Showing papers on "Kernel (image processing) published in 2009"

Linear spatial pyramid matching using sparse coding for image classification

Abstract: Recently SVMs using spatial pyramid matching (SPM) kernel have been highly successful in image classification. Despite its popularity, these nonlinear SVMs have a complexity O(n2 ~ n3) in training and O(n) in testing, where n is the training size, implying that it is nontrivial to scaleup the algorithms to handle more than thousands of training images. In this paper we develop an extension of the SPM method, by generalizing vector quantization to sparse coding followed by multi-scale spatial max pooling, and propose a linear SPM kernel based on SIFT sparse codes. This new approach remarkably reduces the complexity of SVMs to O(n) in training and a constant in testing. In a number of image categorization experiments, we find that, in terms of classification accuracy, the suggested linear SPM based on sparse coding of SIFT descriptors always significantly outperforms the linear SPM kernel on histograms, and is even better than the nonlinear SPM kernels, leading to state-of-the-art performance on several benchmarks by using a single type of descriptors.

Super-resolution from a single image

Abstract: Methods for super-resolution can be broadly classified into two families of methods: (i) The classical multi-image super-resolution (combining images obtained at subpixel misalignments), and (ii) Example-Based super-resolution (learning correspondence between low and high resolution image patches from a database). In this paper we propose a unified framework for combining these two families of methods. We further show how this combined approach can be applied to obtain super resolution from as little as a single image (with no database or prior examples). Our approach is based on the observation that patches in a natural image tend to redundantly recur many times inside the image, both within the same scale, as well as across different scales. Recurrence of patches within the same image scale (at subpixel misalignments) gives rise to the classical super-resolution, whereas recurrence of patches across different scales of the same image gives rise to example-based super-resolution. Our approach attempts to recover at each pixel its best possible resolution increase based on its patch redundancy within and across scales.

Understanding and evaluating blind deconvolution algorithms

Abstract: Blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown. Recent algorithms have afforded dramatic progress, yet many aspects of the problem remain challenging and hard to understand. The goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally. We explain the previously reported failure of the naive MAP approach by demonstrating that it mostly favors no-blur explanations. On the other hand we show that since the kernel size is often smaller than the image size a MAP estimation of the kernel alone can be well constrained and accurately recover the true blur. The plethora of recent deconvolution techniques makes an experimental evaluation on ground-truth data important. We have collected blur data with ground truth and compared recent algorithms under equal settings. Additionally, our data demonstrates that the shift-invariant blur assumption made by most algorithms is often violated.

Multiple kernels for object detection

Abstract: Our objective is to obtain a state-of-the art object category detector by employing a state-of-the-art image classifier to search for the object in all possible image sub-windows. We use multiple kernel learning of Varma and Ray (ICCV 2007) to learn an optimal combination of exponential χ2 kernels, each of which captures a different feature channel. Our features include the distribution of edges, dense and sparse visual words, and feature descriptors at different levels of spatial organization.

Compressive Sensing by Random Convolution

Abstract: This paper demonstrates that convolution with random waveform followed by random time-domain subsampling is a universally efficient compressive sensing strategy. We show that an $n$-dimensional signal which is $S$-sparse in any fixed orthonormal representation can be recovered from $m\gtrsim S\log n$ samples from its convolution with a pulse whose Fourier transform has unit magnitude and random phase at all frequencies. The time-domain subsampling can be done in one of two ways: in the first, we simply observe $m$ samples of the random convolution; in the second, we break the random convolution into $m$ blocks and summarize each with a single randomized sum. We also discuss several imaging applications where convolution with a random pulse allows us to superresolve fine-scale features, allowing us to recover high-resolution signals from low-resolution measurements.

Image deblurring with Poisson data: from cells to galaxies

Abstract: Image deblurring is an important topic in imaging science. In this review, we consider together fluorescence microscopy and optical/infrared astronomy because of two common features: in both cases the imaging system can be described, with a sufficiently good approximation, by a convolution operator, whose kernel is the so-called point-spread function (PSF); moreover, the data are affected by photon noise, described by a Poisson process. This statistical property of the noise, that is common also to emission tomography, is the basis of maximum likelihood and Bayesian approaches introduced in the mid eighties. From then on, a huge amount of literature has been produced on these topics. This review is a tutorial and a review of a relevant part of this literature, including some of our previous contributions. We discuss the mathematical modeling of the process of image formation and detection, and we introduce the so-called Bayesian paradigm that provides the basis of the statistical treatment of the problem. Next, we describe and discuss the most frequently used algorithms as well as other approaches based on a different description of the Poisson noise. We conclude with a review of other topics related to image deblurring such as boundary effect correction, space-variant PSFs, super-resolution, blind deconvolution and multiple-image deconvolution.

