Software & Industrial workshop II and ESR Days

André Lieutier (Geometry Engineering) – From topological inference to meshing algorithms

In this tutorial we consider the general problem of retrieving a topologically correct model from partial geometric information. Applications areas span from automated 3D scene faithful reconstruction from scanned points clouds to abstract submanifolds inference from high dimensional data in the context of machine learning.
In a first part, the tutorial will recall several topological notions and consider their possible inference from data. In a second part, we focus on the computation of simplicial complexes homeomorphic to manifolds known through point samples, in other words, manifolds triangulation algorithms with topological guarantees.

Leonidas Guibas (Stanford university) – Learning to Vary and Varying to Learn

Variations in how a 3D object or scene is presented to a learning algorithm, for example the coordinate system chosen, can significantly impact the learned outcome. At the same time, the space of intrinsic variations of the scene itself is intimately connected with the semantics of the scene and the continuous or discrete attributes we are trying to learn. Certain variations may be just nuisance while others crucial to the task at hand. The talk highlight a few efforts that address this issue of disentangling how variations of a scene or of its presentation affect learning tasks, aiming to show the value of low dimensional parametrizations of the semantic tangent space of object and scene representations, towards both analysis and synthesis learning tasks.

A first vignette looks at how to design neural architectures that are invariant or equivariant to spatial transforms like rigid motions that affect scene presentation and introduces the vector neuron machinery for neural components that operate on vectors and not scalars. In the second vignette we look at how to shape neural scene representations such as NeRFs to better reflect the compositional structure of the scene by doing contrastive learning based on co-variation patterns between scene points or pixels (in scene views) with high mutual information. These learned “resonances” allow efficient propagation of sparse annotations or semantically coherent scene edits. Finally, in the third vignette we look at how language that differentiates related object geometries can be used for segmentation as well as for the generation of object variants based on written/spoken instructions.

Christoph Hofer (RISC-Software) – Numerical and automatic differentiation

In this tutorial session, we will investigate different ways to program the computer to calculate derivatives of functions. To be precise we consider difference-quotients, the complex step, and automatic/algorithmic differentiation methods. We discuss their advantages, disadvantages, and limitations. Besides the algorithmic realization, we will also look at their mathematical properties. The different algorithms and examples will be implemented in small programming exercises.

The preferred language for the exercises is python, but in principle the participants are free to use any language as long as it provides operator overloading, graphs of functions/line charts can be plotted, and complex numbers are supported. For python various plotting libraries exist, a common one is plotly (https://plotly.com/python/). A very basic understanding of python numpy is advantageous. The participants, who use python should have the packages numpy, plotly and pandas installed. I advise to use PyCharm as an IDE.

XMANAI team (Theodore Dalamagas, Eleni Lavasa, Vasilis Gkolemis – Athena RC) – XAI application in Industrial Metrology — SLIDES: Interpretable Machine Learning, eXplainable Artificial Intelligence Application in Metrology

Nowadays, quality Control of manufactured parts (e.g., automotive, aeronautical and energy sectors) is performed with advanced optical technology (3D laser scanning) in the Industry 4.0 era to achieve dimensional quality requirements and tolerances with high precision and in minimum time. Each part under metrological study is captured in a 3D Point Cloud, which is subsequently analyzed with domain-specific software to obtain the dimensional measurement and estimate the associated accuracy of the measurement (tolerance). In this tutorial we examine the data science applications for industrial metrology scenarios: starting from the manipulation of Point Cloud data, moving on to the prediction of an instrument’s accuracy in point capturing using popular Machine Learning algorithms, and closing with the application of post-hoc explainability techniques to interpret the predictions of the ML models. Our goal is to showcase the benefits explainable AI (XAI) has to offer in complex industrial settings such as Industrial Metrology.

Tutorial outline:

• Part A (1h)
  1. Introduction to Explainable AI and the XMANAI research project (5 min)
  2. Industrial Metrology: the Use Case of UNIMETRIK pilot in XMANAI (15 min)
  3. Lab#1: Point Cloud analysis and feature extraction (30 min)
     Software: Python3 / numpy, pandas, jupyter notebook, open3d
  4. Discussion (10min)
• Part B (1.5h)
  1. Lab#2: Building a predictor for point capturing accuracy (30 min)
     Software: Python3 / numpy, pandas, jupyter, scikit-learn
  2. Discussion: Quantitative & Qualitative model evaluation (15 min)
  3. Lab#3: Explainability study of the predictive models (30 min)
     Software: Python3 / scikit-learn (permutation importance, pdp), SHAP
  4. Discussion: Assessing the quality/impact of explanations (15 min)

Claudio Mancinelli (University of Genoa) – Vector Graphics on Discrete Surfaces, (pdf version)

Software packages for the generation of vector graphics in 2D are available in many forms nowadays. The concept of geometric primitive is at the core of this technology. Essentially, geometric primitives are basic geometric shapes that can be used and combined to generate more complex ones. Such primitives are defined in a plane endowed with the Euclidean metric, together with a Cartesian coordinate system, and the algorithms to generate them are based on this structure.

