Jiahao Pang

Optimal graph laplacian regularization for natural image denoising

Image denoising is an under-determined problem, and hence it is important to define appropriate image priors for regularization. One recent popular prior is the graph Laplacian regularizer, where a given pixel patch is assumed to be smooth in the graph-signal domain. The strength and direction of the resulting graph-based filter are computed from the graphs edge weights. In this paper, we derive the optimal edge weights for local graph-based filtering using gradient estimates from non-local pixel patches that are self-similar. To analyze the effects of the gradient estimates on the graph Laplacian regularizer, we first show theoretically that, given graph-signal hD is a set of discrete samples on continuous function h(x; y) in a closed region Ω, graph Laplacian regularizer (hD)TLhD converges to a continuous functional SΩ integrating gradient norm of h in metric space G-i.e., (∇h)TG-1(∇h)-over Ω. We then derive the optimal metric space G*: one that leads to a graph Laplacian regularizer that is discriminant when the gradient estimates are accurate, and robust when the gradient estimates are noisy. Finally, having derived G* we compute the corresponding edge weights to define the Laplacian L used for filtering. Experimental results show that our image denoising algorithm using the per-patch optimal metric space G* outperforms non-local means (NLM) by up to 1.5 dB in PSNR.

Redefining self-similarity in natural images for denoising using graph signal gradient

Image denoising is the most basic inverse imaging problem. As an under-determined problem, appropriate definition of image priors to regularize the problem is crucial. Among recent proposed priors for image denoising are: i) graph Laplacian regularizer where a given pixel patch is assumed to be smooth in the graph-signal domain; and ii) self-similarity prior where image patches are assumed to recur throughout a natural image in non-local spatial regions. In our first contribution, we demonstrate that the graph Laplacian regularizer converges to a continuous time functional counterpart, and careful selection of its features can lead to a discriminant signal prior. In our second contribution, we redefine patch self-similarity in terms of patch gradients and argue that the new definition results in a more accurate estimate of the graph Laplacian matrix, and thus better image denoising performance. Experiments show that our designed algorithm based on graph Laplacian regularizer and gradient-based self-similarity can outperform non-local means (NLM) denoising by up to 1.4 dB in PSNR.

Color clustering matting

Natural image matting refers to the problem of extracting regions of interest such as foreground object from an image based on user inputs like scribbles or trimap. More specifically, we need to estimate the color information of background, foreground and the corresponding opacity, which is an ill-posed problem inherently. Inspired by closed-form matting and KNN matting, in this paper, we extend the local color line model which is based on the assumption of linear color clustering within a small local window, to nonlocal feature space neighborhood. New affinity matrix is defined to achieve better clustering. Further, we demonstrate that good clustering ensures better prediction of alpha matte. Experimental evaluations on benchmark datasets and comparisons show that our matting algorithm is of higher accuracy and better visual quality than some state-of-the-art matting algorithms.

Image colorization using sparse representation

Image colorization is the task to color a grayscale image with limited color cues. In this work, we present a novel method to perform image colorization using sparse representation. Our method first trains an over-complete dictionary in YUV color space. Then taking a grayscale image and a small subset of color pixels as inputs, our method colorizes overlapping image patches via sparse representation; it is achieved by seeking sparse representations of patches that are consistent with both the grayscale image and the color pixels. After that, we aggregate the colorized patches with weights to get an intermediate result. This process iterates until the image is properly colorized. Experimental results show that our method leads to high-quality colorizations with small number of given color pixels. To demonstrate one of the applications of the proposed method, we apply it to transfer the color of one image onto another to obtain a visually pleasing image.

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain

Inverse imaging problems are inherently underdetermined, and hence, it is important to employ appropriate image priors for regularization. One recent popular prior—the graph Laplacian regularizer—assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper, we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, providing insights into several fundamental aspects of graph Laplacian regularization for image denoising. Specifically, we first show the convergence of the graph Laplacian regularizer to a continuous-domain functional, integrating a norm measured in a locally adaptive metric space. Focusing on image denoising, we derive an optimal metric space assuming non-local self-similarity of pixel patches, leading to an optimal graph Laplacian regularizer for denoising in the discrete domain. We then interpret graph Laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations, e.g., its tendency to promote piecewise smooth signals under certain settings. To verify our analysis, an iterative image denoising algorithm is developed. Experimental results show that our algorithm performs competitively with state-of-the-art denoising methods, such as BM3D for natural images, and outperforms them significantly for piecewise smooth images.

