Filleting is a fundamental operation in CAD systems, akin to a ball rolling between two adjacent surface patches, resulting in a seamless connection. The reverse process, which we refer to as DeFillet in this paper, is crucial for CAE analysis and secondary design phases. However, it presents significant challenges, particularly when the input data originates from surface reconstruction or discretization processes. Our DeFillet algorithm is inspired by the observation that the rolling-ball center defines an osculating sphere, while the Voronoi diagram of surface samples provides sufficiently many rolling-ball center candidates. By leveraging this insight, we compute a transformation between the Voronoi vertices and the surface samples, enabling the efficient identification of fillet regions. Subsequently, we formulate the reconstruction of sharp features as a quadratic optimization problem. Our method's effectiveness has been validated through extensive testing using self-constructed models and 100 filleted models selected from the Fusion 360 Gallery dataset. The code for this paper is publicly available at https://github.com/xiaowuga/DeFillet.

This paper presents a novel non-rigid point set registration method that is inspired by unsupervised clustering analysis. Unlike previous approaches that treat the source and target point sets as separate entities, we develop a holistic framework where they are formulated as clustering centroids and clustering members, separately. We then adopt Tikhonov regularization with an$\ell_{1}$-induced Laplacian kernel instead of the commonly used Gaussian kernel to ensure smooth and more robust displacement fields. Our formulation delivers closed-form solutions, theoretical guarantees, independence from dimensions, and the ability to handle large deformations. Subsequently, we introduce a clustering-improved Nyström method to effectively reduce the computational complexity and storage of the Gram matrix to linear, while providing a rigorous bound for the low-rank approximation. Our method achieves high accuracy results across various scenarios and surpasses competitors by a significant margin, particularly on shapes with sub-stantial deformations. Additionally, we demonstrate the versatility of our method in challenging tasks such as shape transfer and medical registration. [Code release]

This work presents a novel and effective method for fitting multidimensional ellipsoids (i.e., ellipsoids embedded in [Formula: see text]) to scattered data in the contamination of noise and outliers. Unlike conventional algebraic or geometric fitting paradigms that assume each measurement point is a noisy version of its nearest point on the ellipsoid, we approach the problem as a Bayesian parameter estimate process and maximize the posterior probability of a certain ellipsoidal solution given the data. We establish a more robust correlation between these points based on the predictive distribution within the Bayesian framework, i.e., considering each model point as a potential source for generating each measurement. Concretely, we incorporate a uniform prior distribution to constrain the search for primitive parameters within an ellipsoidal domain, ensuring ellipsoid-specific results regardless of inputs. We then establish the connection between measurement point and model data via Bayes' rule to enhance the method's robustness against noise. Due to independent of spatial dimensions, the proposed method not only delivers high-quality fittings to challenging elongated ellipsoids but also generalizes well to multidimensional spaces. To address outlier disturbances, often overlooked by previous approaches, we further introduce a uniform distribution on top of the predictive distribution to significantly enhance the algorithm's robustness against outliers. Thanks to the uniform prior, our maximum a posterior probability coincides with a more tractable maximum likelihood estimation problem, which is subsequently solved by a numerically stable Expectation Maximization (EM) framework. Moreover, we introduce an ε-accelerated technique to expedite the convergence of EM considerably. We also investigate the relationship between our algorithm and conventional least-squares-based ones, during which we theoretically prove our method's superior robustness. To the best of our knowledge, this is the first comprehensive method capable of performing multidimensional ellipsoid-specific fitting within the Bayesian optimization paradigm under diverse disturbances. We evaluate it across lower and higher dimensional spaces in the presence of heavy noise, outliers, and substantial variations in axis ratios. Also, we apply it to a wide range of practical applications such as microscopy cell counting, 3D reconstruction, geometric shape approximation, and magnetometer calibration tasks. In all these test contexts, our method consistently delivers flexible, robust, ellipsoid-specific performance, and achieves the state-of-the-art results.

The registration of unitary-modality geometric data has been successfully explored over past decades. However, existing approaches typically struggle to handle cross-modality data due to the intrinsic difference between different models. To address this problem, in this article, we formulate the cross-modality registration problem as a consistent clustering process. First, we study the structure similarity between different modalities based on an adaptive fuzzy shape clustering, from which a coarse alignment is successfully operated. Then, we optimize the result using fuzzy clustering consistently, in which the source and target models are formulated as clustering memberships and centroids, respectively. This optimization casts new insight into point set registration, and substantially improves the robustness against outliers. Additionally, we investigate the effect of fuzzier in fuzzy clustering on the cross-modality registration problem, from which we theoretically prove that the classical Iterative Closest Point (ICP) algorithm is a special case of our newly defined objective function. Comprehensive experiments and analysis are conducted on both synthetic and real-world cross-modality datasets. Qualitative and quantitative results demonstrate that our method outperforms state-of-the-art approaches with higher accuracy and robustness. Our code is publicly available at https://github.com/zikai1/CrossModReg.

We propose a novel and efficient method for reconstructing manifold surfaces from point clouds. Unlike previous approaches that use dense implicit reconstructions or piecewise approximations and overlook inherent structures like quadrics in CAD models, our method faithfully preserves these quadric structures by assembling primitives. To achieve high-quality primitive extraction, we use a variational shape approximation, followed by a mesh arrangement for space partitioning and candidate primitive patches generation. We then introduce an effective pruning mechanism to classify candidate primitive patches as active or inactive, and further prune inactive patches to reduce the search space and speed up surface extraction significantly. Finally, the optimal active patches are computed by a binary linear programming and assembled as manifold and watertight surfaces. We perform extensive experiments on a wide range of CAD objects to validate its effectiveness.

We present a novel yet effective method for detecting elliptical primitives in cluttered, occluded images, which has versatile applications in computer vision and multimedia processing fields. We begin by the fast extraction of smooth arcs from the edge map, followed by the construction of a directed graph and a disjoint-set forest, whereby the arc relationships are effectively encoded to enhance the arc grouping process. Compared with representative approaches such as the depth-first search, the disjoint-set forest enables complete grouping of arcs to generate candidate ellipses. Moreover, it merely has linear memory complexity and constant access time, hence guarantees fast detection. To boost precision and remove false positives, we propose to project the candidate ellipses onto the original image, to align the gradients of ellipses and the image pixels. We also vectorize the elliptical parameters to depress duplicated candidates. We perform extensive experiments on both synthetic and challenging real-world datasets, to show that our detector is accurate and efficient, as well as versatile in many practical tasks. The source code and datasets are available at https://github.com/xiaowuga/EDSF.