIP [7,16]	0.94	0.99	124.31

Appendix

Table 7: Counting visible and invisible objects separately.

Figure 15: Dataset statistics. The histograms represent the distributions of object count and occupancy ratio, respectively, and each bar plots the number of scenes in a given bin. In scatter plots, each point represents a physically simulated 3D scene. In particular, the occupancy ratio $\gamma$ spans a large range between $1\%$ and 65 $\%$

Object Counting

Object counting estimates the number and locations of target instances in images or video, from dense crowds to fine-grained categories.

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Counting Machine Parts

Benedict Florance Arockiaraj, Elizabeth Dinella, Ankit Billa, Ajay Anand

Object Counting Industrial Inspection

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Counting objects in an image is a task applicable across many domains. For instance, crowd counting, inventory counting, and cell counting have been the focus of recent research. The major challenges in estimating the count of objects include overlapping objects, object scale issues, occlusions, and varying lighting conditions. In this report, we explore the problem of counting machine washer parts. Our technique is an extension of FamNet with an additional loss component, trained on the given dataset. We compare to three baseline methods: a traditional image processing pipeline, instance segmentation, and density map estimation. We evaluate the performance of these algorithms by computing the Mean Absolute Error (MAE) and the Root Mean Squared Error (RMSE) between the true object counts and the model outputs. Our approach achieves a performance of 1.96 MAE.

Abstract

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