Piecewise Constant Image Model Research Articles

Iterative CT Reconstruction Using Shearlet-Based Regularization

Total variation (TV) methods have been proposed to improve the image quality in count-reduced images, by reducing the variation between neighboring pixels. Although very easy to implement and fast to compute, TV-based methods may lead to a loss of texture information when applied to images with complex textures, such as high-resolution abdominal CT images. Here, we investigate the use of another regularization approach in the context of medical images based on multiresolution transformations. One such transformation is the shearlet transform, which is optimally sparse for images that are C2 except for discontinuities along C2 curves, and has better directional sensitivity than most other, related, wavelet transform approaches. We propose to solve the convex problem using the split-Bregman (augmented Lagrangian) approach. One of the primary advantages of the split-Bregman approach, is that the shearlet transform can easily be incorporated into the sparse-view CT reconstruction. The required sparsity prior is the l1 norm of the shearlet coefficients. Results are shown for this method in comparison to the same framework with TV as the regularization term on simulated data. The noise-resolution performance is investigated at different contrast levels. At equal image noise, TV-based regularization outperforms shearlet-based regularization. However, when image texture is analyzed on measured mouse data, shearlets outperform TV, which suffers from staircasing effects. Our results show that there are benefits in using shearlets in CT imaging: texture is reconstructed more accurately compared to when TV is used, without biasing the image towards a piecewise constant image model. However, due to the larger support of the basis functions, our results suggest that uncareful usage of shearlets may lead to wavy artifacts, which can be equally unwanted as staircasing effects.

Context Coding of Depth Map Images Under the Piecewise-Constant Image Model Representation

This paper introduces an efficient method for lossless compression of depth map images, using the representation of a depth image in terms of three entities: 1) the crack-edges; 2) the constant depth regions enclosed by them; and 3) the depth value over each region. The starting representation is identical with that used in a very efficient coder for palette images, the piecewise-constant image model coding, but the techniques used for coding the elements of the representation are more advanced and especially suitable for the type of redundancy present in depth images. Initially, the vertical and horizontal crack-edges separating the constant depth regions are transmitted by 2D context coding using optimally pruned context trees. Both the encoder and decoder can reconstruct the regions of constant depth from the transmitted crack-edge image. The depth value in a given region is encoded using the depth values of the neighboring regions already encoded, exploiting the natural smoothness of the depth variation, and the mutual exclusiveness of the values in neighboring regions. The encoding method is suitable for lossless compression of depth images, obtaining compression of about 10-65 times, and additionally can be used as the entropy coding stage for lossy depth compression.

Geometric feature‐based multimodal image registration of contrast‐enhanced cardiac CT with gated myocardial perfusion SPECT

Cardiac computed tomography (CT) and single photon emission computed tomography (SPECT) provide clinically complementary information in the diagnosis of coronary artery disease (CAD). Fused anatomical and physiological data acquired sequentially on separate scanners can be coregistered to accurately diagnose CAD in specific coronary vessels. A fully automated registration method is presented utilizing geometric features from a reliable segmentation of gated myocardial perfusion SPECT (MPS) volumes, where regions of myocardium and blood pools are extracted and used as an anatomical mask to de-emphasize the inhomogeneities of intensity distribution caused by perfusion defects and physiological variations. A multiresolution approach is employed to represent coarse-to-fine details of both volumes. The extracted voxels from each level are aligned using a similarity measure with a piecewise constant image model and minimized using a gradient descent method. The authors then perform limited nonlinear registration of gated MPS to adjust for phase differences by automatic cardiac phase matching between CT and MPS. For phase matching, they incorporate nonlinear registration using thin-plate-spline-based warping. Rigid registration has been compared with manual alignment (n=45) on 20 stress/rest MPS and coronary CTA data sets acquired from two different sites and five stress CT perfusion data sets. Phase matching was also compared to expert visual assessment. As compared with manual alignment obtained from two expert observers, the mean and standard deviation of absolute registration errors of the proposed method for MPS were 4.3 +/- 3.5, 3.6 +/- 2.6, and 3.6 +/- 2.1 mm for translation and 2.1 +/- 3.2 degrees, 0.3 +/- 0.8 degree, and 0.7 +/- 1.2 degrees for rotation at site A and 3.8 +/- 2.7, 4.0 +/- 2.9, and 2.2 +/- 1.8mm for translation and 1.1 +/- 2.0 degrees, 1.6 +/- 3.1 degrees, and 1.9 +/- 3.8 degrees for rotation at site B. The results for CT perfusion were 3.0 +/- 2.9, 3.5 +/- 2.4, and 2.8 +/- 1.0 mm for translation and 3.0 +/- 2.4 degrees, 0.6 +/- 0.9 degree, and 1.2 +/- 1.3 degrees for rotation. The registration error shows that the proposed method achieves registration accuracy of less than 1 voxel (6.4 x 6.4 x 6.4 mm) misalignment. The proposed method was robust for different initializations in the range from -80 to 70, -80 to 70, and -50 to 50 mm in the x-, y-, and z-axes, respectively. Validation results of finding best matching phase showed that best matching phases were not different by more than two phases, as visually determined. The authors have developed a fast and fully automated method for registration of contrast cardiac CT with gated MPS which includes nonlinear cardiac phase matching and is capable of registering these modalities with accuracy <10 mm in 87% of the cases.

