Craig S. Kaplan

Computational Symmetry in Computer Vision and Computer Graphics

In the arts and sciences, as well as in our daily lives, symmetry has made a profound and lasting impact. Likewise, a computational treatment of symmetry and group theory (the ultimate mathematical formalization of symmetry) has the potential to play an important role in computational sciences. Though the term computational symmetry was formally defined a decade ago by the first author, referring to algorithmic treatment of symmetries, seeking symmetry from digital data has been attempted for over four decades. Computational symmetry on real world data turns out to be challenging enough that, after decades of effort, a fully automated symmetry–savvy system remains elusive for real world applications. The recent resurging interests in computational symmetry for computer vision and computer graphics applications have shown promising results. Recognizing the fundamental relevance and Full text available at: http://dx.doi.org/10.1561/0600000008

Bimanual and unimanual image alignment: an evaluation of mouse-based techniques

We present an evaluation of three mouse-based techniques for aligning digital images. We investigate the physical image alignment task and discuss the implications for interacting with virtual images. In a formal evaluation we show that a symmetric bimanual technique outperforms an asymmetric bimanual technique which in turn outperforms a unimanual technique. We show that even after mode switching times are removed, the symmetric technique outperforms the single mouse technique. Subjects also exhibited more parallel interaction using the symmetric technique than when using the asymmetric technique.

Image-guided maze construction

We present a set of graphical and combinatorial algorithms for designing mazes based on images. The designer traces regions of interest in an image and annotates the regions with style parameters. They can optionally specify a solution path, which provides a rough guide for laying out the mazes actual solution. The system uses novel extensions to well-known maze construction algorithms to build mazes that approximate the tone of the source image, express the desired style in each region, and conform to the users solution path.

Real-time texture-mapped vector glyphs

We present a vector graphics representation suitable for real-time rendering on GPUs. Our representation can be used in place of a texture map, and renders precise antialiased edges at any magnification. A combination of texture data and procedural computation is used to evaluate an exact signed distance to a contour and its gradient. An optimized uniform grid accelerator is created using Voronoi analysis and redundancy elimination, so only the distances to a small constant number of features need be computed at every access. Contours and sharp features can be exactly reconstructed using a constant amount of computation per pixel. Our representation supports inexpensive high-quality anisotropic antialiasing as well as special effects such as outlining (with both rounded and sharp miters) and embossing.We have applied our representation to the important application of glyph rendering. Variations in glyph complexity are handled by storing different glyphs at different grid resolutions. Large blocks of glyphs can be rendered efficiently with a single indirection through an index texture.

symSpline: symmetric two-handed spline manipulation

We introduce symSpline: a symmetric, dual-mouse technique for the manipulation of spline curves. In symSpline, two cursors control the positions of the ends of the tangent to an edit point. By moving the tangent with both mice, the tangent and the edit point can be translated while the curvature of the spline is adjusted simultaneously, according to the length and angle of the tangent. We compare the symSpline technique to two asymmetric dual-mouse spline manipulation techniques and to a standard single-mouse technique. In a spline matching experiment, symSpline outperformed the two asymmetric dual-mouse techniques and all three dual-mouse techniques proved to be faster than the single-mouse technique. Additionally, symSpline was the technique most preferred by test participants.

Cut-out image mosaics

An image mosaic is a rendering of a large target image by arranging a collection of small source images, often in an array, each chosen specifically to fit a particular block of the target image. Most mosaicking methods are simplistic in the sense that they break the target image into regular tiles (e.g., squares or hexagons) and take extreme shortcuts when evaluating the similarity between target tiles and source images. In this paper, we propose an efficient method to obtain higher quality mosaics that incorporate a number of process improvements. The Fast Fourier Transform (FFT) is used to compute a more fine-grained image similarity metric, allowing for optimal colour correction and arbitrarily shaped target tiles. In addition, the framework can find the optimal sub-image within a source image, further improving the quality of the matching. The similarity scores generated by these high-order cost computations are fed into a matching algorithm to find the globally-optimal assignment of source images to target tiles. Experiments show that each improvement, by itself, yields a more accurate mosaic. Combined, the innovations produce very high quality image mosaics, even with only a few hundred source images.

