Abstract Cutout animation is one of the earliest forms of animation, and to this day remains a popular technique featured in numerous films including Monty Python and South Park series. Most computer animation systems, however, focus on different styles, including cel animation, making cutout animation somewhat underexplored. As creating cutouts is meticulous, we propose a novel generative cutout animation system. Taking a skeletal animation and a text prompt as input, we automatically generate a 2.5D cutout rig ready for production in films and games. Our system optimizes cutout images with an SDS (Score Distillation Sampling) loss with a LoRA (Low‐Rank Adaptation) prior, in multiple target poses. Naïvely optimizing an SDS loss, however, would lead to inconsistent target pose images, and, as a result, blurry or transparent cutouts. To address this, we introduce a novel optimization with techniques targeting pose and noise consistency, resulting in coherent target images and sharp cutouts. We validate our system by demonstrating a gallery of results, comparing with previous works, ablations, and other analyses. Once generated, our cutout rigs can be used both for the given input animation and repurposed for other animations or edited as independent assets.

Generalized winding numbers provide a robust measure of point insidedness for 3D surfaces—whether open, self-intersecting, or non-manifold—and are central to numerous geometry processing tasks. However, existing methods trade off between accuracy and computational efficiency, limiting their use in interactive and large-scale applications. We introduce a new formulation and algorithm for computing generalized winding numbers that is both fast and accurate to arbitrary precision, applicable to meshes and parametric surfaces. Our approach expresses the winding number as the sum of two intuitive geometric quantities: the signed number of ray-surface intersections and a boundary integral over the surface's projection onto the unit sphere. This insight leads to an efficient discretization that avoids expensive surface integrals and spherical arrangements. For meshes, our method achieves average speedups of 22X on a CPU compared to the fastest precise methods and 3X compared to the fastest approximation method, while maintaining full precision. On a GPU, for moderately complex meshes we reach a throughput of 10 9 queries per second, or 4 K generalized winding number slices at 120 FPS (13X faster than a naïve GPU method). For parametric surfaces, our method is on average 5.6X faster than the state-of-the-art method, with the same precision. Our method naturally handles complex topologies and non-manifold inputs. We extensively validate its accuracy, robustness, and time performance. Our code is available at https://github.com/MartensCedric/antipodal.

3D sketches are an effective representation of a 3D shape, convenient to create via modern Virtual or Augmented Reality (VR/AR) interfaces or from 2D sketches. For 3D sketches drawn by designers, human observers can consistently imagine the surface they imply, yet reconstructing such a surface with modern methods remains an open problem. Existing methods either assume a clean, well-structured 3D curve network (while in reality most 3D sketches are rough and unstructured), or make no effort to produce a surface consistent with perceptual observations. We propose a novel method that addresses this challenge by designing a system that reconstructs a surface that better aligns with human perception from a clean or rough set of 3D sketches. As the topology of the desired surface is unknown, we use an implicit neural surface representation, parameterized via its gradient field.

Abstract Sketches are a powerful and natural form of communication and are used in numerous systems for modelling, animation, shape retrieval, and editing. Despite their popularity, rough sketches — whether raster or vector, 2D or 3D — are often too complex and imprecise to be used directly and thus need special processing. For instance, many downstream applications, such as shape reconstruction, have strict requirements for cleanliness and accuracy of the input sketch. Alternatively, if a drawing is the final result, users might want to further process the sketch through tasks such as vectorization, beautification, cleanup, flat colorization, and more. In this state‐of‐the‐art report, we identify core geometrical and topological challenges shared by many processing methods, such as identifying endpoints, strokes, and junctions. Building upon that analysis, we then survey sketch processing methods in each task category. Furthermore, we outline the commonly used sketch datasets and promising avenues for future research in sketch processing.

