Continuous Medial Representation Research Articles

Medial Representation Based Font Recognition Method

In this article, a method of font recognition based on the medial representation, integrated into the font recognition system based on a digital image of text is described. This system searches for similar fonts, ordered by similarity, to the font shown in the user-entered text image. The system is based on solving two machine learning problems: text recognition on an image and font recognition on a text image. To solve the first problem, we use the concept of a mathematical model of a grapheme based on a continuous medial representation of a symbol. The solution to the font recognition problem is based on the concept of the morphological width of the figure, which is also closely related to the medial representation. We propose a method for using the morphological width function to find the most similar fonts from a known database. The experiments show high accuracy of searching for the most similar fonts. For a database consisting of 2543 fonts, the accuracy is 0.991 according to the metric top@5 for correctly recognized text in the font size of 100 pixels in the image.

4D CONTINUOUS MEDIAL REPRESENTATION BY GEODESIC SHAPE REGRESSION.

Longitudinal shape analysis has shown great potential to model anatomical processes from baseline to follow-up observations. Shape regression estimates a continuous trajectory of time-discrete anatomical shapes to quantify temporal changes. The need for shape alignment and point-to-point correspondences represent limitations of current shape analysis methodologies, and present significant challenges in shape evaluation. We propose a method that estimates a continuous trajectory of continuous medial representations (CM-Rep) from a set of time-discrete observed shapes. To avoid the traditional step of aligning individual objects, shape changes are modeled via diffeomorphic ambient space deformations. Using a medial shape representation, we separately capture object pose changes and intrinsic geometry changes. Tests and validation with synthetic and real anatomical shapes demonstrate that the new method captures extrinsic shape changes as well as intrinsic shape changes encoded with CM-Reps, a highly relevant property for studying growth and disease processes.

Medially constrained deformable modeling for segmentation of branching medial structures: Application to aortic valve segmentation and morphometry.

Deformable modeling with medial axis representation is a useful means of segmenting and parametrically describing the shape of anatomical structures in medical images. Continuous medial representation (cm-rep) is a "skeleton-first" approach to deformable medial modeling that explicitly parameterizes an object's medial axis and derives the object's boundary algorithmically. Although cm-rep has effectively been used to segment and model a number of anatomical structures with non-branching medial topologies, the framework is challenging to apply to objects with branching medial geometries since branch curves in the medial axis are difficult to parameterize. In this work, we demonstrate the first clinical application of a new "boundary-first" deformable medial modeling paradigm, wherein an object's boundary is explicitly described and constraints are imposed on boundary geometry to preserve the branching configuration of the medial axis during model deformation. This "boundary-first" framework is leveraged to segment and morphologically analyze the aortic valve apparatus in 3D echocardiographic images. Relative to manual tracing, segmentation with deformable medial modeling achieves a mean boundary error of 0.41 ± 0.10 mm (approximately one voxel) in 22 3DE images of normal aortic valves at systole. Deformable medial modeling is additionally demonstrated on pathological cases, including aortic stenosis, Marfan syndrome, and bicuspid aortic valve disease. This study demonstrates a promising approach for quantitative 3DE analysis of aortic valve morphology.

Segmentation of the Aortic Valve Apparatus in 3D Echocardiographic Images: Deformable Modeling of a Branching Medial Structure.

3D echocardiographic (3DE) imaging is a useful tool for assessing the complex geometry of the aortic valve apparatus. Segmentation of this structure in 3DE images is a challenging task that benefits from shape-guided deformable modeling methods, which enable inter-subject statistical shape comparison. Prior work demonstrates the efficacy of using continuous medial representation (cm-rep) as a shape descriptor for valve leaflets. However, its application to the entire aortic valve apparatus is limited since the structure has a branching medial geometry that cannot be explicitly parameterized in the original cm-rep framework. In this work, we show that the aortic valve apparatus can be accurately segmented using a new branching medial modeling paradigm. The segmentation method achieves a mean boundary displacement of 0.6 ± 0.1 mm (approximately one voxel) relative to manual segmentation on 11 3DE images of normal open aortic valves. This study demonstrates a promising approach for quantitative 3DE analysis of aortic valve morphology.