In this talk, we will start by describing the theoretical and computational challenges that one needs to overcome when trying to bring this technology onto a (discrete) surface. The theoretical ones, are mainly due to the fact that we can no longer rely on the Euclidean metric. From a computational point of view instead, one needs to ensure the correctness, robustness and efficiency of its implementation, in order to reproduce the behaviour of the 2D drawing systems. We will then present some examples of publicly available implementations in which both of these problems have been successfully addressed.

Arturs Berzins (SINTEF) – Neural Implicit Shape Editing using Boundary Sensitivity.

Neural fields are receiving increased attention as a geometric representation due to their ability to compactly store detailed and smooth shapes and easily undergo topological changes. Compared to classic geometry representations, however, neural representations do not allow the user to exert intuitive control over the shape. Motivated by this, we leverage boundary sensitivity to express how perturbations in parameters move the shape boundary. This allows to interpret the effect of each learnable parameter and study achievable deformations. With this, we perform geometric editing: finding a parameter update which best approximates a globally prescribed deformation. Prescribing the deformation only locally allows to deform the rest of the shape according to some prior, such as semantics or deformation rigidity. Different to previous efforts, our method is model-agnostic and can be applied to any pre-trained NN and update it in-place. Furthermore, we show how boundary sensitivity helps to optimize and constrain objectives (such as surface area and volume), which are difficult to compute without first converting to another representation, such as a mesh.

Rao Fu (GF) – Local feature size adaptive surface reconstruction from unoriented point sets

This work seeks to design a surface reconstruction algorithm from unoriented point sets by adapting to the local feature size. The method has three steps: constructing an envelope, signing the envelope, and adaptive meshing. First, a Delaunay refinement process produces the envelope from the iso-level of the unsigned distance function field. Afterward, we use a globally optimized solver to solve the sign of the envelope by a signing guess from the edges. Finally, we use another Delaunay refinement process to mesh the target shape by a sizing function adaptive to the local feature size. This method is easy to implement and can guarantee the output of an isotropic mesh in a single pass. Experiments prove that our algorithm outperforms two-stage algorithms.

Amrutha Balachandran Nair (Inria) – Mu-Basis of Parametrizations of Surfaces 

Mu-basis is the basis of syzygy module of a parametrization from which we can retrieve the parametrization back. We will be looking at certain parametrizations in two variables, that describes surfaces and how to find mu-basis. In particular we will be looking at translational surfaces and generalized surfaces of revolution. Translational surfaces, which are surfaces generated by two rational curves by sliding one along the other. Generalized surfaces of revolution are surfaces are generated by rotating a rational space curve around another curve.

Konstantinos Tertikas (Athena RC) – Generating Part-Aware Editable 3D Shapes without 3D Supervision 

Impressive progress in generative models and implicit representations gave rise to methods that can generate 3D shapes of high quality. However, being able to locally control and edit shapes is another essential property that can unlock several content creation applications. Local control can be achieved with part-aware models, but existing methods require 3D supervision and cannot produce textures. In this work, we devise a novel part-aware generative model for editable 3D shape synthesis that does not require any explicit 3D supervision. Our model generates objects as a set of locally defined NeRFs, augmented with an affine transformation. This enables several editing operations such as applying transformations on parts, mixing parts from different objects etc. To ensure distinct, manipulable parts we enforce a hard assignment of rays to parts that makes sure that the color of each ray is only determined by a single NeRF. As a result, altering one part does not affect the appearance of the others. Evaluations on various ShapeNet categories demonstrate the ability of our model to generate editable 3D objects of improved fidelity, compared to previous part-based generative approaches that require 3D supervision or models relying on NeRFs.

TBA

Thanasis Zoumpekas (UB) – Temporal 3D Point Cloud Processing and Understanding

Point clouds have emerged as a crucial data type in the field of 3D analysis, owing to their ability to provide a comprehensive and accurate representation of real-world environments. They are utilized in various areas such as autonomous driving, geoscience, construction, manufacturing, and heritage preservation. However, analyzing large and dynamic point clouds poses several challenges, such as dealing with noise, missing data, and temporal consistency. This talk presents some of our studies on processing and understanding temporal and static 3D point clouds, with a focus on geoscience and manufacturing applications. The studies include a proposed framework for rockfall detection, a novel application of temporal 3D point clouds in manufacturing for machining tool identification, and an ongoing study on unsupervised 3D detection of complex geometrical shapes in 3D point cloud scenes both indoors and outdoors.

Francesco Patrizi (University of Florence) – An Algorithmic Introduction to LR B-splines

In this tutorial we shall introduce LR B-splines. These are generalization of B-splines over locally refined quadrilateral meshes and are exploited for a wide range of applications in Computer Aided Design (CAD) and Computer Aided Engineering (CAE), such as isogeometric analysis and quasi-interpolation, in particular for bathymetry and terrain datasets.
There are several ways to introduce the LR B-splines. In this tutorial we will focus on an algorithmic approach: provided an initial set of tensor B-splines on a coarse tensor mesh we shall see the procedure to generate the LR B-splines while updating such mesh with local insertions.

