On curvature estimation of ISO surfaces in 3D gray-value images and the computation of shape descriptors

Empirical Comparison of Curvature Estimators on Volume Images and Triangle Meshes

In the development of graphical algorithms, choosing an appropriate data representation plays a pivotal role. Hence, there is a need for studies that support corresponding decision making. Here, we investigate curvature estimation based on two discrete representations-volume images and triangle meshes-and present a comprehensive cross-comparison. For doing so, four carefully selected geometries, represented as implicit functions, have been discretized to volume images and triangle meshes in different resolutions on a comparable scale. Afterwards, implementations available in open-source libraries (CGAL, DIPimage, libigl, trimesh2, VTK) and our own implementation of a relevant paper [1] were applied to them and the resulting estimations of mean and Gaussian curvature were compared in terms of quality and runtime. Independent of the underlying discrete representation, all estimators generated similar errors, but overall, mesh-based methods allowed for more accurate estimations. We measured a maximum normalized mean absolute error difference of 6.36 percent between the most precise mesh-based method compared to corresponding image-based methods when considering only discretizations of sufficient resolution. In terms of runtime, methods working on triangle meshes were faster when geometries had a small surface density. For geometries with larger surface densities, which is fairly common when considering real data, e.g., in material or medical science, the runtimes for both representations were similar.

Computational analysis in epilepsy neuroimaging: A survey of features and methods

Epilepsy affects 65 million people worldwide, a third of whom have seizures that are resistant to anti-epileptic medications. Some of these patients may be amenable to surgical therapy or treatment with implantable devices, but this usually requires delineation of discrete structural or functional lesion(s), which is challenging in a large percentage of these patients.

Advances in neuroimaging and machine learning allow semi-automated detection of malformations of cortical development (MCDs), a common cause of drug resistant epilepsy. A frequently asked question in the field is what techniques currently exist to assist radiologists in identifying these lesions, especially subtle forms of MCDs such as focal cortical dysplasia (FCD) Type I and low grade glial tumors. Below we introduce some of the common lesions encountered in patients with epilepsy and the common imaging findings that radiologists look for in these patients. We then review and discuss the computational techniques introduced over the past 10 years for quantifying and automatically detecting these imaging findings. Due to large variations in the accuracy and implementation of these studies, specific techniques are traditionally used at individual centers, often guided by local expertise, as well as selection bias introduced by the varying prevalence of specific patient populations in different epilepsy centers. We discuss the need for a multi-institutional study that combines features from different imaging modalities as well as computational techniques to definitively assess the utility of specific automated approaches to epilepsy imaging. We conclude that sharing and comparing these different computational techniques through a common data platform provides an opportunity to rigorously test and compare the accuracy of these tools across different patient populations and geographical locations. We propose that these kinds of tools, quantitative imaging analysis methods and open data platforms for aggregating and sharing data and algorithms, can play a vital role in reducing the cost of care, the risks of invasive treatments, and improve overall outcomes for patients with epilepsy.

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We introduce common epileptogenic lesions encountered in patients with drug resistant epilepsy.

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We discuss state of the art computational techniques used to detect lesions.

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There is a need for multi-institutional studies that combine these techniques.

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Clinically validated pipelines alongside the advances in imaging and electrophysiology will improve outcomes.

Tensor scale: An analytic approach with efficient computation and applications

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as "tensor scale" using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert's structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods.

Improved curvature estimation for computer-aided detection of colonic polyps in CT colonography

RATIONALE AND OBJECTIVES

Current schemes for computer-aided detection (CAD) of colon polyps usually use kernel methods to perform curvature-based shape analysis. However, kernel methods may deliver spurious curvature estimations if the kernel contains two surfaces, because of the vanished gradient magnitudes. The aim of this study was to use the Knutsson mapping method to deal with the difficulty of providing better curvature estimations and to assess the impact of improved curvature estimation on the performance of CAD schemes.

MATERIALS AND METHODS

The new method was compared to two widely used kernel methods in terms of the performance of two stages of CAD: initial detection and true-positive and false-positive classification. The evaluation was conducted on a database of 130 computed tomographic scans from 67 patients. In these patient scans, there were 104 clinically significant polyps and masses >5 mm.

RESULTS

In the initial detection stage, the detection sensitivity of the three methods was comparable. In the classification stage, at a 90% sensitivity level on the basis of the input of this step, the new technique yielded 3.15 false-positive results per scan, demonstrating reductions in false-positive findings of 30.2% (P < .01) and 27.9% (P < .01) compared to the two kernel methods.

CONCLUSIONS

The new method can benefit CAD schemes with reduced false-positive rates, without sacrificing detection sensitivity.

