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Pascal Monasse

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Computer Vision Computational Geometry

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preprint2026arXiv

Generalize cross-ratios in n-dimensional Plane-Based Geometric Algebra

We develop a complete theory of projective cross-ratios in n-dimensional Plane-Based Geometric Algebra (PGA), R(n,0,1), covering geometric objects of every grade: finite and ideal points, hyperplanes, and intermediate flats. For each object type and configuration, we establish an explicit cross-ratio formula, prove that it recovers the appropriate classical invariant, and identify the canonical pairwise measurement operator. A systematic duality analysis further revealed that all eight configurations organize into four dual pairs under the Hodge dual, and that all measurement operators reduce to either the commutator or the commutator dual, depending solely on the geometric configuration rather than on object grade. In each case the formula recovers the appropriate classical invariant: signed distance ratios for parallel configurations and sine cross-ratios for secant ones. These results establish the cross-ratio as a grade-agnostic projective invariant within PGA, and provide a constructive foundation for defining n-dimensional homographies directly from prescribed invariants.

preprint2022arXiv

Improving neural implicit surfaces geometry with patch warping

Neural implicit surfaces have become an important technique for multi-view 3D reconstruction but their accuracy remains limited. In this paper, we argue that this comes from the difficulty to learn and render high frequency textures with neural networks. We thus propose to add to the standard neural rendering optimization a direct photo-consistency term across the different views. Intuitively, we optimize the implicit geometry so that it warps views on each other in a consistent way. We demonstrate that two elements are key to the success of such an approach: (i) warping entire patches, using the predicted occupancy and normals of the 3D points along each ray, and measuring their similarity with a robust structural similarity (SSIM); (ii) handling visibility and occlusion in such a way that incorrect warps are not given too much importance while encouraging a reconstruction as complete as possible. We evaluate our approach, dubbed NeuralWarp, on the standard DTU and EPFL benchmarks and show it outperforms state of the art unsupervised implicit surfaces reconstructions by over 20% on both datasets.

preprint2021arXiv

Deep Multi-View Stereo gone wild

Deep multi-view stereo (MVS) methods have been developed and extensively compared on simple datasets, where they now outperform classical approaches. In this paper, we ask whether the conclusions reached in controlled scenarios are still valid when working with Internet photo collections. We propose a methodology for evaluation and explore the influence of three aspects of deep MVS methods: network architecture, training data, and supervision. We make several key observations, which we extensively validate quantitatively and qualitatively, both for depth prediction and complete 3D reconstructions. First, complex unsupervised approaches cannot train on data in the wild. Our new approach makes it possible with three key elements: upsampling the output, softmin based aggregation and a single reconstruction loss. Second, supervised deep depthmap-based MVS methods are state-of-the art for reconstruction of few internet images. Finally, our evaluation provides very different results than usual ones. This shows that evaluation in uncontrolled scenarios is important for new architectures.

preprint2012arXiv

High-precision camera distortion measurements with a "calibration harp"

This paper addresses the high precision measurement of the distortion of a digital camera from photographs. Traditionally, this distortion is measured from photographs of a flat pattern which contains aligned elements. Nevertheless, it is nearly impossible to fabricate a very flat pattern and to validate its flatness. This fact limits the attainable measurable precisions. In contrast, it is much easier to obtain physically very precise straight lines by tightly stretching good quality strings on a frame. Taking literally "plumb-line methods", we built a "calibration harp" instead of the classic flat patterns to obtain a high precision measurement tool, demonstrably reaching 2/100 pixel precisions. The harp is complemented with the algorithms computing automatically from harp photographs two different and complementary lens distortion measurements. The precision of the method is evaluated on images corrected by state-of-the-art distortion correction algorithms, and by popular software. Three applications are shown: first an objective and reliable measurement of the result of any distortion correction. Second, the harp permits to control state-of-the art global camera calibration algorithms: It permits to select the right distortion model, thus avoiding internal compensation errors inherent to these methods. Third, the method replaces manual procedures in other distortion correction methods, makes them fully automatic, and increases their reliability and precision.