Abstract The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to compute a generalized winding number, based only on the surface boundary and the intersections of a single ray with the surface, supporting any oriented surface representations that support a ray intersection query. Due to the focus on the boundary, our algorithm has a unique set of properties. For 2D parametric curves, on a regular grid of query points, our method is up to 4× faster than the current state of the art, maintaining the same precision. In 3D, our method can compute a winding number of a surface without discretizing it, including parametric surfaces. For some meshes with many triangles and a simple boundary, our method is faster than the hierarchical evaluation of the generalized winding number while still being precise. Similarly, on some parametric surfaces with a simple boundary, our method can be faster than adaptive quadrature. We validate our algorithms theoretically, numerically, and by demonstrating a gallery of results on a variety of parametric surfaces and meshes, as well uses in a variety of applications, including voxelizations and boolean operations.

Accurate segmentation of anatomical substructures within 3D curvilinear structures in medical imaging remains challenging due to their complex geometry and the scarcity of diverse, large-scale datasets for algorithm development and evaluation. In this paper, we use dendritic spine segmentation as a case study and address these challenges by introducing a novel Frenet-Serret Frame-based Decomposition, which decomposes 3D curvilinear structures into a globally smooth continuous curve that captures the overall shape, and a cylindrical primitive that encodes local geometric properties. This approach leverages Frenet-Serret Frames and arc length parameterization to preserve essential geometric features while reducing representational complexity, facilitating data-efficient learning, improved segmentation accuracy, and generalization on 3D curvilinear structures. To rigorously evaluate our method, we introduce two datasets: CurviSeg, a synthetic dataset for 3D curvilinear structure segmentation that validates our method's key properties, and DenSpineEM, a benchmark for dendritic spine segmentation, which comprises 4,476 manually annotated spines from 70 dendrites across three public electron microscopy datasets, covering multiple brain regions and species. Our experiments on DenSpineEM demonstrate exceptional cross-region and cross-species generalization: models trained on the mouse somatosensory cortex subset achieve 94.43% Dice, maintaining strong performance in zero-shot segmentation on both mouse visual cortex (95.61% Dice) and human frontal lobe (86.63% Dice) subsets. Moreover, we test the generalizability of our method on the IntrA dataset, where it achieves 77.08% Dice (5.29% higher than prior arts) on intracranial aneurysm segmentation from entire artery models. These findings demonstrate the potential of our approach for accurately analyzing complex curvilinear structures across diverse medical imaging fields. Our dataset, code, and models are available at https://github.com/VCG/FFD4DenSpineEM to support future research.

We propose a novel method (FaCE) for normal estimation of unoriented point clouds and VR ribbon sketches that leverages a modeling of the Faraday cage effect. Input points, or a sampling of the ribbons, form a conductive cage and shield the interior from external fields. The gradient of the maximum field strength over external field scenarios is used to estimate a normal at each input point or ribbon. The electrostatic effect is modeled with a simple Poisson system, accommodating intuitive user-driven sculpting via the specification of point charges and Faraday cage points. On inputs sampled from clean, watertight meshes, our method achieves comparable normal quality to existing methods tailored for this scenario. On inputs containing interior structures and artifacts, our method produces superior surfacing output when combined with Poisson Surface Reconstruction. In the case of ribbon sketches, our method accommodates sparser ribbon input while maintaining an accurate geometry, allowing for greater flexibility in the artistic process. We demonstrate superior performance to an existing approach for surfacing ribbon sketches in this sparse setting.

One of the primary reasons for the high cost of traditional animation is the inbetweening process, where artists manually draw each intermediate frame necessary for smooth motion. Making this process more efficient has been at the core of computer graphics research for years, yet the industry has adopted very few solutions. Most existing solutions either require vector input or resort to tight inbetweening; often, they attempt to fully automate the process. In industry, however, keyframes are often spaced far apart, drawn in raster format, and contain occlusions. Moreover, inbetweening is fundamentally an artistic process, so the artist should maintain high-level control over it. We address these issues by proposing a novel inbetweening system for bitmap character drawings, supporting both tight and far inbetweening. In our setup, the artist can control motion by animating a skeleton between the keyframe poses. Our system then performs skeleton-based deformation of the bitmap drawings into the same pose and employs discrete optimization and deep learning to blend the deformed images. Besides the skeleton and the two drawn bitmap keyframes, we require very little annotation. However, deforming drawings with occlusions is complex, as it requires a piecewise smooth deformation field. To address this, we observe that this deformation field is smooth when the drawing is lifted into 3D. Our system therefore optimizes topology of a 2.5D partially layered template that we use to lift the drawing into 3D and get the final piecewise-smooth deformaton, effectively resolving occlusions. We validate our system through a series of animations, qualitative and quantitative comparisons, and user studies, demonstrating that our approach consistently outperforms the state of the art and our results are consistent with the viewers' perception. Code and data for our paper are available at http://www-labs.iro.umontreal.ca/~bmpix/inbetweening/.