Three-Dimensional Ultrasound-Derived Physical Mitral Valve Modeling

Advances in mitral valve repair and adoption have been partly attributed to improvements in echocardiographic imaging technology. To educate and guide repair surgery further, we have developed a methodology for fast production of physical models of the valve using novel three-dimensional (3D) echocardiographic imaging software in combination with stereolithographic printing. Quantitative virtual mitral valve shape models were developed from 3D transesophageal echocardiographic images using software based on semiautomated image segmentation and continuous medial representation algorithms. These quantitative virtual shape models were then used as input to a commercially available stereolithographic printer to generate a physical model of the each valve at end systole and end diastole. Physical models of normal and diseased valves (ischemic mitral regurgitation and myxomatous degeneration) were constructed. There was good correspondence between the virtual shape models and physical models. It was feasible to create a physical model of mitral valve geometry under normal, ischemic, and myxomatous valve conditions using 3D printing of 3D echocardiographic data. Printed valves have the potential to guide surgical therapy for mitral valve disease.

Fully automatic segmentation of the mitral leaflets in 3D transesophageal echocardiographic images using multi-atlas joint label fusion and deformable medial modeling.

Comprehensive visual and quantitative analysis of in vivo human mitral valve morphology is central to the diagnosis and surgical treatment of mitral valve disease. Real-time 3D transesophageal echocardiography (3D TEE) is a practical, highly informative imaging modality for examining the mitral valve in a clinical setting. To facilitate visual and quantitative 3D TEE image analysis, we describe a fully automated method for segmenting the mitral leaflets in 3D TEE image data. The algorithm integrates complementary probabilistic segmentation and shape modeling techniques (multi-atlas joint label fusion and deformable modeling with continuous medial representation) to automatically generate 3D geometric models of the mitral leaflets from 3D TEE image data. These models are unique in that they establish a shape-based coordinate system on the valves of different subjects and represent the leaflets volumetrically, as structures with locally varying thickness. In this work, expert image analysis is the gold standard for evaluating automatic segmentation. Without any user interaction, we demonstrate that the automatic segmentation method accurately captures patient-specific leaflet geometry at both systole and diastole in 3D TEE data acquired from a mixed population of subjects with normal valve morphology and mitral valve disease.

Development of a semi-automated method for mitral valve modeling with medial axis representation using 3D ultrasound

Precise 3D modeling of the mitral valve has the potential to improve our understanding of valve morphology, particularly in the setting of mitral regurgitation (MR). Toward this goal, the authors have developed a user-initialized algorithm for reconstructing valve geometry from transesophageal 3D ultrasound (3D US) image data. Semi-automated image analysis was performed on transesophageal 3D US images obtained from 14 subjects with MR ranging from trace to severe. Image analysis of the mitral valve at midsystole had two stages: user-initialized segmentation and 3D deformable modeling with continuous medial representation (cm-rep). Semi-automated segmentation began with user-identification of valve location in 2D projection images generated from 3D US data. The mitral leaflets were then automatically segmented in 3D using the level set method. Second, a bileaflet deformable medial model was fitted to the binary valve segmentation by Bayesian optimization. The resulting cm-rep provided a visual reconstruction of the mitral valve, from which localized measurements of valve morphology were automatically derived. The features extracted from the fitted cm-rep included annular area, annular circumference, annular height, intercommissural width, septolateral length, total tenting volume, and percent anterior tenting volume. These measurements were compared to those obtained by expert manual tracing. Regurgitant orifice area (ROA) measurements were compared to qualitative assessments of MR severity. The accuracy of valve shape representation with cm-rep was evaluated in terms of the Dice overlap between the fitted cm-rep and its target segmentation. The morphological features and anatomic ROA derived from semi-automated image analysis were consistent with manual tracing of 3D US image data and with qualitative assessments of MR severity made on clinical radiology. The fitted cm-reps accurately captured valve shape and demonstrated patient-specific differences in valve morphology among subjects with varying degrees of MR severity. Minimal variation in the Dice overlap and morphological measurements was observed when different cm-rep templates were used to initialize model fitting. This study demonstrates the use of deformable medial modeling for semi-automated 3D reconstruction of mitral valve geometry using transesophageal 3D US. The proposed algorithm provides a parametric geometrical representation of the mitral leaflets, which can be used to evaluate valve morphology in clinical ultrasound images.