Clustering-Based Denoising With Locally Learned Dictionaries

Abstract: In this paper, we propose K-LLD: a patch-based, locally adaptive denoising method based on clustering the given noisy image into regions of similar geometric structure. In order to effectively perform such clustering, we employ as features the local weight functions derived from our earlier work on steering kernel regression . These weights are exceedingly informative and robust in conveying reliable local structural information about the image even in the presence of significant amounts of noise. Next, we model each region (or cluster)-which may not be spatially contiguous-by ldquolearningrdquo a best basis describing the patches within that cluster using principal components analysis. This learned basis (or ldquodictionaryrdquo) is then employed to optimally estimate the underlying pixel values using a kernel regression framework. An iterated version of the proposed algorithm is also presented which leads to further performance enhancements. We also introduce a novel mechanism for optimally choosing the local patch size for each cluster using Stein's unbiased risk estimator (SURE). We illustrate the overall algorithm's capabilities with several examples. These indicate that the proposed method appears to be competitive with some of the most recently published state of the art denoising methods.

The three-dimensional normal-distributions transform : an efficient representation for registration, surface analysis, and loop detection

Abstract: This dissertation is concerned with three-dimensional (3D) sensing and 3D scan representation. Three-dimensional records are important tools in several disciplines; such as medical imaging, archaeology, and mobile robotics. This dissertation proposes the normal-distributions transform, NDT, as a general 3D surface representation with applications in scan registration, localisation, loop detection, and surface-structure analysis. After applying NDT, the surface is represented by a smooth function with analytic derivatives. This representation has several attractive properties. The smooth function representation makes it possible to use standard numerical optimisation methods, such as Newton’s method, for 3D registration. This dissertation extends the original two-dimensional NDT registration algorithm of Biber and Straser to 3D and introduces a number of improvements. The 3D-NDT scan-registration algorithm is compared to current de facto standard registration algorithms. 3D-NDT scan registration with the proposed extensions is shown to be more robust, more accurate, and faster than the popular ICP algorithm. An additional benefit is that 3D-NDT registration provides a confidence measure of the result with little additional effort. Furthermore, a kernel-based extension to 3D-NDT for registering coloured data is proposed. Approaches based on local visual features typically use only a small fraction of the available 3D points for registration. In contrast, Colour-NDT uses all of the available 3D data. The dissertation proposes to use a combination of local visual features and Colour-NDT for robust registration of coloured 3D scans. Also building on NDT, a novel approach using 3D laser scans to perform appearance-based loop detection for mobile robots is proposed. Loop detection is an importantproblem in the SLAM (simultaneous localisation and mapping) domain. The proposed approach uses only the appearance of 3D point clouds to detect loops and requires nopose information. It exploits the NDT surface representation to create histograms based on local surface orientation and smoothness. The surface-shape histograms compress the input data by two to three orders of magnitude. Because of the high compression rate, the histograms can be matched efficiently to compare the appearance of two scans. Rotation invariance is achieved by aligning scans with respect to dominant surface orientations. In order to automatically determine the threshold that separates scans at loop closures from nonoverlapping ones, the proposed approach uses expectation maximisation to fit a Gamma mixture model to the output similarity measures. In order to enable more high-level tasks, it is desirable to extract semantic information from 3D models. One important task where such 3D surface analysis is useful is boulder detection for mining vehicles. This dissertation presents a method, also inspired by NDT, that provides clues as to where the pile is, where the bucket should be placed for loading, and where there are obstacles. The points of 3D point clouds are classified based on the surrounding surface roughness and orientation. Other potential applications include extraction of drivable paths over uneven surfaces.