Abstract State‐of‐the‐art methods for line drawing vectorization rely on generated frame fields for robust direction disambiguation, with each of the two axes aligning to different intersecting curve tangents around junctions. However, a common source of topological error for such methods are frame field singularities. To remedy this, we introduce the first frame field optimization framework guaranteed to produce singularity‐free fields aligned to a line drawing. We first perform a convex solve for a roughly‐aligned orthogonal frame field (cross field), and then comb away its internal singularities with an optimal transport–based matching. The resulting topology of the field is strictly maintained with the machinery of discrete trivial connections in a final, non‐convex optimization that allows non‐orthogonality of the field, improving smoothness and tangent alignment. Our frame fields can serve as a drop‐in replacement for frame field optimizations used in previous work, improving the quality of the final vectorizations.

Artist sketches often use multiple overdrawn strokes to depict a single intended curve. Humans effortlessly mentally consolidate such sketches by detecting groups of overdrawn strokes and replacing them with the corresponding intended curves. While this mental process is near instantaneous, manually annotating or retracing sketches to communicate this intended mental image is highly time consuming; yet most sketch applications are not designed to handle overdrawing and can only operate on overdrawing-free, consolidated sketches. We propose StripMaker , a new and robust learning based method for automatic consolidation of raw vector sketches. We avoid the need for an unsustainably large manually annotated learning corpus by leveraging observations about artist workflow and perceptual cues viewers employ when mentally consolidating sketches. We train two perception-aware classifiers that assess the likelihood that a pair of stroke groups jointly depicts the same intended curve: our first classifier is purely local and only accounts for the properties of the evaluated strokes; our second classifier incorporates global context and is designed to operate on approximately consolidated sketches. We embed these classifiers within a consolidation framework that leverages artist workflow: we first process strokes in the order they were drawn and use our local classifier to arrive at an approximate consolidation output, then use the contextual classifier to refine this output and finalize the consolidated result. We validate StripMaker by comparing its results to manual consolidation outputs and algorithmic alternatives. StripMaker achieves comparable performance to manual consolidation. In a comparative study participants preferred our results by a 53% margin over those of the closest algorithmic alternative (67% versus 14%, other/neither 19%).

A vector sketch is a popular and natural geometry representation depicting a 2D shape. When viewed from afar, the disconnected vector strokes of a sketch and the empty space around them visually merge into positive space and negative space , respectively. Positive and negative spaces are the key elements in the composition of a sketch and define what we perceive as the shape. Nevertheless, the notion of positive or negative space is mathematically ambiguous: While the strokes unambiguously indicate the interior or boundary of a 2D shape, the empty space may or may not belong to the shape's exterior. For standard discrete geometry representations, such as meshes or point clouds, some of the most robust pipelines rely on discretizations of differential operators, such as Laplace-Beltrami. Such discretizations are not available for vector sketches; defining them may enable numerous applications of classical methods on vector sketches. However, to do so, one needs to define the positive space of a vector sketch, or the sketch shape. Even though extracting this 2D sketch shape is mathematically ambiguous, we propose a robust algorithm, Alpha Contours , constructing its conservative estimate: a 2D shape containing all the input strokes, which lie in its interior or on its boundary, and aligning tightly to a sketch. This allows us to define popular differential operators on vector sketches, such as Laplacian and Steklov operators. We demonstrate that our construction enables robust tools for vector sketches, such as As-Rigid-As-Possible sketch deformation and functional maps between sketches, as well as solving partial differential equations on a vector sketch.

