Abstract This paper presents a new method for constructing a clustered hierarchy of Level‐of‐Detail (LOD) with As‐Simplified‐As‐Possible cluster boundaries to represent large scale triangular meshes at varying resolution, making them suitable for interactive applications. Ensuring consistency between nodes in a clustered hierarchy remains a challenging problem, cracks may appear when dealing with nodes of different resolutions. Bypassing the issue by locking boundary vertices leads to under‐simplification causing quality loss or non‐volume‐preserving simplifications. To address these limitations, we propose a novel approach: a hierarchy construction that enables nodes boundaries simplification at each level, maintaining consistency between neighboring clusters. Building upon existing methods, we represent the model as a clustered hierarchy of Progressive Meshes. Nodes are formed by a partition of a progressive internal mesh and a set of progressive boundary portions in bijection with the node neighbors, allowing for continuous refinement of the boundary while ensuring the LOD mesh to be crack‐free (neighboring clusters in the view‐dependent LOD have consistent boundaries). This new degree of freedom results in an LOD of better quality and/or a more simplified model, and also reduces popping effects that may occur when abruptly simplifying locked boundaries. Our method focuses on the construction of this adaptive representation while ensuring that it is compatible with the standard rendering pipeline, and we provide an example of implementation.

Abstract We present an adaptive, semantics‐based abstraction approach that balances aesthetic quality and structural coherence within the practical constraints of robotic painting. We apply panoptic segmentation with color‐based over‐segmentation to partition images into meaningful regions aligned with semantic objects, while providing flexible abstraction levels. Automatic parameter selection for region merging is enabled by semantic saliency maps, derived from Out‐of‐Distribution segmentation techniques in combination with machine learning methods for feature detection. This preserves the boundaries of salient objects while simplifying less prominent regions. A graph‐based community detection step further refines the abstraction by grouping regions according to local connectivity and semantic coherence. The runtime of our method outperforms optimization‐based image vectorization methods, enabling the efficient generation of multiple abstraction levels that can serve as hierarchical layers for robotic painting. We demonstrate the quality of our method by showing abstraction results, robotic paintings with the e‐David robot, and a comparison to other abstraction methods.

Abstract We present a new, high‐quality compositing pipeline and navigation approach for variable resolution imagery. The motivation of this work is to explore the use of variable resolution images as a quick and accessible alternative to traditional gigapixel mosaics. Instead of the common tedious acquisition of many images using specialized hardware, variable resolution images can achieve similarly deep zooms as large mosaics, but with only a handful of images. For this approach to be a viable alternative, the state‐of‐the‐art in variable resolution compositing needs to be improved to match the high‐quality approaches commonly used in mosaic compositing. To this end, we provide a novel, variable resolution mosaic seam calculation and gradient domain color correction. This approach includes a new priority order graph cuts computation along with a practical data structure to keep memory overhead low. In addition, navigating variable resolution images is challenging, especially at the zoom factors targeted in this work. To address this challenge, we introduce a new image interaction for variable resolution imagery: a pan that automatically, and smoothly, hugs available resolution. Finally, we provide several real‐world examples of our approach producing high‐quality variable resolution mosaics with deep zooms typically associated with gigapixel photography.

This paper presents a new approach for the visualization and analysis of the spatial variability of features of interest represented by critical points in ensemble data. Our framework, called Persistence Atlas, enables the visualization of the dominant spatial patterns of critical points, along with statistics regarding their occurrence in the ensemble. The persistence atlas represents in the geometrical domain each dominant pattern in the form of a confidence map for the appearance of critical points. As a by-product, our method also provides 2-dimensional layouts of the entire ensemble, highlighting the main trends at a global level. Our approach is based on the new notion of Persistence Map, a measure of the geometrical density in critical points which leverages the robustness to noise of topological persistence to better emphasize salient features. We show how to leverage spectral embedding to represent the ensemble members as points in a low-dimensional Euclidean space, where distances between points measure the dissimilarities between critical point layouts and where statistical tasks, such as clustering, can be easily carried out. Further, we show how the notion of mandatory critical point can be leveraged to evaluate for each cluster confidence regions for the appearance of critical points. Most of the steps of this framework can be trivially parallelized and we show how to efficiently implement them. Extensive experiments demonstrate the relevance of our approach. The accuracy of the confidence regions provided by the persistence atlas is quantitatively evaluated and compared to a baseline strategy using an off-the-shelf clustering approach. We illustrate the importance of the persistence atlas in a variety of real-life datasets, where clear trends in feature layouts are identified and analyzed. We provide a lightweight VTK-based C++ implementation of our approach that can be used for reproduction purposes.

Abstract We introduce Flexible Live‐Wire, a generalization of the Live‐Wire interactive segmentation technique with floating anchors. In our approach, the user input for Live‐Wire is no longer limited to the setting of pixel‐level anchor nodes, but can use more general anchor sets. These sets can be of any dimension, size, or connectedness. The generality of the approach allows the design of a number of user interactions while providing the same functionality as the traditional Live‐Wire. In particular, we experiment with this new flexibility by designing four novel Live‐Wire interactions based on specific primitives: paint, pinch, probable, and pick anchors. These interactions are only a subset of the possibilities enabled by our generalization. Moreover, we discuss the computational aspects of this approach and provide practical solutions to alleviate any additional overhead. Finally, we illustrate our approach and new interactions through several example segmentations.