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Register a new userReverse engineering of CAD models via clustering and approximate implicitization
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Georg Muntingh PhD
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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In applications like computer aided design, geometric models are often represented numerically as polynomial splines or NURBS, even when they originate from primitive geometry. For purposes such as redesign and isogeometric analysis, it is of interest to extract information about the underlying geometry through reverse engineering. In this work we develop a novel method to determine these primitive shapes by combining clustering analysis with approximate implicitization. The proposed method is automatic and can recover algebraic hypersurfaces of any degree in any dimension. In exact arithmetic, the algorithm returns exact results. All the required parameters, such as the implicit degree of the patches and the number of clusters of the model, are inferred using numerical approaches in order to obtain an algorithm that requires as little manual input as possible. The effectiveness, efficiency and robustness of the method are shown both in a theoretical analysis and in numerical examples implemented in Python.
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We propose a novel method to generate fabrication blueprints from images of carpentered items. While 3D reconstruction from images is a well-studied problem, typical approaches produce representations that are ill-suited for computer-aided design and fabrication applications. Our key insight is that fabrication processes define and constrain the design space for carpentered objects, and can be leveraged to develop novel reconstruction methods. Our method makes use of domain-specific constraints to recover not just valid geometry, but a semantically valid assembly of parts, using a combination of image-based and geometric optimization techniques. We demonstrate our method on a variety of wooden objects and furniture, and show that we can automatically obtain designs that are both easy to edit and accurate recreations of the ground truth. We further illustrate how our method can be used to fabricate a physical replica of the captured object as well as a customized version, which can be produced by directly editing the reconstructed model in CAD software.
State-of-the-art (SOTA) Generative Models (GMs) can synthesize photo-realistic images that are hard for humans to distinguish from genuine photos. We propose to perform reverse engineering of GMs to infer the model hyperparameters from the images generated by these models. We define a novel problem, model parsing, as estimating GM network architectures and training loss functions by examining their generated images -- a task seemingly impossible for human beings. To tackle this problem, we propose a framework with two components: a Fingerprint Estimation Network (FEN), which estimates a GM fingerprint from a generated image by training with four constraints to encourage the fingerprint to have desired properties, and a Parsing Network (PN), which predicts network architecture and loss functions from the estimated fingerprints. To evaluate our approach, we collect a fake image dataset with $100$K images generated by $100$ GMs. Extensive experiments show encouraging results in parsing the hyperparameters of the unseen models. Finally, our fingerprint estimation can be leveraged for deepfake detection and image attribution, as we show by reporting SOTA results on both the recent Celeb-DF and image attribution benchmarks.
Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to networks of moderate or higher complexity. In general, approximate solutions tend to sacrifice accuracy for speed, where the aim is to minimise the loss in accuracy and maximise the gain in speed. While some approximate algorithms are optimised to handle thousands of variables, these algorithms may still be unable to learn such high dimensional structures. Some of the most efficient score-based algorithms cast the structure learning problem as a combinatorial optimisation of candidate parent sets. This paper explores a strategy towards pruning the size of candidate parent sets, aimed at high dimensionality problems. The results illustrate how different levels of pruning affect the learning speed relative to the loss in accuracy in terms of model fitting, and show that aggressive pruning may be required to produce approximate solutions for high complexity problems.
In this paper we consider two metric covering/clustering problems - textit{Minimum Cost Covering Problem} (MCC) and $k$-clustering. In the MCC problem, we are given two point sets $X$ (clients) and $Y$ (servers), and a metric on $X cup Y$. We would like to cover the clients by balls centered at the servers. The objective function to minimize is the sum of the $alpha$-th power of the radii of the balls. Here $alpha geq 1$ is a parameter of the problem (but not of a problem instance). MCC is closely related to the $k$-clustering problem. The main difference between $k$-clustering and MCC is that in $k$-clustering one needs to select $k$ balls to cover the clients. For any $eps > 0$, we describe quasi-polynomial time $(1 + eps)$ approximation algorithms for both of the problems. However, in case of $k$-clustering the algorithm uses $(1 + eps)k$ balls. Prior to our work, a $3^{alpha}$ and a ${c}^{alpha}$ approximation were achieved by polynomial-time algorithms for MCC and $k$-clustering, respectively, where $c > 1$ is an absolute constant. These two problems are thus interesting examples of metric covering/clustering problems that admit $(1 + eps)$-approximation (using $(1+eps)k$ balls in case of $k$-clustering), if one is willing to settle for quasi-polynomial time. In contrast, for the variant of MCC where $alpha$ is part of the input, we show under standard assumptions that no polynomial time algorithm can achieve an approximation factor better than $O(log |X|)$ for $alpha geq log |X|$.
Assembly modeling is a core task of computer aided design (CAD), comprising around one third of the work in a CAD workflow. Optimizing this process therefore represents a huge opportunity in the design of a CAD system, but current research of assembly based modeling is not directly applicable to modern CAD systems because it eschews the dominant data structure of modern CAD: parametric boundary representations (BREPs). CAD assembly modeling defines assemblies as a system of pairwise constraints, called mates, between parts, which are defined relative to BREP topology rather than in world coordinates common to existing work. We propose SB-GCN, a representation learning scheme on BREPs that retains the topological structure of parts, and use these learned representations to predict CAD type mates. To train our system, we compiled the first large scale dataset of BREP CAD assemblies, which we are releasing along with benchmark mate prediction tasks. Finally, we demonstrate the compatibility of our model with an existing commercial CAD system by building a tool that assists users in mate creation by suggesting mate completions, with 72.2% accuracy.
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