Semi-automated mitral valve morphometry and computational stress analysis using 3D ultrasound

In vivo human mitral valves (MV) were imaged using real-time 3D transesophageal echocardiography (rt-3DTEE), and volumetric images of the MV at mid-systole were analyzed by user-initialized segmentation and 3D deformable modeling with continuous medial representation, a compact representation of shape. The resulting MV models were loaded with physiologic pressures using finite element analysis (FEA). We present the regional leaflet stress distributions predicted in normal and diseased (regurgitant) MVs. Rt-3DTEE, semi-automated leaflet segmentation, 3D deformable modeling, and FEA modeling of the in vivo human MV is tenable and useful for evaluation of MV pathology.

A tract-specific framework for white matter morphometry combining macroscopic and microscopic tract features.

Diffusion tensor imaging plays a key role in our understanding of white matter both in normal populations and in populations with brain disorders. Existing techniques focus primarily on using diffusivity-based quantities derived from diffusion tensor as surrogate measures of microstructural tissue properties of white matter. In this paper, we describe a novel tract-specific framework that enables the examination of white matter morphometry at both the macroscopic and microscopic scales. The framework leverages the skeleton-based modeling of sheet-like white matter fasciculi using the continuous medial representation, which gives a natural definition of thickness and supports its comparison across subjects. The thickness measure provides a macroscopic characterization of white matter fasciculi that complements existing analysis of microstructural features. The utility of the framework is demonstrated in quantifying white matter atrophy in Amyotrophic Lateral Sclerosis, a severe neurodegenerative disease of motor neurons. We show that, compared to using microscopic features alone, combining the macroscopic and microscopic features gives a more complete characterization of the disease.

A tract-specific framework for white matter morphometry combining macroscopic and microscopic tract features.

Diffusion tensor imaging plays a key role in our understanding of white matter (WM) both in normal populations and in populations with brain disorders. Existing techniques focus primarily on using diffusivity-based quantities derived from diffusion tensor as surrogate measures of microstructural tissue properties of WM. In this paper, we describe a novel tract-specific framework that enables the examination of WM morphometry at both the macroscopic and microscopic scales. The framework leverages the skeleton-based modeling of sheet-like WM fasciculi using the continuous medial representation, which gives a natural definition of thickness and supports its comparison across subjects. The thickness measure provides a macroscopic characterization of WM fasciculi that complements existing analysis of microstructural features. The utility of the framework is demonstrated in quantifying WM atrophy in Amyotrophic Lateral Sclerosis, a severe neurodegenerative disease of motor neurons. We show that, compared to using microscopic features alone, combining the macroscopic and microscopic features gives a more holistic characterization of the disease.

Continuous medial representation of brain structures using the biharmonic PDE

A new approach for constructing deformable continuous medial models for anatomical structures is presented. Medial models describe geometrical objects by first specifying the skeleton of the object and then deriving the boundary surface corresponding to the skeleton. However, an arbitrary specification of a skeleton will not be “valid” unless a certain set of sufficient conditions is satisfied. The most challenging of these is the non-linear equality constraint that must hold along the boundaries of the manifolds forming the skeleton. The main contribution of this paper is to leverage the biharmonic partial differential equation as a mapping from a codimension-0 subset of Euclidean space to the space of skeletons that satisfy the equality constraint. The PDE supports robust numerical solution on freeform triangular meshes, providing additional flexibility for shape modeling. The approach is evaluated by generating continuous medial models for a large dataset of hippocampus shapes. Generalizations to modeling more complex shapes and to representing branching skeletons are demonstrated.

Shape-Based Normalization of the Corpus Callosum for DTI Connectivity Analysis

The continuous medial representation (cm-rep) is an approach that makes it possible to model, normalize, and analyze anatomical structures on the basis of medial geometry. Having recently presented a partial differential equation (PDE)-based approach for 3-D cm-rep modeling [1], here we present an equivalent 2-D approach that involves solving an ordinary differential equation. This paper derives a closed form solution of this equation and shows how Pythagorean hodograph curves can be used to express the solution as a piecewise polynomial function, allowing efficient and robust medial modeling. The utility of the approach in medical image analysis is demonstrated by applying it to the problem of shape-based normalization of the midsagittal section of the corpus callosum. Using diffusion tensor tractography, we show that shape-based normalization aligns subregions of the corpus callosum, defined by connectivity, more accurately than normalization based on volumetric registration. Furthermore, shape-based normalization helps increase the statistical power of group analysis in an experiment where features derived from diffusion tensor tractography are compared between two cohorts. These results suggest that cm-rep is an appropriate tool for normalizing the corpus callosum in white matter studies.

