Modeling and Inverse Problems in Imaging Analysis

Chalmond, Bernard

doi:10.1007/978-0-387-21662-1

Cited by 49 publications

(27 citation statements)

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“…A typical example is the Canny edge detector; see [4]. Other operations can be found, e.g., in [6,11]. Here we restrict our discussion, as mentioned above, to linear operators.…”

Section: Ams Subject Classifications 65r32 45q05mentioning

confidence: 99%

Combining Image Reconstruction and Image Analysis with an Application to Two-Dimensional Tomography

Louis¹

2008

SIAM J. Imaging Sci.

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Abstract. The tasks of image reconstruction from measured data and the analysis of the resulting images are more or less strictly separated. One group of scientists computes by applying reconstruction algorithms to the images; the other then operates on these images to enhance the analysis. First attempts at combining image reconstruction and image analysis, in a nonsystematic way, are known as Lambda tomography or Tikhonov-Phillips methods with 1-norms or with level-set methods. The aim of this paper is to provide a general tool to combine these two steps; i.e., even in the reconstruction step the future image analysis step is taken into account, leading to a new reconstruction kernel. Here we concentrate on linear methods. As a practical example we consider the image reconstruction problem in computerized tomography followed by an edge detection. We calculate a new reconstruction kernel and present results from simulations.Key words. image analysis, image reconstruction, approximate inverse AMS subject classifications. 65R32, 45Q05DOI. 10.1137/0707008631. Introduction. In order to extract information from a given image, analysis tools are used. In a first step one applies operators on that image; then the searched-for information is found by operating on these enhanced versions of the original picture. Images typically are twodimensional arrays of numbers. Of course, three-dimensional arrays for volume data or even time-dependent data, which may amount to four-dimensional data, are conceivable. Prominent analysis tools are edge detection methods where first partial derivatives of smoothed versions of the image are computed, followed by recognition methods. A typical example is the Canny edge detector; see [4]. Other operations can be found, e.g., in [6,11]. Here we restrict our discussion, as mentioned above, to linear operators. In denoising one can think of solving the heat equation with homogeneous boundary conditions and the original image as initial condition, at the final time T the image is considered to be denoised.We have to mention, of course, that nonlinear methods also play an essential role. But this does not-at least at the moment-fit into our framework.Attempts to combine reconstruction and analysis are known, but are not systematically pursued. As an example we mention the Λ computerized tomography, in which local inversion formulas produce images where the singular support is preserved; this means that those images have jumps wherever the original image has them (see, e.g., [10,13,21]). The use of TikhonovPhillips regularization with 1 -norms results in smooth images; see, e.g., [5]. Level-set methods

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“…A typical example is the Canny edge detector; see [4]. Other operations can be found, e.g., in [6,11]. Here we restrict our discussion, as mentioned above, to linear operators.…”

Section: Ams Subject Classifications 65r32 45q05mentioning

confidence: 99%

Combining Image Reconstruction and Image Analysis with an Application to Two-Dimensional Tomography

Louis¹

2008

SIAM J. Imaging Sci.

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“…Expectation maximization (EM) [10] and its variants (Stochastic EM [11,12], Gibbsian EM [13]), as well as iterated conditional expectation (ICE) [14,15] are widely used to solve such problems. It is important to note, however, that these methods calculate a local maximum [6].…”

Section: Introductionmentioning

confidence: 99%

“…Note that U is finite, although huge. A widely accepted standard, also motivated by the human visual system [4,5], is to construct this probability measure in a Bayesian framework [6][7][8]: we shall assume that we have a set of observed (Y) and hidden (X) random variables. In our context, the observation F 2Y represents the low-level features used for partitioning the image, and the hidden entity u2X represents the segmentation itself.…”

Section: Introductionmentioning

confidence: 99%

A Markov random field image segmentation model for color textured images

Kató

Pong

2006

Image and Vision Computing

178

113

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We propose a Markov random field (MRF) image segmentation model, which aims at combining color and texture features. The theoretical framework relies on Bayesian estimation via combinatorial optimization (simulated annealing). The segmentation is obtained by classifying the pixels into different pixel classes. These classes are represented by multi-variate Gaussian distributions. Thus, the only hypothesis about the nature of the features is that an additive Gaussian noise model is suitable to describe the feature distribution belonging to a given class. Here, we use the perceptually uniform CIE-L*u*v* color values as color features and a set of Gabor filters as texture features. Gaussian parameters are either computed using a training data set or estimated from the input image. We also propose a parameter estimation method using the EM algorithm. Experimental results are provided to illustrate the performance of our method on both synthetic and natural color images. q

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“…In our case, m is defined over the grid G which is larger than the data support F = {F k } and furthermore some data are missing when a black hole is present. In this situation, the EM algorithm becomes completely justified and then we really take advantage of its property to deal with missing data [10]. Procedures for deconvoluting images in the case of non-organized and non-uniform data include the OS-EM algorithm [11].…”

Section: Deconvolution In the Case Of Missing Datamentioning

confidence: 99%

“…We have to emphasize that our deconvolution process does not integrate any regularization component. Since regularization is well known to be crucial to solve inverse problems (see [10,12] among many others), in our firsts experiments, we have tested the role of regularization components and in particularly the total variation term as in [13]. But, on the light of the experimental results, we consider this regularization has no benefit effect for micro-rotation volume deconvolution.…”

Section: With Respect To the Conditional Distribution P(x|s M(t)) Whmentioning

confidence: 99%

Micro-rotation imaging deconvolution

Saux

Chalmond

et al. 2008

2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro

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Recently, micro-rotation confocal microscopy has enabled the acquisition of a sequence of slices of non adherent living cells obtained during a partially controlled rotation movement of the cell through the focal plane. Although we are now able to estimate the 3D position of every slice with respect to the frame, the reconstruction of the cell from the positioned slices remains a problem that this paper address. In our context, 3D spatially-varying PSF and missing data are the two main particularities of this problem. Experiments illustrate the ability of the classical EM algorithm to deconvolve efficiently cell volume and also to deal with missing data.

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Modeling and Inverse Problems in Imaging Analysis

Cited by 49 publications

References 0 publications

Combining Image Reconstruction and Image Analysis with an Application to Two-Dimensional Tomography

Combining Image Reconstruction and Image Analysis with an Application to Two-Dimensional Tomography

A Markov random field image segmentation model for color textured images

Micro-rotation imaging deconvolution

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