R. Donida Labati, A. Genovese, V. Piuri, F. Scotti, Low-cost volume estimation by two-view acquisitions: a computational intelligence approach, Proc. of the 2012 IEEE-INNS Int. Joint Conf. on Neural Networks (IJCNN 2012), pp. 1092-1099, Brisbane, QLD, Australia, June 2012, ISSN 978-1-4673-1489-3.
Industrial informatics
Volume Estimation
The Volume Estimation project investigates fast and affordable techniques for measuring the volume of physical objects without direct contact. Volume information is relevant in granulometry, industrial quality control, food analysis, and archaeology, where conventional methods based on Archimedes’ principle may be too slow, difficult to automate, or unsuitable for fragile, porous, inaccessible, or immovable objects.
Traditional image-based approaches generally estimate volume by reconstructing a complete three-dimensional model from silhouettes, stereo images, or laser scans. Their accuracy can be strongly affected by object orientation, occlusions, surface texture, camera position, and the quality of the acquisition hardware. Producing a sufficiently dense and accurate 3D model may also require complex setups and considerable computation.
The proposed method instead uses a simple stereo configuration composed of two synchronized cameras observing an object placed on a flat surface. Following offline calibration, a single pair of images is acquired and processed to extract a limited number of significant reference points. Harris corners are used for textured surfaces, while Canny edges provide reference points for more uniform objects.
Corresponding points are identified through normalized cross-correlation, constrained by the homography and fundamental matrices of the calibrated system. Invalid correspondences are removed using epipolar geometry, edge consistency, local variance, and statistical outlier rejection. The remaining matches are rectified and triangulated to obtain a sparse three-dimensional point cloud.
Only about 250 points are required because the objective is not to reconstruct the complete surface. This reduced representation lowers computational requirements and makes the approach suitable for inexpensive acquisition and processing hardware.
An initial estimate of the volume is computed from the convex hull of the reconstructed points. A three-dimensional Delaunay triangulation divides the enclosed region into tetrahedra, whose individual volumes are summed to obtain the preliminary approximation.
Because the convex-hull estimate is sensitive to viewing angle, object position, incomplete reconstruction, and surface visibility, the project introduces a computational-intelligence refinement stage. Fourteen descriptors are extracted from the point cloud and the preliminary volume, including parameters derived from a three-dimensional bounding ellipsoid, sphere fitting, and plane interpolation.
These features are processed by a feed-forward neural network with one hidden layer. Separate models are trained for four broad shape categories: parallelepiped-shaped, cylindrical, spherical, and mixed-shaped objects. The neural model learns the relationship between the sparse geometric representation and the true object volume, compensating for variations in position, orientation, illumination, and reconstruction density.
The experimental setup used two synchronized CCD colour cameras with uniform illumination. Calibration produced a reported 3D reconstruction error of 0.019 mm. The evaluation dataset contained 52 everyday objects, each captured 30 times at different positions and angles, for a total of 1,560 stereo acquisitions.
Different neural configurations were assessed through ten-fold cross-validation. The best models achieved a mean relative error of 1.4% for parallelepiped-shaped objects and below 1% for cylindrical, spherical, and mixed-shaped objects. In comparison, direct convex-hull estimation produced much larger mean errors, ranging from 19.3% for mixed shapes to 50% for parallelepiped-shaped objects.
The results demonstrate that neural refinement substantially improves both accuracy and robustness, making the estimate less dependent on how the object is positioned with respect to the cameras. The approach therefore avoids the need for a dense 3D reconstruction while retaining precise metric information.
The method is especially suitable for objects whose general shape family can be identified in advance and whose visible surfaces provide enough reference information for stereo matching. The paper notes reduced accuracy for highly complex shapes, major occlusions, or very uniform surfaces, where the selected geometric descriptors may not fully represent the object.
Overall, the project provides a compact pipeline combining stereo acquisition, sparse 3D reconstruction, convex-hull geometry, feature extraction, and neural correction. Its principal contribution is an accurate, view-independent, and computationally efficient alternative to full 3D volume reconstruction, suitable for low-cost industrial and scientific measurement systems.
Traditional image-based approaches generally estimate volume by reconstructing a complete three-dimensional model from silhouettes, stereo images, or laser scans. Their accuracy can be strongly affected by object orientation, occlusions, surface texture, camera position, and the quality of the acquisition hardware. Producing a sufficiently dense and accurate 3D model may also require complex setups and considerable computation.
The proposed method instead uses a simple stereo configuration composed of two synchronized cameras observing an object placed on a flat surface. Following offline calibration, a single pair of images is acquired and processed to extract a limited number of significant reference points. Harris corners are used for textured surfaces, while Canny edges provide reference points for more uniform objects.
Corresponding points are identified through normalized cross-correlation, constrained by the homography and fundamental matrices of the calibrated system. Invalid correspondences are removed using epipolar geometry, edge consistency, local variance, and statistical outlier rejection. The remaining matches are rectified and triangulated to obtain a sparse three-dimensional point cloud.
Only about 250 points are required because the objective is not to reconstruct the complete surface. This reduced representation lowers computational requirements and makes the approach suitable for inexpensive acquisition and processing hardware.
An initial estimate of the volume is computed from the convex hull of the reconstructed points. A three-dimensional Delaunay triangulation divides the enclosed region into tetrahedra, whose individual volumes are summed to obtain the preliminary approximation.
Because the convex-hull estimate is sensitive to viewing angle, object position, incomplete reconstruction, and surface visibility, the project introduces a computational-intelligence refinement stage. Fourteen descriptors are extracted from the point cloud and the preliminary volume, including parameters derived from a three-dimensional bounding ellipsoid, sphere fitting, and plane interpolation.
These features are processed by a feed-forward neural network with one hidden layer. Separate models are trained for four broad shape categories: parallelepiped-shaped, cylindrical, spherical, and mixed-shaped objects. The neural model learns the relationship between the sparse geometric representation and the true object volume, compensating for variations in position, orientation, illumination, and reconstruction density.
The experimental setup used two synchronized CCD colour cameras with uniform illumination. Calibration produced a reported 3D reconstruction error of 0.019 mm. The evaluation dataset contained 52 everyday objects, each captured 30 times at different positions and angles, for a total of 1,560 stereo acquisitions.
Different neural configurations were assessed through ten-fold cross-validation. The best models achieved a mean relative error of 1.4% for parallelepiped-shaped objects and below 1% for cylindrical, spherical, and mixed-shaped objects. In comparison, direct convex-hull estimation produced much larger mean errors, ranging from 19.3% for mixed shapes to 50% for parallelepiped-shaped objects.
The results demonstrate that neural refinement substantially improves both accuracy and robustness, making the estimate less dependent on how the object is positioned with respect to the cameras. The approach therefore avoids the need for a dense 3D reconstruction while retaining precise metric information.
The method is especially suitable for objects whose general shape family can be identified in advance and whose visible surfaces provide enough reference information for stereo matching. The paper notes reduced accuracy for highly complex shapes, major occlusions, or very uniform surfaces, where the selected geometric descriptors may not fully represent the object.
Overall, the project provides a compact pipeline combining stereo acquisition, sparse 3D reconstruction, convex-hull geometry, feature extraction, and neural correction. Its principal contribution is an accurate, view-independent, and computationally efficient alternative to full 3D volume reconstruction, suitable for low-cost industrial and scientific measurement systems.