Blind motion deblurring from a single image using sparse approximation

Abstract: Restoring a clear image from a single motion-blurred image due to camera shake has long been a challenging problem in digital imaging. Existing blind deblurring techniques either only remove simple motion blurring, or need user interactions to work on more complex cases. In this paper, we present an approach to remove motion blurring from a single image by formulating the blind blurring as a new joint optimization problem, which simultaneously maximizes the sparsity of the blur kernel and the sparsity of the clear image under certain suitable redundant tight frame systems (curvelet system for kernels and framelet system for images). Without requiring any prior information of the blur kernel as the input, our proposed approach is able to recover high-quality images from given blurred images. Furthermore, the new sparsity constraints under tight frame systems enable the application of a fast algorithm called linearized Bregman iteration to efficiently solve the proposed minimization problem. The experiments on both simulated images and real images showed that our algorithm can effectively removing complex motion blurring from nature images.

Beyond the Euclidean distance: Creating effective visual codebooks using the Histogram Intersection Kernel

Abstract: Common visual codebook generation methods used in a Bag of Visual words model, e.g. k-means or Gaussian Mixture Model, use the Euclidean distance to cluster features into visual code words. However, most popular visual descriptors are histograms of image measurements. It has been shown that the Histogram Intersection Kernel (HIK) is more effective than the Euclidean distance in supervised learning tasks with histogram features. In this paper, we demonstrate that HIK can also be used in an unsupervised manner to significantly improve the generation of visual codebooks. We propose a histogram kernel k-means algorithm which is easy to implement and runs almost as fast as k-means. The HIK codebook has consistently higher recognition accuracy over k-means codebooks by 2–4%. In addition, we propose a one-class SVM formulation to create more effective visual code words which can achieve even higher accuracy. The proposed method has established new state-of-the-art performance numbers for 3 popular benchmark datasets on object and scene recognition. In addition, we show that the standard k-median clustering method can be used for visual codebook generation and can act as a compromise between HIK and k-means approaches.

Implementation of a Lattice Boltzmann kernel using the Compute Unified Device Architecture developed by nVIDIA

Abstract: In this article a very efficient implementation of a 2D-Lattice Boltzmann kernel using the Compute Unified Device Architecture (CUDA™) interface developed by nVIDIA® is presented. By exploiting the explicit parallelism exposed in the graphics hardware we obtain more than one order in performance gain compared to standard CPUs. A non-trivial example, the flow through a generic porous medium, shows the performance of the implementation.

Visualization of vessel movements

Abstract: We propose a geographical visualization to support operators of coastal surveillance systems and decision making analysts to get insights in vessel movements. For a possibly unknown area, they want to know where significant maritime areas, like highways and anchoring zones, are located. We show these features as an overlay on a map. As source data we use AIS data: Many vessels are currently equipped with advanced GPS devices that frequently sample the state of the vessels and broadcast them. Our visualization is based on density fields that are derived from convolution of the dynamic vessel positions with a kernel. The density fields are shown as illuminated height maps. Combination of two fields, with a large and small kernel provides overview and detail. A large kernel provides an overview of area usage revealing vessel highways. Details of speed variations of individual vessels are shown with a small kernel, highlighting anchoring zones where multiple vessels stop. Besides for maritime applications we expect that this approach is useful for the visualization of moving object data in general.

Difference imaging photometry of blended gravitational microlensing events with a numerical kernel

Abstract: The numerical kernel approach to difference imaging has been implemented and applied to gravitational microlensing events observed by the PLANET collaboration. The effect of an error in the source-star coordinates is explored and a new algorithm is presented for determining the precise coordinates of the microlens in blended events, essential for accurate photometry of difference images. It is shown how the photometric reference flux need not be measured directly from the reference image but can be obtained from measurements of the difference images combined with the knowledge of the statistical flux uncertainties. The improved performance of the new algorithm, relative to ISIS2, is demonstrated.

A food image recognition system with Multiple Kernel Learning

Abstract: Since health care on foods is drawing people's attention recently, a system that can record everyday meals easily is being awaited. In this paper, we propose an automatic food image recognition system for recording people's eating habits. In the proposed system, we use the Multiple Kernel Learning (MKL) method to integrate several kinds of image features such as color, texture and SIFT adaptively. MKL enables to estimate optimal weights to combine image features for each category. In addition, we implemented a prototype system to recognize food images taken by cellular-phone cameras. In the experiment, we have achieved the 61.34% classification rate for 50 kinds of foods. To the best of our knowledge, this is the first report of a food image classification system which can be applied for practical use.