A multiscale expectation-maximization semisupervised classifier suitable for badly posed image classification

This paper deals with the problem of badly posed image classification. Although underestimated in practice, bad-posedness is likely to affect many real-world image classification tasks, where reference samples are difficult to collect (e.g., in remote sensing (RS) image mapping) and/or spatial autocorrelation is relevant. In an image classification context affected by a lack of reference samples, an original inductive learning multiscale image classifier, termed multiscale semisupervised expectation maximization (MSEM), is proposed. The rationale behind MSEM is to combine useful complementary properties of two alternative data mapping procedures recently published outside of image processing literature, namely, the multiscale modified Pappas adaptive clustering (MPAC) algorithm and the sample-based semisupervised expectation maximization (SEM) classifier. To demonstrate its potential utility, MSEM is compared against nonstandard classifiers, such as MPAC, SEM and the single-scale contextual SEM (CSEM) classifier, besides against well-known standard classifiers in two RS image classification problems featuring few reference samples and modestly useful texture information. These experiments yield weak (subjective) but numerous quantitative map quality indexes that are consistent with both theoretical considerations and qualitative evaluations by expert photointerpreters. According to these quantitative results, MSEM is competitive in terms of overall image mapping performance at the cost of a computational overhead three to six times superior to that of its most interesting rival, SEM. More in general, our experiments confirm that, even if they rely on heavy class-conditional normal distribution assumptions that may not be true in many real-world problems (e.g., in highly textured images), semisupervised classifiers based on the iterative expectation maximization Gaussian mixture model solution can be very powerful in practice when: 1) there is a lack of reference samples with respect to the problem/model complexity and 2) texture information is considered negligible (i.e., a piecewise constant image model holds).

The piecewise-constant image model

The piecewise-constant image model (PWC) is a new technique for lossless compression of palette images. PWC is a blend of traditional scanline-oriented and newer object-based methods. Remarkably, PWC delivers the best known compression across a wide variety palette of image types while delivering translation speeds comparable to highly tuned one-dimensional methods. This paper introduces the topic of palette image coding and traces the development of the piecewise-constant model from a completely object-oriented code requiring two image passes to a high-performance scanline-oriented code.

Centered pyramids

Quadtree-like pyramids have the advantage of re-suiting in a multiresolution representation where each pyramid node has four unambiguous parents. Such a centered topology guarantees a clearly defined up-projection of labels. This concept has been successfully and extensively used in applications of contour detection, object recognition and segmentation. Unfortunately, the quadtree-like type of pyramid has poor approximation powers because of the employed piecewise-constant image model. This paper deals with the construction of improved centered image pyramids in terms of general approximation functions. The advantages of the centered topology such a symmetry, consistent boundary conditions and accurate up-projection of labels are combined with a more faithful image representation at coarser pyramid levels. We start by introducing a general framework for the design of least squares pyramids using the standard filtering and decimation tools. We give the most general explicit formulas for the computation of the filter coefficients by any (well behaving) approximation function in both the continuous (L/sub 2/) and the discrete (l/sub 2/) norm. We then define centered pyramids and provide the filter coefficients for odd spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications.