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We present a method for organizing a heterogeneous collection of 3D shapes for overview and exploration. Instead of relying on quantitative distances, which may become unreliable between dissimilar shapes, we introduce a qualitative analysis which utilizes multiple distance measures but only in cases where the measures can be reliably compared. Our analysis is based on the notion of quartets, each defined by two pairs of shapes, where the shapes in each pair are close to each other, but far apart from the shapes in the other pair. Combining the information from many quartets computed across a shape collection using several distance measures, we create a hierarchical structure we call categorization tree of the shape collection. This tree satisfies the topological (qualitative) constraints imposed by the quartets creating an effective organization of the shapes. We present categorization trees computed on various collections of shapes and compare them to ground truth data from human categorization. We further introduce the concept of degree of separation chart for every shape in the collection and show the effectiveness of using it for interactive shapes exploration.

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This work presents Sketch2Scene, a framework that automatically turns a freehand sketch drawing inferring multiple scene objects to semantically valid, well arranged scenes of 3D models. Unlike the existing works on sketch-based search and composition of 3D models, which typically process individual sketched objects one by one, our technique performs co-retrieval and co-placement of 3D relevant models by jointly processing the sketched objects. This is enabled by summarizing functional and spatial relationships among models in a large collection of 3D scenes as structural groups. Our technique greatly reduces the amount of user intervention needed for sketch-based modeling of 3D scenes and fits well into the traditional production pipeline involving concept design followed by 3D modeling. A pilot study indicates that the 3D scenes automatically synthesized by our technique in seconds are comparable to those manually created by an artist in hours in terms of visual aesthetics.

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This paper presents an algorithm for extending B-spline curves and surfaces. Based on the unclamping algorithm for B-spline curves, we propose a new algorithm for extending B-spline curves that extrapolates using the recurrence property of the de Boor algorithm. This algorithm provides a nice extension, with maximum continuity, to the original curve segment. Moreover, it can be applied to the extension of B-spline surfaces. Extension to both single and multiple target points/curves are considered in this paper.

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Surface Ricci flow is a powerful tool to design Riemannian metrics by user defined curvatures. Discrete surface Ricci flow has been broadly applied for surface parameterization, shape analysis, and computational topology. Conventional discrete Ricci flow has limitations. For meshes with low quality triangulations, if high conformality is required, the flow may get stuck at the local optimum of the Ricci energy. If convergence to the global optimum is enforced, the conformality may be sacrificed. This work introduces a novel method to generalize the traditional discrete Ricci flow. The generalized Ricci flow is more flexible, more robust and conformal for meshes with low quality triangulations. Conventional method is based on circle packing, which requires two circles on an edge intersect each other at an acute angle. Generalized method allows the two circles either intersect or separate from each other. This greatly improves the flexibility and robustness of the method. Furthermore, the generalized Ricci flow preserves the convexity of the Ricci energy, this ensures the uniqueness of the global optimum. Therefore the algorithm won't get stuck at the local optimum. Generalized discrete Ricci flow algorithms are explained in details for triangle meshes with both Euclidean and hyperbolic background geometries. Its advantages are demonstrated by theoretic proofs and practical applications in graphics, especially surface parameterization.

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The human eye can perceive a vast array of colors. Whether light or dark, the colors that our eyes can see are supposedly unlimited. However, this is not the case. In reality, every image has two aspects or descriptors to it, a reflectance and an illumination. While the reflectance essentially shows an images true color, the illumination is what causes the colors to seem different to the human eye. This effect, originally discovered by Helmholtz, is known as Color Constancy. Color Constancy ensures that the color the Human Visual System (HVS) receives is the true color of the image, regardless of illumination. As a result of this effect, in 1971, Land and McCann created the Retinex theory. Using the pixels in the image, Land tried to estimate the value of the reflectances and thus reveal the true color of the image. This theory was basically a color constancy algorithm that tried to explain why colors look different when exposed to lighting. By calculating the pixels, Land was able to depict the sameness in a gradient of colors in an image. However, the algorithm is both inefficient and complicated. Following their footsteps, many other people have tried to formulate new algorithms around the Lands original Retinex algorithm. In this paper, different methods such as least squares and discrete cosine transform are explained as well as how to enhance images using both Lands idea and histogram equalization.

