The Pre-Image Problem in Kernel Methods

Kwok, James T.; Tsang, Ivor W.

doi:10.1109/tnn.2004.837781

Cited by 362 publications

(287 citation statements)

References 8 publications

(4 reference statements)

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“…Many methods were proposed for the K-PCA reconstruction, and different cost functions could lead to different optimization problems. In this work, we used Kwok & Tsang's algorithm for reconstruction [12].…”

Section: Motion Modeling Using Kernel-pcamentioning

confidence: 99%

Online 4-D CT Estimation for Patient-Specific Respiratory Motion Based on Real-Time Breathing Signals

Xue

Xie

et al. 2010

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010

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Abstract. In image-guided lung intervention, the electromagnetic (EM) tracked needle can be visualized in a pre-procedural CT by registering the EM tracking and the CT coordinate systems. However, there exist discrepancies between the static pre-procedural CT and the patient due to respiratory motion. This paper proposes an online 4-D CT estimation approach to patient-specific respiratory motion compensation. First, the motion patterns between 4-D CT data and respiratory signals such as fiducials from a number of patients are trained in a template space after image registration. These motion patterns can be used to estimate the patient-specific serial CTs from a static 3-D CT and the real-time respiratory signals of that patient, who do not generally take 4-D CTs. Specifically, the respiratory lung field motion vectors are projected onto the Kernel Principal Component Analysis (K-PCA) space, and a motion estimation model is constructed to estimate the lung field motion from the fiducial motion using the ridge regression method based on the least squares support vector machine (LS-SVM). The algorithm can be performed onsite prior to the intervention to generate the serial CT images according to the respiratory signals in advance, and the estimated CTs can be visualized in real-time during the intervention. In experiments, we evaluated the algorithm using leave-one-out strategy on 30 4-D CT data, and the results showed that the average errors of the lung field surfaces are 1.63mm.

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Section: Motion Modeling Using Kernel-pcamentioning

confidence: 99%

Online 4-D CT Estimation for Patient-Specific Respiratory Motion Based on Real-Time Breathing Signals

Xue

Xie

et al. 2010

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010

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“…In this paper, we do not show these procedures for brief explanation. The details of these procedures are shown in [12]. In the texture classification using Eq.…”

Section: Texture Classification Algorithmmentioning

confidence: 99%

“…Since an exact pre-image, which is the inverse mapping from the feature space back to the input space, typically does not exist [12],x satisfies the following equation:…”

Section: [Constraint 2]mentioning

confidence: 99%

POCS-Based Texture Reconstruction Method Using Clustering Scheme by Kernel PCA

Ogawa¹,

Haseyama²

2007

IEICE Transactions on Fundamentals of Electronics, Communicatio

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SUMMARYA new framework for reconstruction of missing textures in digital images is introduced in this paper. The framework is based on a projection onto convex sets (POCS) algorithm including a novel constraint. In the proposed method, a nonlinear eigenspace of each cluster obtained by classification of known textures within the target image is applied to the constraint. The main advantage of this approach is that the eigenspace can approximate the textures classified into the same cluster in the leastsquares sense. Furthermore, by monitoring the errors converged by the POCS algorithm, a selection of the optimal cluster to reconstruct the target texture including missing intensities can be achieved. This POCS-based approach provides a solution to the problem in traditional methods of not being able to perform the selection of the optimal cluster due to the missing intensities within the target texture. Consequently, all of the missing textures are successfully reconstructed by the selected cluster's eigenspaces which correctly approximate the same kinds of textures. Experimental results show subjective and quantitative improvement of the proposed reconstruction technique over previously reported reconstruction techniques.

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“…Kernel methods, in particular, kernel PCA has been the focus of research in the pattern recognition community [16,17]. The basic idea behind these methods is to map the data in the input space φ ∈ χ to a feature space F via some nonlinear map Ψ , and then apply a linear method in F to do further analysis.…”

Section: Kernel Pcamentioning

confidence: 99%

“…However, this method is dependent on the initial starting point and is highly susceptible to local minima. To circumvent this problem, [17] and more recently [15] proposed an algorithm to reconstruct an approximate pre-image of the projection as described briefly in the remainder of this section. Kernel PCA performs the traditional linear PCA in the feature space corresponding to the kernel k(., .).…”

Section: Kernel Pcamentioning

confidence: 99%

Comparative Analysis of Kernel Methods for Statistical Shape Learning

Rathi

Dambreville

Tannenbaum

2006

Computer Vision Approaches to Medical Image Analysis

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Abstract. Prior knowledge about shape may be quite important for image segmentation. In particular, a number of different methods have been proposed to compute the statistics on a set of training shapes, which are then used for a given image segmentation task to provide the shape prior. In this work, we perform a comparative analysis of shape learning techniques such as linear PCA, kernel PCA, locally linear embedding and propose a new method, kernelized locally linear embedding for doing shape analysis. The surfaces are represented as the zero level set of a signed distance function and shape learning is performed on the embeddings of these shapes. We carry out some experiments to see how well each of these methods can represent a shape, given the training set.

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The Pre-Image Problem in Kernel Methods

Cited by 362 publications

References 8 publications

Online 4-D CT Estimation for Patient-Specific Respiratory Motion Based on Real-Time Breathing Signals

Online 4-D CT Estimation for Patient-Specific Respiratory Motion Based on Real-Time Breathing Signals

POCS-Based Texture Reconstruction Method Using Clustering Scheme by Kernel PCA

Comparative Analysis of Kernel Methods for Statistical Shape Learning

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