Yuanfeng Zhou

Adaptive sparse coding on PCA dictionary for image denoising

Sparse coding is a popular technique in image denoising. However, owing to the ill-posedness of denoising problems, it is difficult to obtain an accurate estimation of the true code. To improve denoising performance, we collect the sparse coding errors of a dataset on a principal component analysis dictionary, make an assumption on the probability of errors and derive an energy optimization model for image denoising, called adaptive sparse coding on a principal component analysis dictionary (ASC-PCA). The new method considers two aspects. First, with a PCA dictionary-related observation of the probability distributions of sparse coding errors on different dimensions, the regularization parameter balancing the fidelity term and the nonlocal constraint can be adaptively determined, which is critical for obtaining satisfying results. Furthermore, an intuitive interpretation of the constructed model is discussed. Second, to solve the new model effectively, a filter-based iterative shrinkage algorithm containing the filter-based back-projection and shrinkage stages is proposed. The filter in the back-projection stage plays an important role in solving the model. As demonstrated by extensive experiments, the proposed method performs optimally in terms of both quantitative and visual measurements.

Mesh resizing based on hierarchical saliency detection

Mesh saliency is a perception-inspired metric for regional importance which is helpful to many aspects of mesh processing. However, existing mesh saliency cannot be used in mesh resizing directly because of the neglect of resizing direction. In this paper, we propose a region descriptor based on its vulnerability to a resizing direction, and use this descriptor to compute the regions saliency based on its contrast to neighboring regions. In order to avoid being misled by repeated small-scale features on the mesh, we put forward a hierarchical method for saliency computing. We build a hierarchical coarse-to-fine segmentations of the input mesh, and evaluate the saliency value on different levels of segmentations. Finally these saliency values are integrated into one saliency map after applying non-linear suppression. Equipped with the saliency map, a framework for non-homogeneous mesh resizing is presented. We regard every edge as a spring, and scale the mesh by stretching the edge. Based on the salience value, we build a global energy function on the mesh. Experiments show that our resizing method based on hierarchical saliency analysis can produce visually appealing results.

Extension of B-Spline Curves with G2 Continuity

This paper presents a new method for extending B-Spline curve. Cubic Bezier curve is used to construct the extending segment and G 2 continuity is used to describe the smoothness of joint point. Optimization objective functions are established based on the minimum precise exact energy and the minimum precise curvature variation of the extending curve, respectively. The degree of freedom of the extended curve is determined by minimizing the objective functions. The non-linear optimization can be transform to non-linear least-square problem which can be linearized by a Gauss-Newton iterative algorithm. New control points are computed by extending curve and original curve. The comparison of the curves with different objective functions is included.

Non-local feature back-projection for image super-resolution

Image super-resolution (SR) for a single low-resolution image is an important and challenging task in image processing. In this study, the authors propose a novel non-local feature back-projection method for image SR, which can effectively reduce jaggy and ringing artefacts common, in general, iterative back-projection (IBP) method. In their method, the objective high-resolution (HR) image is obtained by projecting reconstructed errors back to HR image iteratively. To optimise the initial HR image and constrain anisotropic errors propagation during IBP process, an efficient non-local feature interpolation algorithm is designed. Specially, edge information is used as constraints to make the interpolation surface preserve better shape. Furthermore, as post-processing, non-local similarities are utilised to remove noise and irregularities induced by errors propagation. Experimental results show that their method achieves better performance than state-of-the-art methods in terms of both quantitative metrics and visual qualities.

A nonlocal gradient concentration method for image smoothing

It is challenging to consistently smooth natural images, yet smoothing results determine the quality of a broad range of applications in computer vision. To achieve consistent smoothing, we propose a novel optimization model making use of the redundancy of natural images, by defining a nonlocal concentration regularization term on the gradient. This nonlocal constraint is carefully combined with a gradient-sparsity constraint, allowing details throughout the whole image to be removed automatically in a data-driven manner. As variations in gradient between similar patches can be suppressed effectively, the new model has excellent edge preserving, detail removal, and visual consistency properties. Comparisons with state-of-the-art smoothing methods demonstrate the effectiveness of the new method. Several applications, including edge manipulation, image abstraction, detail magnification, and image resizing, show the applicability of the new method.

Global contrast of superpixels based salient region detection

Reliable estimation of visual saliency has become an essential tool in image processing. In this paper, we propose a novel salient region detection algorithm, superpixel contrast (SC), consisting of three basic steps. First, we decompose a given image into compact, regular superpixels that abstract unnecessary details by a new superpixel algorithm, hexagonal simple linear iterative clustering (HSLIC). Then we define the saliency of each perceptually meaningful superpixel instead of rigid pixel grid, simultaneously evaluating global contrast differences and spatial coherence. Finally, we locate the key region and enhance its saliency by a focusing step. The proposed algorithm is simple to implement and computationally efficient. Our algorithm consistently outperformed all state-of-the-art detection methods, yielding higher precision and better recall rates, when evaluated on well-known publicly available data sets.