We propose a method of reconstructing 3D machine-made shapes from bitmap sketches by separating an input image into individual patches and jointly optimizing their geometry. We rely on two main observations: (1) human observers interpret sketches of man-made shapes as a collection of simple geometric primitives, and (2) sketch strokes often indicate occlusion contours or sharp ridges between those primitives. Using these main observations we design a system that takes a single bitmap image of a shape, estimates image depth and segmentation into primitives with neural networks, then fits primitives to the predicted depth while determining occlusion contours and aligning intersections with the input drawing via optimization. Unlike previous work, our approach does not require additional input, annotation, or templates, and does not require retraining for a new category of man-made shapes. Our method produces triangular meshes that display sharp geometric features and are suitable for downstream applications, such as editing, rendering, and shading.

We present a volumetric mesh-based algorithm for parameterizing the placenta to a flattened template to enable effective visualization of local anatomy and function. MRI shows potential as a research tool as it provides signals directly related to placental function. However, due to the curved and highly variable in vivo shape of the placenta, interpreting and visualizing these images is difficult. We address interpretation challenges by mapping the placenta so that it resembles the familiar ex vivo shape. We formulate the parameterization as an optimization problem for mapping the placental shape represented by a volumetric mesh to a flattened template. We employ the symmetric Dirichlet energy to control local distortion throughout the volume. Local injectivity in the mapping is enforced by a constrained line search during the gradient descent optimization. We validate our method using a research study of 111 placental shapes extracted from BOLD MRI images. Our mapping achieves sub-voxel accuracy in matching the template while maintaining low distortion throughout the volume. We demonstrate how the resulting flattening of the placenta improves visualization of anatomy and function. Our code is freely available at https://github.com/mabulnaga/placenta-flattening.

Artists frequently capture character poses via raster sketches, then use these drawings as a reference while posing a 3D character in a specialized 3D software --- a time-consuming process, requiring specialized 3D training and mental effort. We tackle this challenge by proposing the first system for automatically inferring a 3D character pose from a single bitmap sketch, producing poses consistent with viewer expectations. Algorithmically interpreting bitmap sketches is challenging, as they contain significantly distorted proportions and foreshortening. We address this by predicting three key elements of a drawing, necessary to disambiguate the drawn poses: 2D bone tangents, self-contacts, and bone foreshortening. These elements are then leveraged in an optimization inferring the 3D character pose consistent with the artist's intent. Our optimization balances cues derived from artistic literature and perception research to compensate for distorted character proportions. We demonstrate a gallery of results on sketches of numerous styles. We validate our method via numerical evaluations, user studies, and comparisons to manually posed characters and previous work. Code and data for our paper are available at http://www-labs.iro.umontreal.ca/bmpix/sketch2pose/.

When creating freeform drawings, artists routinely employ clusters of overdrawn strokes to convey intended, aggregate curves. The ability to algorithmically fit these intended curves to their corresponding clusters is central to many applications that use artist drawings as inputs. However, while human observers effortlessly envision the intended curves given stroke clusters as input, existing fitting algorithms lack robustness and frequently fail when presented with input stroke clusters with non-trivial geometry or topology. We present StrokeStrip , a new and robust method for fitting intended curves to vector-format stroke clusters. Our method generates fitting outputs consistent with viewer expectations across a vast range of input stroke cluster configurations. We observe that viewers perceive stroke clusters as continuous, varying-width strips whose paths are described by the intended curves. An arc length parameterization of these strips defines a natural mapping from a strip to its path. We recast the curve fitting problem as one of parameterizing the cluster strokes using a joint 1D parameterization that is the restriction of the natural arc length parameterization of this strip to the strokes in the cluster. We simultaneously compute the joint cluster parameterization and implicitly reconstruct the a priori unknown strip geometry by solving a variational problem using a discrete-continuous optimization framework. We use this parameterization to compute parametric aggregate curves whose shape reflects the geometric properties of the cluster strokes at the corresponding isovalues. We demonstrate StrokeStrip outputs to be significantly better aligned with observer preferences compared to those of prior art; in a perceptual study, viewers preferred our fitting outputs by a factor of 12:1 compared to alternatives. We further validate our algorithmic choices via a range of ablation studies; extend our framework to raster data; and illustrate applications that benefit from the parameterizations produced.