Hippocampus-specific fMRI group activation analysis using the continuous medial representation

We present a new shape-based approach for regional group activation analysis in fMRI studies. The method restricts anatomical normalization, spatial smoothing and random effects statistical analysis to the space inside and around a structure of interest. Normalization involves finding intersubject correspondences between manually outlined masks, and it leverages the continuous medial representation, which makes it possible to extend surface-based shape correspondences to the space inside and outside of structures. Our approach is an alternative to whole-brain normalization in cases where the latter may fail due to anatomical variability or pathology. It also provides an opportunity to analyze the shape and thickness of structures concurrently with functional activation. We apply the technique to the hippocampus and evaluate it using data from a visual scene encoding fMRI study, where activation in the hippocampus is expected. We produce detailed statistical maps of hippocampal activation, as well as maps comparing activation inside and outside of the hippocampus. We find that random effects statistics computed by the new approach are more significant than those produced using the Statistical Parametric Mapping framework (Friston, K.J., Holmes, A.P., Worsley, K.J., Poline, J.-P., Firth, C.D., Frackowiak, R.S.J. 1994, Statistical parametric maps in functional imaging: a general linear approach. Human Brain Mapping, 2(4): 189–210) at low levels of smoothing, suggesting that greater specificity can be achieved by the new method without a severe tradeoff in sensitivity.

Continuous Medial Representation for Anatomical Structures

The m-rep approach pioneered by Pizer et al. (2003) is a powerful morphological tool that makes it possible to employ features derived from medial loci (skeletons) in shape analysis. This paper extends the medial representation paradigm into the continuous realm, modeling skeletons and boundaries of three-dimensional objects as continuous parametric manifolds, while also maintaining the proper geometric relationship between these manifolds. The parametric representation of the boundary-medial relationship makes it possible to fit shape-based coordinate systems to the interiors of objects, providing a framework for combined statistical analysis of shape and appearance. Our approach leverages the idea of inverse skeletonization, where the skeleton of an object is defined first and the object's boundary is derived analytically from the skeleton. This paper derives a set of sufficient conditions ensuring that inverse skeletonization is well-posed for single-manifold skeletons and formulates a partial differential equation whose solutions satisfy the sufficient conditions. An efficient variational algorithm for deformable template modeling using the continuous medial representation is described and used to fit a template to the hippocampus in 87 subjects from a schizophrenia study with sub-voxel accuracy and 95% mean overlap.

P.1.e.010 Multivariate voxel-based morphometry to map structural characteristics associated with gender differences in schizophrenia

We present a new shape-based approach for regional group activation analysis in fMRI studies. The method restricts anatomical normalization, spatial smoothing and random effects statistical analysis to the space inside and around a structure of interest. Normalization involves finding intersubject correspondences between manually outlined masks, and it leverages the continuous medial representation, which makes it possible to extend surface-based shape correspondences to the space inside and outside of structures. Our approach is an alternative to whole-brain normalization in cases where the latter may fail due to anatomical variability or pathology. It also provides an opportunity to analyze the shape and thickness of structures concurrently with functional activation. We apply the technique to the hippocampus and evaluate it using data from a visual scene encoding fMRI study, where activation in the hippocampus is expected. We produce detailed statistical maps of hippocampal activation, as well as maps comparing activation inside and outside of the hippocampus. We find that random effects statistics computed by the new approach are more significant than those produced using the Statistical Parametric Mapping framework (Friston, K.J., Holmes, A.P., Worsley, K.J., Poline, J.-P., Firth, C.D., Frackowiak, R.S.J. 1994, Statistical parametric maps in functional imaging: a general linear approach. Human Brain Mapping, 2(4): 189–210) at low levels of smoothing, suggesting that greater specificity can be achieved by the new method without a severe tradeoff in sensitivity.

Continuous medial representations for geometric object modeling in 2D and 3D

We describe a novel continuous medial representation for object geometry and a deformable templates method for fitting the representation to images. Our representation simultaneously describes the boundary and medial loci of geometrical objects, always maintaining Blum's symmetric axis transform (SAT) relationship. Cubic b-splines define the continuous medial locus and the associated thickness field, which in turn generate the object boundary. We present geometrical properties of the representation and derive a set of constraints on the b-spline parameters. The 2D representation encompasses branching medial loci; the 3D version can model objects with a single medial surface, and the extension to branching medial surfaces is a subject of ongoing research. We present preliminary results of segmenting 2D and 3D medical images. The representation is ultimately intended for use in statistical shape analysis.