We introduce Delaunay Point Processes, a framework for the extraction of geometric structures from images. Our approach simultaneously locates and groups geometric primitives (line segments, triangles) to form extended structures (line networks, polygons) for a variety of image analysis tasks. Similarly to traditional point processes, our approach uses Markov Chain Monte Carlo to minimize an energy that balances fidelity to the input image data with geometric priors on the output structures. However, while existing point processes struggle to model structures composed of inter-connected components, we propose to embed the point process into a Delaunay triangulation, which provides high-quality connectivity by construction. We further leverage key properties of the Delaunay triangulation to devise a fast Markov Chain Monte Carlo sampler. We demonstrate the flexibility of our approach on a variety of applications, including line network extraction, object contouring, and mesh-based image compression.

We present a method to create vector cliparts from photographs. Our approach aims at reproducing two key properties of cliparts: they should be easily editable, and they should represent image content in a clean, simplified way. We observe that vector artists satisfy both of these properties by modeling cliparts with linear color gradients, which have a small number of parameters and approximate well smooth color variations. In addition, skilled artists produce intricate yet editable artworks by stacking multiple gradients using opaque and semi-transparent layers. Motivated by these observations, our goal is to decompose a bitmap photograph into a stack of layers, each layer containing a vector path filled with a linear color gradient. We cast this problem as an optimization that jointly assigns each pixel to one or more layer and finds the gradient parameters of each layer that best reproduce the input. Since a trivial solution would consist in assigning each pixel to a different, opaque layer, we complement our objective with a simplicity term that favors decompositions made of few, semi-transparent layers. However, this formulation results in a complex combinatorial problem combining discrete unknowns (the pixel assignments) and continuous unknowns (the layer parameters). We propose a Monte Carlo Tree Search algorithm that efficiently explores this solution space by leveraging layering cues at image junctions. We demonstrate the effectiveness of our method by reverse-engineering existing cliparts and by creating original cliparts from studio photographs.

Vector drawing is a popular representation in graphic design because of the precision, compactness and editability offered by parametric curves. However, prior work on line drawing vectorization focused solely on faithfully capturing input bitmaps, and largely overlooked the problem of producing a compact and editable curve network. As a result, existing algorithms tend to produce overly-complex drawings composed of many short curves and control points, especially in the presence of thick or sketchy lines that yield spurious curves at junctions. We propose the first vectorization algorithm that explicitly balances fidelity to the input bitmap with simplicity of the output, as measured by the number of curves and their degree. By casting this trade-off as a global optimization, our algorithm generates few yet accurate curves, and also disambiguates curve topology at junctions by favoring the simplest interpretations overall. We demonstrate the robustness of our algorithm on a variety of drawings, sketchy cartoons and rough design sketches.

Many design tasks involve the creation of new objects in the context of an existing scene. Existing work in computer vision only provides partial support for such tasks. On the one hand, multi-view stereo algorithms allow the reconstruction of real-world scenes, while on the other hand algorithms for line-drawing interpretation do not take context into account. Our work combines the strength of these two domains to interpret line drawings of imaginary objects drawn over photographs of an existing scene. The main challenge we face is to identify the existing 3D structure that correlates with the line drawing while also allowing the creation of new structure that is not present in the real world. We propose a labeling algorithm to tackle this problem, where some of the labels capture dominant orientations of the real scene while a free label allows the discovery of new orientations in the imaginary scene. We illustrate our algorithm by interpreting line drawings for urban planing, home remodeling, furniture design and cultural heritage.