Line drawing vectorization is a daily task in graphic design, computer animation, and engineering, necessary to convert raster images to a set of curves for editing and geometry processing. Despite recent progress in the area, automatic vectorization tools often produce spurious branches or incorrect connectivity around curve junctions; or smooth out sharp corners. These issues detract from the use of such vectorization tools, both from an aesthetic viewpoint and for feasibility of downstream applications (e.g., automatic coloring or inbetweening). We address these problems by introducing a novel line drawing vectorization algorithm that splits the task into three components: (1) finding keypoints, i.e., curve endpoints, junctions, and sharp corners; (2) extracting drawing topology, i.e., finding connections between keypoints; and (3) computing the geometry of those connections. We compute the optimal geometry of the connecting curves via a novel geometric flow --- PolyVector Flow --- that aligns the curves to the drawing, disambiguating directions around Y-, X-, and T-junctions. We show that our system robustly infers both the geometry and topology of detailed complex drawings. We validate our system both quantitatively and qualitatively, demonstrating that our method visually outperforms previous work.

Abstract A major challenge in line drawing vectorization is segmenting the input bitmap into separate curves. This segmentation is especially problematic for rough sketches, where curves are depicted using multiple overdrawn strokes. Inspired by feature‐aligned mesh quadrangulation methods in geometry processing, we propose to extract vector curve networks by parametrizing the image with local drawing‐aligned integer grids. The regular structure of the grid facilitates the extraction of clean line junctions; due to the grid's discrete nature, nearby strokes are implicitly grouped together. We demonstrate that our method successfully vectorizes both clean and rough line drawings, whereas previous methods focused on only one of those drawing types.

Image tracing is a foundational component of the workflow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean line drawings, modern algorithms often fail to faithfully vectorize junctions, or points at which curves meet; this produces vector drawings with incorrect connectivity. This subtle issue undermines the practical application of vectorization tools and accounts for hesitance among artists and engineers to use automatic vectorization software. To address this issue, we propose a novel image vectorization method based on state-of-the-art mathematical algorithms for frame field processing. Our algorithm is tailored specifically to disambiguate junctions without sacrificing quality.

Abstract This paper presents a new preconditioning technique for large‐scale geometric optimization problems, inspired by applications in mesh parameterization. Our positive (semi‐)definite preconditioner acts on the gradients of optimization problems whose variables are positions of the vertices of a triangle mesh in ℝ2or of a tetrahedral mesh in ℝ3, converting localized distortion gradients into the velocity of a globally near‐rigid motion via a linear solve. We pose our preconditioning tool in terms of the Killing energy of a deformation field and provide new efficient formulas for constructing Killing operators on triangle and tetrahedral meshes. We demonstrate that our method is competitive with state‐of‐the‐art algorithms for locally injective parameterization using a variety of optimization objectives and show applications to two‐ and three‐dimensional mesh deformation.

