LoVis: Local Pattern Visualization for Model Refinement

Linear models are commonly used to identify trends in data. While it is an easy task to build linear models using pre‐selected variables, it is challenging to select the best variables from a large number of alternatives. Most metrics for selecting variables are global in nature, and thus not useful for identifying local patterns. In this work, we present an integrated framework with visual representations that allows the user to incrementally build and verify models in three model spaces that support local pattern discovery and summarization: model complementarity, model diversity, and model representivity. Visual representations are designed and implemented for each of the model spaces. Our visualizations enable the discovery of complementary variables, i.e., those that perform well in modeling different subsets of data points. They also support the isolation of local models based on a diversity measure. Furthermore, the system integrates a hierarchical representation to identify the outlier local trends and the local trends that share similar directions in the model space. A case study on financial risk analysis is discussed, followed by a user study.     

Variational Tree Synthesis

Modelling trees according to desired shapes is important for many applications. Despite numerous methods having been proposed in tree modelling, it is still a non‐trivial task and challenging. In this paper, we present a new variational computing approach for generating realistic trees in specific shapes. Instead of directly modelling trees from symbolic rules, we formulate the tree modelling as an optimization process, in which a variational cost function is iteratively minimized. This cost function measures the difference between the guidance shape and the target tree crown. In addition, to faithfully capture the branch structure of trees, several botanical factors, including the minimum total branches volume and spatial branches patterns, are considered in the optimization to guide the tree modelling process. We demonstrate that our approach is applicable to generate trees with different shapes, from interactive design and complex polygonal meshes.     

A Projective Framework for Polyhedral Mesh Modelling

We present a novel framework for polyhedral mesh editing with face‐based projective maps that preserves planarity by definition. Such meshes are essential in the field of architectural design and rationalization. By using homogeneous coordinates to describe vertices, we can parametrize the entire shape space of planar‐preserving deformations with bilinear equations. The generality of this space allows for polyhedral geometric processing methods to be conducted with ease. We demonstrate its usefulness in planar‐quadrilateral mesh subdivision, a resulting multi‐resolution editing algorithm, and novel shape‐space exploration with prescribed transformations. Furthermore, we show that our shape space is a discretization of a continuous space of conjugate‐preserving projective transformation fields on surfaces. Our shape space directly addresses planar‐quad meshes, on which we put a focus, and we further show that our framework naturally extends to meshes with faces of more than four vertices as well.     

Importance Sampling Microfacet‐Based BSDFs using the Distribution of Visible Normals

We present a new approach to microfacet‐based BSDF importance sampling. Previously proposed sampling schemes for popular analytic BSDFs typically begin by choosing a microfacet normal at random in a way that is independent of direction of incident light. To sample the full BSDF using these normals requires arbitrarily large sample weights leading to possible fireflies. Additionally, at grazing angles nearly half of the sampled normals face away from the incident ray and must be rejected, making the sampling scheme inefficient. Instead, we show how to use the distribution of visible normals directly to generate samples, where normals are weighted by their projection factor toward the incident direction. In this way, no backfacing normals are sampled and the sample weights contain only the shadowing factor of outgoing rays (and additionally a Fresnel term for conductors). Arbitrarily large sample weights are avoided and variance is reduced. Since the BSDF depends on the microsurface model, we describe our sampling algorithm for two models: the V‐cavity and the Smith models. We demonstrate results for both isotropic and anisotropic rough conductors and dielectrics with Beckmann and GGX distributions.     

Sparse Localized Decomposition of Deformation Gradients

Sparse localized decomposition is a useful technique to extract meaningful deformation components out of a training set of mesh data. However, existing methods cannot capture large rotational motion in the given mesh dataset. In this paper we present a new decomposition technique based on deformation gradients. Given a mesh dataset, the deformation gradient field is extracted, and decomposed into two groups: rotation field and stretching field, through polar decomposition. These two groups of deformation information are further processed through the sparse localized decomposition into the desired components. These sparse localized components can be linearly combined to form a meaningful deformation gradient field, and can be used to reconstruct the mesh through a least squares optimization step. Our experiments show that the proposed method addresses the rotation problem associated with traditional deformation decomposition techniques, making it suitable to handle not only stretched deformations, but also articulated motions that involve large rotations.     