Photo album compression By leveraging temporal-spatial correlations and HEVC

The advancing digital photography technology has resulted in a large number of photos stored in personal computers. Photo album compression algorithms aim to save storage space and efficiently manage photos. In this paper, a general forest structure model involving depth constrain for photo album compression is proposed, which further exploits the correlations between images in the photo album. We firstly represent the images as nodes in a graph and directed edges between them as predictive coding relationship. Affinity propagation is then applied to compute for a depth-constrained forest. Finally, we adopt depth-first search algorithm to generate the compression order according to forest structure and HEVC to compress the images with adaptive GOPs and reference list. Experimental results show that the proposed compression method provides much better rate-distortion performance compared to JPEG and significantly reduce the storage space.

Self-similarity-based image colorization

In this work, we tackle the problem of coloring black-and-white images, which is image colorization. Existing image colorization algorithms can be categorized into two types: scribble-based colorization algorithms and example-based colorization algorithms. Differently, we propose a hybrid scheme that combines the advantages of both categories. Given the grayscale image to be colorized and a few color scribbles (or scattered color labels) as input, the proposed method manages to colorize the grayscale image with high quality. Similar to the mechanisms in example-based colorization methods, our algorithm firstly propagates chrominance information based on the assumption that similar image patches should have similar colors. Therefore colors of some pixels can be transferred from similar patches with known colors. After that, we apply scribble-based colorization algorithm to fully colorize the grayscale image, with different confidences assigned onto the transferred color labels. Experimental results show that, the proposed method effectively utilizes the known chrominance, and provides pleasant colorizations with very few user interventions.

Image colorization via color propagation and rank minimization

Image colorization aims to add colors to grayscale images, which used to be a time-consuming and tedious task that requires lots of human efforts. In this paper, we present a novel colorization method based on color propagation and rank minimization. Given a small portion of chrominance values and a grayscale image, we firstly propagate the known color values to other pixels to be colorized. As the colorized image after color propagation is not accurate, we then define a confidence matrix to measure the propagation fidelity. Finally, pixels that have propagated chrominance values with confidence are colorized by rank minimization, which exploits the redundancy of natural images. Experimental results on real data set show that our proposed method achieves state-of-the-art colorization quality.

Hiding a Secret Pattern into Color Halftone Images

This paper proposes an effective color halftone image visual cryptography method to embed a binary secret pattern into dot diffused color halftone images, Data Hiding by Dual Color Conjugate Dot Diffusion (DCCDD). DCCDD considers inter-channel correlation in order to restrict the embedding distortions between different channels within an acceptable range. Compared to the previous method, the proposed method can hide a secret pattern into two halftone color images which come from different original multitone images. The experimental results show that DCCDD can embed a binary secret pattern into two color halftone images which can be generated from identical or different original multitone color images. When the two halftone images are overlaid, the secret pattern will be revealed.

Arbitrary factor image interpolation using geodesic distance weighted 2D autoregressive modeling

Least square regression has been widely used in image interpolation. Some existing regression-based interpolation methods used ordinary least squares (OLS) to formulate cost functions. These methods usually have difficulties at object boundaries because OLS is sensitive to outliers. Weighted least squares (WLS) is then adopted to solve the outlier problem. Some weighting schemes have been proposed in the literature. In this paper we propose to use geodesic distance weighting in that geodesic distance can simultaneously measure both the spatial distance and color difference. Another contribution of this paper is that we propose an optimization scheme that can handle arbitrary factor interpolation. The idea is to separate the problem into two parts, an adaptive pixel correlation model and a convolution based image degradation model. Geodesic distance weighted 2D autoregressive model is used to model the pixel correlation which preserves local geometry. The convolution based image degradation model provides the flexibility to handle arbitrary interpolation factor. The entire problem is formulated as a WLS problem constrained by a linear equality.