Next, we shall see the main refinement algorithms for LR B-splines, i.e., the procedures that automatically generate LR B-splines on the regions where they are needed to reduce the error in some sense. Namely, we will see 6 strategies: the minimum span, the full span, the structured mesh, the non-nested-support-structured mesh, the hierachical mesh and the effective grading refinements.
Finally, if we have time, we should address the linear dependence problem and how to solve it with the peeling algorithm.

Eriola Hoxhaj (JKU) and Jean Michel Menjanahary (VU) – Reconstruction of Darboux cyclides from a single view apparent contour

The task of recognizing an algebraic surface from its apparent contour can be reduced to the recovering of a homogeneous equation in four variables from its discriminant. We present a reconstruction algorithm that applies to Darboux cyclidic surfaces up to Euclidean transformation similarities.

Carles Checa (Athena RC) and Pablo González-Mazón (Inria) – Approximating swept volumes with Bezier patches

The computation of the volume swept by a tool along a trajectory is an important step in the simulation of a machining process. One approach for this computation consists of sampling the surface of the tool with multiple points at different instants of the motion, and fitting the resulting point cloud with an approximate surface using implicit functions. In our work, we describe the pipeline of this computation with several types of volume representations. Namely, we present an approach based on Bezier patches. In this approach, the machining tool is given as a point cloud that is fitted by a curvilinear mesh, i.e., it is described by Bezier patches. The computation of the swept volume is then performed using algebraic methods over the polynomial parametrizations given by these patches. Finally, we use a routine of ray-tracing with elimination matrices that can be used for both visualization and point cloud reconstruction.

Michelangelo Marsala (Inria) – Point Cloud Data Fitting via G1 Smooth Spline Basis Functions

Geometrically smooth spline functions are piecewice polynomial functions defined on a mesh, that satisfy properties of differentiability across shared edges; their unstructured nature provide them a wide range of application like, for example, the point data fitting. Point cloud fitting is a very important topic especially in CAD theory, which permits in fact to translate CAD data into Bézier representation. In the presentation we consider G1splines on quadrangular mesh defined with quadratic gluing data function along shared edges. We will describe shortly their construction, their properties, analyze their space, and provide dimension formula. After having showed how to construct an efficient basis for the considered space, numerical results will be presented to illustrate the quality of the fitting.  

Krunal Raval (UTV) – Adaptive isogeometric analysis based on Tchebycheffian splines

Tchebycheffian splines are piecewise smooth functions with pieces in Tchebycheff spaces, the natural generalization of polynomial spaces. Under suitable assumptions, Tchebycheffian splines can be represented in terms of B-spline like basis functions, called Tchebycheffian B-splines, with structural similarities and all fundamental properties of classical polynomial B-splines (compact support, non-negativity, partition of unity, etc.). Tchebycheffian splines offer a huge flexibility compared to classical polynomial splines: they are equipped with parameters that can be selected according to a problem-oriented strategy, taking into account the geometrical and/or analytical issues of the specific addressed problem.
While the tensor-product approach can easily build multivariate splines, they lack adequate adaptive local refinement, which could be important in both geometric modelling and numerical simulation. This triggered the interest in alternative (polynomial) spline structures supporting local refinement still retaining the local tensor-product structure. Since Tchebycheffian B-splines are plug-to-plug compatible with polynomial B-splines, they are naturally compatible with the local refinement structures known for polynomial B-splines (Hierarchical mesh, T-spline mesh and Locally Refined(LR-) mesh).  
In this talk, we discuss the use of Tchebycheffian splines equipped with a local tensor-product structure as a possible tool in isogeometric analysis with adaptive refinement.

Shahroz Khan (U.Strathclyde) – Shape-Supervised Dimension Reduction

In shape optimisation problems, subspaces generated with conventional feature extraction-based design space dimension reduction (DSDR) approaches often fail to extract the intrinsic geometric features of the shape that would allow the exploration of diverse but valid candidate solutions. More importantly, they also lack incorporation of any notion of physics against which shape is optimised. To simultaneously tackle these deficiencies, the proposed shape-supervised DSDR uses higher-level information about the shape in terms of its geometric integral properties, such as geometric moments and their invariants. Their usage is based on the fact that moments of a shape are intrinsic features of its geometry, providing a unifying medium between geometry and physics. To enrich the subspace with latent features associated with the shape’s geometrical features and physics, we also evaluate a set of composite geometric moments, using the divergence theorem, for appropriate shape decomposition. These moments are combined with the shape modification function to form a decomposed SSV uniquely representing a shape. Afterwards, the generalised Karhunen–Loève expansion is applied to SSV, embedded in a generalised (disjoint) Hilbert space, which results in a basis of the shape-supervised subspace retaining the highest geometric and physical variance.

Alexandros Georgiou (USI) – Diffusion models for graph-structured data

Diffusion (probabilistic) models form a family of generative models that have found great success in various tasks and, most notably, image synthesis. We will discuss recent results of diffusion models on graph-structured data and some ideas on how these can be improved.