A Quasi-Laplacian Smoothing Approach on Arbitrary Triangular Meshes

A new method for smoothing triangular meshes is presented. Mean curvature normal is used to define a Quasi-Laplacian for smoothing inner vertices at a local region. Vertices are moved along the normal direction in a more appropriate velocity which can make mesh smoothing and shape preserving harmonizing well. For the boundary vertices, a new method for estimating the mean curvature normal is presented, so that for an arbitrary triangular mesh, the inner and the boundary vertices can be smoothed by the same smoothing process. Features of the original mesh can be preserved by the weighted mean curvature normal restriction of the neighbors of one vertex effectively. Experiments of comparison between the new method and previous methods are included in this paper.

Two-dimensional shape retrieval using the distribution of extrema of Laplacian eigenfunctions

We propose a new method using the distribution of extrema of Laplacian eigenfunctions for two-dimensional (2D) shape description and matching. We construct a weighted directed graph, which we call signed natural neighbor graph, to represent a Laplacian eigenfunction of a shape. The nodes of this sparse graph are the extrema of the corresponding eigenfunction, and the edge weights are defined by signed natural neighbor coordinates derived from the local spatial arrangement of extrema. We construct the signed natural neighbor graphs defined by a small number of low-frequency Laplacian eigenfunctions of a shape to describe it. This shape descriptor is invariant under rigid transformations and uniform scaling, and is also insensitive to minor boundary deformations. When using our shape descriptor for matching two shapes, we determine their similarity by comparing the graphs induced by corresponding Laplacian eigenfunctions of the two shapes. Our experimental shape-matching results demonstrate that our method is effective for 2D shape retrieval.

Superpixels of RGB-D Images for Indoor Scenes Based on Weighted Geodesic Driven Metric

Serving as a key step for applications of image processing, superpixel generation has been attracting increasing attention. RGB-D images are used pervasively in scenes reconstruction and representation, benefiting from their contained depth data. In this paper, we present a novel framework for generating superpixels focus on RGB-D images of indoor scenes, based on a weighted geodesic driven metric that combines both color and geometric information. In particular, taking into account the unique structures of indoor scenarios, we first denoise the given RGB-D image, and construct the corresponding triangular mesh. A new weighted geodesic driven metric is defined by introducing a weight function constrained with normal vectors and colors. Under this metric, an energy function is defined to measure our over-segmentation of the triangular mesh, by optimizing which, we can acquire an optimal over-segmentation of the triangular mesh with object boundaries respected, such that vertices in each sub-region have similar geometric structures and color intensities. Re-mapping the over-segmentation of the triangular mesh to the RGB-D image results in desired superpixels. We perform extensive experiments on a large-scale database of RGB-D images to verify the efficacy of our algorithm. The results show that our algorithm has considerable advantages over the existing state-of-the-art methods.Serving as a key step for applications of image processing, superpixel generation has been attracting increasing attention. RGB-D images are used pervasively in scenes reconstruction and representation, benefiting from their contained depth data. In this paper, we present a novel framework for generating superpixels focus on RGB-D images of indoor scenes, based on a weighted geodesic driven metric that combines both color and geometric information. In particular, taking into account the unique structures of indoor scenarios, we first denoise the given RGB-D image, and construct the corresponding triangular mesh. A new weighted geodesic driven metric is defined by introducing a weight function constrained with normal vectors and colors. Under this metric, an energy function is defined to measure our over-segmentation of the triangular mesh, by optimizing which, we can acquire an optimal over-segmentation of the triangular mesh with object boundaries respected, such that vertices in each sub-region have similar geometric structures and color intensities. Re-mapping the over-segmentation of the triangular mesh to the RGB-D image results in desired superpixels. We perform extensive experiments on a large-scale database of RGB-D images to verify the efficacy of our algorithm. The results show that our algorithm has considerable advantages over the existing state-of-the-art methods.

Superpixels by Bilateral Geodesic Distance

We present a novel superpixel generation algorithm based on a new definition of geodesic distance, called bilateral geodesic distance. In contrast to the traditional geodesic distance, the new bilateral geodesic distance of two pixels considers the distance between their positions as well as their color difference. Superpixel generation is essentially a problem of clustering image pixels with respect to a set of properly selected seeds. We first use an adaptive hexagonal subdivision method to determine the initial seed-based image gradient. Then, we use the bilateral geodesic distance to measure the similarity between the pixels and the seeds. We apply an improved fast marching method to generate superpixels’ contour regions with the expansion velocities dependent on a new gradient formulation that depends on the seeds’ properties. The experimental results indicate that our algorithm is not only much faster than the structure-based method, which uses conventional geodesic distance, but also outperforms the existing methods in terms of region compactness and region boundary regularity.