3-D CAD models are an important digital resource in the manufacturing industry. 3-D CAD model retrieval has become a key technology in product lifecycle management enabling the reuse of existing design data. In this paper, we propose a new method to retrieve 3-D CAD models based on 2-D pen-based sketch inputs. Sketching is a common and convenient method for communicating design intent during early stages of product design, e.g., conceptual design. However, converting sketched information into precise 3-D engineering models is cumbersome, and much of this effort can be avoided by reuse of existing data. To achieve this purpose, we present a user-adaptive sketch-based retrieval method in this paper. The contributions of this work are twofold. First, we propose a statistical measure for CAD model retrieval: the measure is based on sketch similarity and accounts for users’ drawing habits. Second, for 3-D CAD models in the database, we propose a sketch generation pipeline that represents each 3-D CAD model by a small yet sufficient set of sketches that are perceptually similar to human drawings. User studies and experiments that demonstrate the effectiveness of the proposed method in the design process are presented.

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In this paper we present a new algorithm which turns an unstructured triangle mesh into a quad dominant mesh with edges well aligned to the principal directions of the underlying surface. Instead of computing a globally smooth parameterization or integrating curvature lines along a tangent vector field, we simply apply an iterative relaxation scheme which incrementally aligns the mesh edges to the principal directions. We further obtain the quad dominant mesh by dropping the not-aligned diagonal edges from the triangle mesh. A post-processing stage is introduced to further improve the results. The major advantage of our algorithm is its conceptual simplicity since it is merely based on elementary mesh operations such as edge collapse, flip, and split. Various results are presented in the paper; they show a good alignment to surface features and rather uniform distribution of mesh vertices. This makes them well suited, e.g., as CatmullClark Subdivision control meshes.

A recent trend in interactive modeling of 3D shapes from a single image is designing minimal interfaces, and accompanying algorithms, for modeling a specific class of objects. Expanding upon the range of shapes that existing minimal interfaces can model, we present an interactive image-guided tool for modeling shapes made up of extruded parts. An extruded part is represented by extruding a closed planar curve, called base, in the direction orthogonal to the base. To model each extruded part, the user only needs to sketch the projected base shape in the image. The main technical contribution is a novel optimization-based approach for recovering the 3D normal of the base of an extruded object by exploring both geometric regularity of the sketched curve and image contents. We developed a convenient interface for modeling multi-part shapes and a method for optimizing the relative placement of the parts. Our tool is validated using synthetic data and tested on real-world images.

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We present a real-time approach for acquiring 3D objects with high fidelity using hand-held consumer-level RGB-D scanning devices. Existing real-time reconstruction methods typically do not take the point of interest into account, and thus might fail to produce clean reconstruction results of desired objects due to distracting objects or backgrounds. In addition, any changes in background during scanning, which can often occur in real scenarios, can easily break up the whole reconstruction process. To address these issues, we incorporate visual saliency into a traditional real-time volumetric fusion pipeline. Salient regions detected from RGB-D frames suggest user-intended objects, and by understanding user intentions our approach can put more emphasis on important targets, and meanwhile, eliminate disturbance of non-important objects. Experimental results on real world scans demonstrate that our system is capable of effectively acquiring geometric information of salient objects in cluttered real-world scenes, even if the backgrounds are changing.

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Sharp edges, ridges, valleys and prongs are critical for the appearance and an accurate representation of a 3D model. In this paper, we propose a novel approach that deals with the global shape of features in a robust way. Based on a remeshing algorithm which delivers an isotropic mesh in a feature sensitive metric, features are recognized on multiple scales via integral invariants of local neighborhoods. Morphological and smoothing operations are then used for feature region extraction and classification into basic types such as ridges, valleys and prongs. The resulting representation of feature regions is further used for feature-specific editing operations.

The computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization.We provide a convergence analysis for widely used registration algorithms such as ICP, using either closest points (Besl and McKay [2]) or tangent planes at closest points (Chen and Medioni [4]), and for a recently developed approach based on quadratic approximants of the squared distance function [24]. ICP based on closest points exhibits local linear convergence only. Its counterpart which minimizes squared distances to the tangent planes at closest points is a Gauss-Newton iteration; it achieves local quadratic convergence for a zero residual problem and - if enhanced by regularization and step size control - comes close to quadratic convergence in many realistic scenarios. Quadratically convergent algorithms are based on the approach in [24]. The theoretical results are supported by a number of experiments; there, we also compare the algorithms with respect to global convergence behavior, stability and running time.