Artists routinely use gesture drawings to communicate ideated character poses for storyboarding and other digital media. During subsequent posing of the 3D character models, they use these drawing as a reference, and perform the posing itself using 3D interfaces which require time and expert 3D knowledge to operate. We propose the first method for automatically posing 3D characters directly using gesture drawings as an input, sidestepping the manual 3D posing step. We observe that artists are skilled at quickly and effectively conveying poses using such drawings, and design them to facilitate a single perceptually consistent pose interpretation by viewers. Our algorithm leverages perceptual cues to parse the drawings and recover the artist-intended poses. It takes as input a vector-format rough gesture drawing and a rigged 3D character model, and plausibly poses the character to conform to the depicted pose. No other input is required. Our contribution is two-fold: we first analyze and formulate the pose cues encoded in gesture drawings; we then employ these cues to compute a plausible image space projection of the conveyed pose and to imbue it with depth. Our framework is designed to robustly overcome errors and inaccuracies frequent in typical gesture drawings. We exhibit a wide variety of character models posed by our method created from gesture drawings of complex poses, including poses with occlusions and foreshortening. We validate our approach via result comparisons to artist-posed models generated from the same reference drawings, via studies that confirm that our results agree with viewer perception, and via comparison to algorithmic alternatives.

We introduce a novel technique for the construction of a 3D character proxy, or canvas , directly from a 2D cartoon drawing and a user-provided correspondingly posed 3D skeleton. Our choice of input is motivated by the observation that traditional cartoon characters are well approximated by a union of generalized surface of revolution body parts, anchored by a skeletal structure. While typical 2D character contour drawings allow ambiguities in 3D interpretation, our use of a 3D skeleton eliminates such ambiguities and enables the construction of believable character canvases from complex drawings. Our canvases conform to the 2D contours of the input drawings, and are consistent with the perceptual principles of Gestalt continuity, simplicity, and contour persistence. We first segment the input 2D contours into individual body-part outlines corresponding to 3D skeletal bones using the Gestalt continuation principle to correctly resolve inter-part occlusions in the drawings. We then use this segmentation to compute the canvas geometry, generating 3D generalized surfaces of revolution around the skeletal bones that conform to the original outlines and balance simplicity against contour persistence. The combined method generates believable canvases for characters drawn in complex poses with numerous inter-part occlusions, variable contour depth, and significant foreshortening. Our canvases serve as 3D geometric proxies for cartoon characters, enabling unconstrained 3D viewing, articulation, and non-photorealistic rendering. We validate our algorithm via a range of user studies and comparisons to ground-truth 3D models and artist-drawn results. We further demonstrate a compelling gallery of 3D character canvases created from a diverse set of cartoon drawings with matching 3D skeletons.

We propose a novel, design-driven, approach to quadrangulation of closed 3D curves created by sketch-based or other curve modeling systems. Unlike the multitude of approaches for quad-remeshing of existing surfaces, we rely solely on the input curves to both conceive and construct the quad-mesh of an artist imagined surface bounded by them. We observe that viewers complete the intended shape by envisioning a dense network of smooth, gradually changing,flow-linesthat interpolates the input curves. Components of the network bridge pairs of input curve segments with similar orientation and shape. Our algorithm mimics this behavior. It first segments the input closed curves into pairs ofmatchingsegments, defining dominant flow line sequences across the surface. It then interpolates the input curves by a network of quadrilateral cycles whose iso-lines define the desired flow line network. We proceed to interpolate these networks with all-quad meshes that convey designer intent. We evaluate our results by showing convincing quadrangulations of complex and diverse curve networks with concave, non-planar cycles, and validate our approach by comparing our results to artist generated interpolating meshes.

We present an algorithm for creating digital micrography images, or micrograms , a special type of calligrams created from minuscule text. These attractive text-art works successfully combine beautiful images with readable meaningful text. Traditional micrograms are created by highly skilled artists and involve a huge amount of tedious manual work. We aim to simplify this process by providing a computerized digital micrography design tool. The main challenge in creating digital micrograms is designing textual layouts that simultaneously convey the input image, are readable and appealing. To generate such layout we use the streamlines of singularity free, low curvature, smooth vector fields, especially designed for our needs. The vector fields are computed using a new approach which controls field properties via a priori boundary condition design that balances the different requirements we aim to satisfy. The optimal boundary conditions are computed using a graph-cut approach balancing local and global design considerations. The generated layouts are further processed to obtain the final micrograms. Our method automatically generates engaging, readable micrograms starting from a vector image and an input text while providing a variety of optional high-level controls to the user.