Image deblurring and denoising using color priors

Abstract: Image blur and noise are difficult to avoid in many situations and can often ruin a photograph. We present a novel image deconvolution algorithm that deblurs and denoises an image given a known shift-invariant blur kernel. Our algorithm uses local color statistics derived from the image as a constraint in a unified framework that can be used for deblurring, denoising, and upsampling. A pixel's color is required to be a linear combination of the two most prevalent colors within a neighborhood of the pixel. This two-color prior has two major benefits: it is tuned to the content of the particular image and it serves to decouple edge sharpness from edge strength. Our unified algorithm for deblurring and denoising out-performs previous methods that are specialized for these individual applications. We demonstrate this with both qualitative results and extensive quantitative comparisons that show that we can out-perform previous methods by approximately 1 to 3 DB.

Gabor-Based Kernel Partial-Least-Squares Discrimination Features for Face Recognition

Abstract: The paper presents a novel method for the extraction of facial features based on the Gabor-wavelet representation of face images and the kernel partial-least-squares discrimination (KPLSD) algorithm. The proposed feature-extraction method, called the Gabor-based kernel partial-least-squares discrimination (GKPLSD), is performed in two consecutive steps. In the first step a set of forty Gabor wavelets is used to extract discriminative and robust facial features, while in the second step the kernel partial-least-squares discrimination technique is used to reduce the dimensionality of the Gabor feature vector and to further enhance its discriminatory power. For optimal performance, the KPLSD-based transformation is implemented using the recently proposed fractional-power-polynomial models. The experimental results based on the XM2VTS and ORL databases show that the GKPLSD approach outperforms feature-extraction methods such as principal component analysis (PCA), linear discriminant analysis (LDA), kernel principal component analysis (KPCA) or generalized discriminant analysis (GDA) as well as combinations of these methods with Gabor representations of the face images. Furthermore, as the KPLSD algorithm is derived from the kernel partial-least-squares regression (KPLSR) model it does not suffer from the small-sample-size problem, which is regularly encountered in the field of face recognition.

Group-sensitive multiple kernel learning for object categorization

Abstract: In this paper, we propose a group-sensitive multiple kernel learning (GS-MKL) method to accommodate the intra-class diversity and the inter-class correlation for object categorization. By introducing an intermediate representation “group” between images and object categories, GS-MKL attempts to find appropriate kernel combination for each group to get a finer depiction of object categories. For each category, images within a group share a set of kernel weights while images from different groups may employ distinct sets of kernel weights. In GS-MKL, such group-sensitive kernel combinations together with the multi-kernels based classifier are optimized in a joint manner to seek a trade-off between capturing the diversity and keeping the invariance for each category. Extensive experiments show that our proposed GS-MKL method has achieved encouraging performance over three challenging datasets.

Kernel Nonparametric Weighted Feature Extraction for Hyperspectral Image Classification

Abstract: In recent years, many studies show that kernel methods are computationally efficient, robust, and stable for pattern analysis. Many kernel-based classifiers were designed and applied to classify remote-sensed data, and some results show that kernel-based classifiers have satisfying performances. Many studies about hyperspectral image classification also show that nonparametric weighted feature extraction (NWFE) is a powerful tool for extracting hyperspectral image features. However, NWFE is still based on linear transformation. In this paper, the kernel method is applied to extend NWFE to kernel-based NWFE (KNWFE). The new KNWFE possesses the advantages of both linear and nonlinear transformation, and the experimental results show that KNWFE outperforms NWFE, decision-boundary feature extraction, independent component analysis, kernel-based principal component analysis, and generalized discriminant analysis.

A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators

Abstract: This paper is concerned with the fast computation of Fourier integral operators of the general form ∫_(R^d) e^[(2πiΦ)(x,k)]f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a standard homogeneity condition, and f is a given input. This is of interest, for such fundamental computations are connected with the problem of finding numerical solutions to wave equations and also frequently arise in many applications including reflection seismology, curvilinear tomography, and others. In two dimensions, when the input and output are sampled on N × N Cartesian grids, a direct evaluation requires O(N^4) operations, which is often times prohibitively expensive. This paper introduces a novel algorithm running in O(N^2 log N) time, i.e., with near-optimal computational complexity, and whose overall structure follows that of the butterfly algorithm. Underlying this algorithm is a mathematical insight concerning the restriction of the kernel e^[2πiΦ(x,k)] to subsets of the time and frequency domains. Whenever these subsets obey a simple geometric condition, the restricted kernel is approximately low-rank; we propose constructing such low-rank approximations using a special interpolation scheme, which prefactors the oscillatory component, interpolates the remaining nonoscillatory part, and finally remodulates the outcome. A byproduct of this scheme is that the whole algorithm is highly efficient in terms of memory requirement. Numerical results demonstrate the performance and illustrate the empirical properties of this algorithm.