Mean-field phase transitions and correlation functions for Gibbs random fields

The use of Gibbs random fields (GRF) to model images poses the important problem of the dependence of the patterns sampled from the Gibbs distribution on its parameters. Sudden changes in these patterns as the parameters are varied are known asphase transitions. In this paper we concentrate on developing a general deterministic theory for the study of phase transitions when a single parameter, namely, the temperature, is varied. This deterministic framework is based on a technique known as themean-field approximation, which is widely used in statistical physics. Our mean-field theory is general in that it is valid for any number of gray levels, any pairwise interaction potential, any neighborhood structure or size, and any set of constraints imposed on the desired images. The mean-field approximation is used to compute closed-form estimates of the critical temperatures at which phase transitions occur for two texture models widely used in the image modeling literature: the Potts model and the autobinomial model. The mean-field model allows us to gain insight into the Gibbs model behavior in the neighborhood of these temperatures. These analytical results are verified by computer simulations that use a novel mean-field descent algorithm. An important spinoff of our mean-field theory is that it allows us to compute approximations for the correlation functions of GRF models, thus bridging the gap between neighborhood-based and correlation-baseda priori image models.The work of I.M. Elfadel was supported in part by the National Science Foundation under grant MIP-91-17724. The work of A.L. Yuille was supported by the Brown, Harvard, and MIT Center for Intelligent Control Systems under U.S. Army Research Office grant DAAL03-86-C-0171, by the Defense Advanced Research Projects Agency under contract AFOSR-89-0506, and by the National Science Foundation under grant IRI-9003306.     

Towards User‐Centered Active Learning Algorithms

The labeling of data sets is a time‐consuming task, which is, however, an important prerequisite for machine learning and visual analytics. Visual‐interactive labeling (VIAL) provides users an active role in the process of labeling, with the goal to combine the potentials of humans and machines to make labeling more efficient. Recent experiments showed that users apply different strategies when selecting instances for labeling with visual‐interactive interfaces. In this paper, we contribute a systematic quantitative analysis of such user strategies. We identify computational building blocks of user strategies, formalize them, and investigate their potentials for different machine learning tasks in systematic experiments. The core insights of our experiments are as follows. First, we identified that particular user strategies can be used to considerably mitigate the bootstrap (cold start) problem in early labeling phases. Second, we observed that they have the potential to outperform existing active learning strategies in later phases. Third, we analyzed the identified core building blocks, which can serve as the basis for novel selection strategies. Overall, we observed that data‐based user strategies (clusters, dense areas) work considerably well in early phases, while model‐based user strategies (e.g., class separation) perform better during later phases. The insights gained from this work can be applied to develop novel active learning approaches as well as to better guide users in visual interactive labeling.     

QuadriFlow: A Scalable and Robust Method for Quadrangulation

QuadriFlow is a scalable algorithm for generating quadrilateral surface meshes based on the Instant Field‐Aligned Meshes of Jakob et al. (ACM Trans. Graph. 34(6):189, 2015). We modify the original algorithm such that it efficiently produces meshes with many fewer singularities. Singularities in quadrilateral meshes cause problems for many applications, including parametrization and rendering with Catmull‐Clark subdivision surfaces. Singularities can rarely be entirely eliminated, but it is possible to keep their number small. Local optimization algorithms usually produce meshes with many singularities, whereas the best algorithms tend to require non‐local optimization, and therefore are slow. We propose an efficient method to minimize singularities by combining the Instant Meshes objective with a system of linear and quadratic constraints. These constraints are enforced by solving a global minimum‐cost network flow problem and local boolean satisfiability problems. We have verified the robustness and efficiency of our method on a subset of ShapeNet comprising 17,791 3D objects in the wild. Our evaluation shows that the quality of the quadrangulations generated by our method is as good as, if not better than, those from other methods, achieving about four times fewer singularities than Instant Meshes. Other algorithms that produce similarly few singularities are much slower; we take less than ten seconds to process each model. Our source code is publicly available.     

Adaptive Compression of Texture Pyramids

High‐quality texture minification techniques, including trilinear and anisotropic filtering, require texture data to be arranged into a collection of pre‐filtered texture maps called mipmaps. In this paper, we present a compression scheme for mipmapped textures which achieves much higher quality than current native schemes by exploiting image coherence across mipmap levels. The basic idea is to use a high‐quality native compressed format for the upper levels of the mipmap pyramid (to retain efficient minification filtering) together with a novel compact representation of the detail provided by the highest‐resolution mipmap. Key elements of our approach include delta‐encoding of the luminance signal, efficient encoding of coherent regions through texel runs following a Hilbert scan, a scheme for run encoding supporting fast random‐access, and a predictive approach for encoding indices of variable‐length blocks. We show that our scheme clearly outperforms native 6:1 compressed texture formats in terms of image quality while still providing real‐time rendering of trilinearly filtered textures.