Predicate Dispatching: A Unified Theory of Dispatch

Predicate dispatching generalizes previous method dispatch mechanisms by permitting arbitrary predicates to control method applicability and by using logical implication between predicates as the overriding relationship. The method selected to handle a message send can depend not just on the classes of the arguments, as in ordinary object-oriented dispatch, but also on the classes of subcomponents, on an arguments state, and on relationships between objects. This simple mechanism subsumes and extends object-oriented single and multiple dispatch, ML-style pattern matching, predicate classes, and classifiers, which can all be regarded as syntactic sugar for predicate dispatching. This paper introduces predicate dispatching, gives motivating examples, and presents its static and dynamic semantics. An implementation of predicate dispatching is available.

Computer-Generated Papercutting

The craft of papercutting is part of the folk art traditions of cultures all over the world. From the point of view of computer graphics, papercutting can be seen as a method of composing bi-level images under a set of geometric connectivity constraints. In this paper, we present a technique for composing digital paper-cut designs. The elements of a design may be images, which are processed via a multilayer thresholding operation, or they may be procedurallygenerated arrangements of shapes. Elements are composed using a set of boolean operators that preserve connectivity. The resulting designs are well suited to being cut by a new generation of inexpensive computer peripherals.Natural mountains and valleys are gradually eroded by rainfall and river flows. Physically-based modeling of this complex phenomenon is a major concern in producing realistic synthesized terrains. However, despite some recent improvements, existing algorithms are still computationally expensive, leading to a time-consuming process fairly impractical for terrain designers and 3D artists. In this paper, we present a new method to model the hydraulic erosion phenomenon which runs at interactive rates on todays computers. The method is based on the velocity field of the running water, which is created with an efficient shallow-water fluid model. The velocity field is used to calculate the erosion and deposition process, and the sediment transportation process. The method has been carefully designed to be implemented totally on GPU, and thus takes full advantage of the parallelism of current graphics hardware. Results from experiments demonstrate that the proposed method is effective and efficient. It can create realistic erosion effects by rainfall and river flows, and produce fast simulation results for terrains with large sizes.

Polygons cuttable by a circular saw

Abstract We introduce and characterize a new class of polygons that models wood, stone, glass and ceramic shapes that can be cut with a table saw, lapidary trim saw, or other circular saw. In this model, a circular saw is a line segment (in projection) that can move freely in empty space, but can only cut straight into a portion of material. Once a region of material is separated from the rest, it can be picked up and removed to allow the saw to move more freely. A polygon is called cuttable by a circular saw if it can be cut out of a convex shape of material by a sufficiently small circular saw. We prove that a polygon has this property precisely if it does not have two adjacent reflex vertices. As a consequence, every polygon can be modified slightly to make it cuttable by a circular saw. We give a linear-time algorithm to cut out such a polygon using a number of cuts and total length of cuts that are at most 2.5 times the optimal. We also study polygons cuttable by an arbitrarily large circular saw, which is equivalent to a ray, and give two linear-time recognition algorithms.

Precise vector textures for real-time 3D rendering

Vector graphics representations of images are resolution independent. Direct use of vector images for real-time texture mapping would be desirable to avoid sampling artifacts such as blurring common with raster images. Scalable Vector Graphics (SVG) files are typical of vector graphics image representations. Such representations composite images from layers of paths and strokes defined with lines, elliptical arcs, and quadratic and cubic parametric splines. High-quality texture mapping requires both random access and anisotropic antialiasing. For vector images, these goals can be achieved by computing the distance to the closest primitives from a sample point and then mapping this distance through a soft threshold function. Representing transparency masks in this way is especially useful, since vector mattes can be used to render complex curvilinear geometry as textures on simple geometric primitives. Unfortunately, computing the exact minimum distance to the parametric curves used in vector images is difficult. Previous work has used approximations, but an accurate minimum distance is desirable in order to enable wide strokes and special effects such as embossing. In this paper, a simple algorithm is presented that can efficiently and accurately compute the minimum distance to a parametric curve when the sample point is within its radius of curvature and the curve can be segmented into monotonic regions. This technique can be used in a GPU shader to render antialiased vector images exactly as defined by SVG files.