Selection and context for action recognition

Abstract: Recognizing human action in non-instrumented video is a challenging task not only because of the variability produced by general scene factors like illumination, background, occlusion or intra-class variability, but also because of subtle behavioral patterns among interacting people or between people and objects in images. To improve recognition, a system may need to use not only low-level spatio-temporal video correlations but also relational descriptors between people and objects in the scene. In this paper we present contextual scene descriptors and Bayesian multiple kernel learning methods for recognizing human action in complex non-instrumented video. Our contribution is threefold: (1) we introduce bag-of-detector scene descriptors that encode presence/absence and structural relations between object parts; (2) we derive a novel Bayesian classification method based on Gaussian processes with multiple kernel covariance functions (MKGPC), in order to automatically select and weight multiple features, both low-level and high-level, out of a large collection, in a principled way, and (3) perform large scale evaluation using a variety of features on the KTH and a recently introduced, challenging, Hollywood movie dataset. On the KTH dataset, we obtain 94.1% accuracy, the best result reported to date. On the Hollywood dataset we obtain promising results in several action classes using fewer descriptors and about 9.1% improvement in a previous benchmark test.1

A fast convolution-based methodology to simulate 2-Dd/3-D cardiac ultrasound images

Abstract: This paper describes a fast convolution-based methodology for simulating ultrasound images in a 2-D/3-D sector format as typically used in cardiac ultrasound. The conventional convolution model is based on the assumption of a space-invariant point spread function (PSF) and typically results in linear images. These characteristics are not representative for cardiac data sets. The spatial impulse response method (IRM) has excellent accuracy in the linear domain; however, calculation time can become an issue when scatterer numbers become significant and when 3-D volumetric data sets need to be computed. As a solution to these problems, the current manuscript proposes a new convolution-based methodology in which the data sets are produced by reducing the conventional 2-D/3-D convolution model to multiple 1-D convolutions (one for each image line). As an example, simulated 2-D/3-D phantom images are presented along with their gray scale histogram statistics. In addition, the computation time is recorded and contrasted to a commonly used implementation of IRM (Field II). It is shown that COLE can produce anatomically plausible images with local Rayleigh statistics but at improved calculation time (1200 times faster than the reference method).

ENCOPLOT: Pairwise Sequence Matching in Linear Time Applied to Plagiarism Detection ∗

Abstract: In this paper we describe a new general plagiarism detection method, that we used in our winning entry to the 1 st International Competition on Plagia- rism Detection, the external plagiarism detection task, which assumes the source documents are available. In the first phase of our method, a matrix of kernel values is computed, which gives a similarity value based on n-grams between each source and each suspicious document. In the second phase, each promising pair is further investigated, in order to extract the precise positions and lengths of the subtexts that have been copied and maybe obfuscated - using encoplot, a novel linear time pairwise sequence matching technique. We solved the significant computational chal- lenges arising from having to compare millions of document pairs by using a library developed by our group mainly for use in network security tools. The performance achieved is comparing more than 49 million pairs of documents in 12 hours on a single computer. The results in the challenge were very good, we outperformed all other methods.

Procedural noise using sparse Gabor convolution

Abstract: Noise is an essential tool for texturing and modeling. Designing interesting textures with noise calls for accurate spectral control, since noise is best described in terms of spectral content. Texturing requires that noise can be easily mapped to a surface, while high-quality rendering requires anisotropic filtering. A noise function that is procedural and fast to evaluate offers several additional advantages. Unfortunately, no existing noise combines all of these properties.In this paper we introduce a noise based on sparse convolution and the Gabor kernel that enables all of these properties. Our noise offers accurate spectral control with intuitive parameters such as orientation, principal frequency and bandwidth. Our noise supports two-dimensional and solid noise, but we also introduce setup-free surface noise. This is a method for mapping noise onto a surface, complementary to solid noise, that maintains the appearance of the noise pattern along the object and does not require a texture parameterization. Our approach requires only a few bytes of storage, does not use discretely sampled data, and is nonperiodic. It supports anisotropy and anisotropic filtering. We demonstrate our noise using an interactive tool for noise design.

