Figure 1: We partition the original image (left) into a grid mesh and deform it to fit the new desired dimensions (right), such that the quad faces covering important image regions are optimized to scale uniformly while regions with homogeneous content are allowed to be distorted. The scaling and stretching of the image content is guided by a significance map which combines the gradient and the saliency maps. AbstractWe present a "scale-and-stretch" warping method that allows resizing images into arbitrary aspect ratios while preserving visually prominent features. The method operates by iteratively computing optimal local scaling factors for each local region and updating a warped image that matches these scaling factors as closely as possible. The amount of deformation of the image content is guided by a significance map that characterizes the visual attractiveness of each pixel; this significance map is computed automatically using a novel combination of gradient and salience-based measures. Our technique allows diverting the distortion due to resizing to image regions with homogeneous content, such that the impact on perceptually important features is minimized. Unlike previous approaches, our method distributes the distortion in all spatial directions, even when the resizing operation is only applied horizontally or vertically, thus fully utilizing the available homogeneous regions to absorb the distortion. We develop an efficient formulation for the nonlinear optimization involved in the warping function computation, allowing interactive image resizing.

Decoupling local geometric features from the spatial location of a mesh is crucial for feature-preserving mesh denoising. This paper focuses on first order features, i.e., facet normals, and presents a simple yet effective anisotropic mesh denoising framework via normal field denoising. Unlike previous denoising methods based on normal filtering, which process normals defined on the Gauss sphere, our method considers normals as a surface signal defined over the original mesh. This allows the design of a novel bilateral normal filter that depends on both spatial distance and signal distance. Our bilateral filter is a more natural extension of the elegant bilateral filter for image denoising than those used in previous bilateral mesh denoising methods. Besides applying this bilateral normal filter in a local, iterative scheme, as common in most of previous works, we present for the first time a global, noniterative scheme for an isotropic denoising. We show that the former scheme is faster and more effective for denoising extremely noisy meshes while the latter scheme is more robust to irregular surface sampling. We demonstrate that both our feature-preserving schemes generally produce visually and numerically better denoising results than previous methods, especially at challenging regions with sharp features or irregular sampling.

Curve-skeleton is a very useful 1D structure to abstract the geometry and topology of a 3D object. Extraction of curve-skeletons is a fundamental problem in computer graphics, visualization, image processing and computer vision.There many useful applications including virtual colonoscopies, collision detection, computer animation, surface reconstruction and shape matching etc. In the literature [1][2], most previous methods require a volumetric discrete representation of the input model. However, transforming them into volumetric representations may raise discretization error in both geometry and connectivity.In this work [3], we propose a novel technique to extract skeletons directly from the mesh domain without requirement of volumetric discretization. Our approach (Figure 1) consists of three main steps: 1) mesh contraction, 2) connectivity surgery and 3) centeredness refinement. First, we contract a given mesh into a zero-volume skeletal shape by applying an iterative Laplacian smoothing procedure [4] with global positional constraints. Second, we execute a connectivity surgery procedure to progressively convert the contracted mesh into a 1D curve skeleton. Finally, to ensure its centeredness within the mesh, we refine the skeleton by moving each skeletal node to the center of its corresponding mesh region. In contrast to previous work, our approach has the following advantages: 1) our extracted skeleton is ensured to be homotopic to the original object, 2) it is inherently robust against noise disturbance (see Figure 2) and avoids volumetric discretization errors, and 3) the method is very fast and it is rotation invariant, and pose insensitive (Figure 3).