Left ventricle segmentation using diffusion wavelets and boosting

We propose a method for the segmentation of medical images based on a novel parameterization of prior shape knowledge and a search scheme based on classifying local appearance. The method uses diffusion wavelets to capture arbitrary and continuous interdependencies in the training data and uses them for an efficient shape model. The lack of classic visual consistency in complex medical imaging data, is tackled by a manifold learning approach handling optimal high-dimensional local features by Gentle Boosting. Appearance saliency is encoded in the model and segmentation is performed through the extraction and classification of the corresponding features in a new data set, as well as a diffusion wavelet based shape model constraint. Our framework supports hierarchies both in the model and the search space, can encode complex geometric and photometric dependencies of the structure of interest, and can deal with arbitrary topologies. Promising results are reported for heart CT data sets, proving the impact of the soft parameterization, and the efficiency of our approach.

A real-time algorithm for the approximation of level-set-based curve evolution

In this paper, we present a complete and practical algorithm for the approximation of level-set-based curve evolution suitable for real-time implementation. In particular, we propose a two-cycle algorithm to approximate level-set-based curve evolution without the need of solving partial differential equations (PDEs). Our algorithm is applicable to a broad class of evolution speeds that can be viewed as composed of a data-dependent term and a curve smoothness regularization term. We achieve curve evolution corresponding to such evolution speeds by separating the evolution process into two different cycles: one cycle for the data-dependent term and a second cycle for the smoothness regularization. The smoothing term is derived from a Gaussian filtering process. In both cycles, the evolution is realized through a simple element switching mechanism between two linked lists, that implicitly represents the curve using an integer valued level-set function. By careful construction, all the key evolution steps require only integer operations. A consequence is that we obtain significant computation speedups compared to exact PDE-based approaches while obtaining excellent agreement with these methods for problems of practical engineering interest. In particular, the resulting algorithm is fast enough for use in real-time video processing applications, which we demonstrate through several image segmentation and video tracking experiments.

A framework for in vivo quantification of regional brain folding in premature neonates

This paper describes and compares novel approaches to in vivo 3D measurement of brain surface folding in clinically acquired neonatal MR image data, which allows regional folding evaluation. Most of the current measures of folding are not independent of the area of the surface they are derived from. Therefore, applying them to whole-brain surfaces or subregions of different sizes results in differences which may or may not reflect true differences in folding. We address this problem by proposing new measures to quantify gyrification and two approaches to normalize previously defined measures. The method was applied to twelve premature infants (age 28-37 weeks) from which cerebrospinal fluid/gray matter and gray matter/white matter interface surfaces were extracted. Experimental results show that previous folding measures are sensitive to the area of the surface of analysis and that the area-independent measures proposed here provide significant improvements. Such a system provides a tool that facilitates the study of structural development in the neonatal brain within specific functional subregions, which may be critical in identifying later neurological impairment.

Classifying CT image data into material fractions by a scale and rotation invariant edge model

A fully automated method is presented to classify 3-D CT data into material fractions. An analytical scale-invariant description relating the data value to derivatives around Gaussian blurred step edges--arch model--is applied to uniquely combine robustness to noise, global signal fluctuations, anisotropic scale, noncubic voxels, and ease of use via a straightforward segmentation of 3-D CT images through material fractions. Projection of noisy data value and derivatives onto the arch yields a robust alternative to the standard computed Gaussian derivatives. This results in a superior precision of the method. The arch-model parameters are derived from a small, but over-determined, set of measurements (data values and derivatives) along a path following the gradient uphill and downhill starting at an edge voxel. The model is first used to identify the expected values of the two pure materials (named L and H) and thereby classify the boundary. Second, the model is used to approximate the underlying noise-free material fractions for each noisy measurement. An iso-surface of constant material fraction accurately delineates the material boundary in the presence of noise and global signal fluctuations. This approach enables straightforward segmentation of 3-D CT images into objects of interest for computer-aided diagnosis and offers an easy tool for the design of otherwise complicated transfer functions in high-quality visualizations. The method is applied to segment a tooth volume for visualization and digital cleansing for virtual colonoscopy.

A system for measuring regional surface folding of the neonatal brain from MRI

This paper describes a novel approach to in-vivo measurement of brain surface folding in clinically acquired neonatal MR image data, which allows evaluation of surface curvature within subregions of the cortex. This paper addresses two aspects of this problem. Firstly: normalization of folding measures to provide area-independent evaluation of surface folding over arbitrary subregions of the cortex. Secondly: automated parcellation of the cortex at a particular developmental stage, based on an approximate spatial normalization of previously developed anatomical boundaries. The method was applied to seven premature infants (age 28-37 weeks) from which gray matter and gray-white matter interface surfaces were extracted. Experimental results show that previous folding measures are sensitive to the size of the surface of analysis, and that the area independent measures proposed here provide significant improvements. Such a system provides a tool to allow the study of structural development in the neonatal brain within specific functional subregions, which may be critical in identifying later neurological impairment.