An Online Algorithm for Large Scale Image Similarity Learning

Abstract: Learning a measure of similarity between pairs of objects is a fundamental problem in machine learning. It stands in the core of classification methods like kernel machines, and is particularly useful for applications like searching for images that are similar to a given image or finding videos that are relevant to a given video. In these tasks, users look for objects that are not only visually similar but also semantically related to a given object. Unfortunately, current approaches for learning similarity do not scale to large datasets, especially when imposing metric constraints on the learned similarity. We describe OASIS, a method for learning pairwise similarity that is fast and scales linearly with the number of objects and the number of non-zero features. Scalability is achieved through online learning of a bilinear model over sparse representations using a large margin criterion and an efficient hinge loss cost. OASIS is accurate at a wide range of scales: on a standard benchmark with thousands of images, it is more precise than state-of-the-art methods, and faster by orders of magnitude. On 2.7 million images collected from the web, OASIS can be trained within 3 days on a single CPU. The non-metric similarities learned by OASIS can be transformed into metric similarities, achieving higher precisions than similarities that are learned as metrics in the first place. This suggests an approach for learning a metric from data that is larger by orders of magnitude than was handled before.

Semisupervised Remote Sensing Image Classification With Cluster Kernels

Abstract: A semisupervised support vector machine is presented for the classification of remote sensing images. The method exploits the wealth of unlabeled samples for regularizing the training kernel representation locally by means of cluster kernels. The method learns a suitable kernel directly from the image and thus avoids assuming a priori signal relations by using a predefined kernel structure. Good results are obtained in image classification examples when few labeled samples are available. The method scales almost linearly with the number of unlabeled samples and provides out-of-sample predictions.

Learning image similarity from Flickr groups using Stochastic Intersection Kernel MAchines

Abstract: Measuring image similarity is a central topic in computer vision In this paper, we learn similarity from Flickr groups and use it to organize photos Two images are similar if they are likely to belong to the same Flickr groups Our approach is enabled by a fast Stochastic Intersection Kernel MAchine (SIKMA) training algorithm, which we propose This proposed training method will be useful for many vision problems, as it can produce a classifier that is more accurate than a linear classifier, trained on tens of thousands of examples in two minutes The experimental results show our approach performs better on image matching, retrieval, and classification than using conventional visual features

Improving Hyperspectral Image Classification Using Spatial Preprocessing

Abstract: Spatial smoothing over the original hyperspectral data based on wavelet and anisotropic partial differential equations is incorporated using composite kernel in graph-based classifiers. The kernels combine spectral-spatial relationships using the smoothed and original hyperspectral images. Experiments with different real hyperspectral scenarios are presented. Comparison with recent graph-based methods shows that the proposed scheme gives better classification with lower computational cost.

Method for reconstruction of pixel color values

Abstract: A method of color reconstruction includes a first process for a first pixel and a second process for the first pixel. The first process includes extracting a first kernel from a multi-color matrix, generating first variance weights from the first kernel, and generating a first color based on the first variance weights and adjacent pixel values of the first color. The second process includes extracting a second kernel from the multi-color matrix, generating second variance offsets from the second kernel, and generating a second color based on the second variance offsets and an adjacent pixel of the second color.

Kernel Nyström method for light transport

Abstract: We propose a kernel Nystrom method for reconstructing the light transport matrix from a relatively small number of acquired images. Our work is based on the generalized Nystrom method for low rank matrices. We introduce the light transport kernel and incorporate it into the Nystrom method to exploit the nonlinear coherence of the light transport matrix. We also develop an adaptive scheme for efficiently capturing the sparsely sampled images from the scene. Our experiments indicate that the kernel Nystrom method can achieve good reconstruction of the light transport matrix with a few hundred images and produce high quality relighting results. The kernel Nystrom method is effective for modeling scenes with complex lighting effects and occlusions which have been challenging for existing techniques.