Dendritic spine shape analysis using disjunctive normal shape models

Analysis of dendritic spines is an essential task to understand the functional behavior of neurons. Their shape variations are known to be closely linked with neuronal activities. Spine shape analysis in particular, can assist neuroscientists to identify this relationship. A novel shape representation has been proposed recently, called Disjunctive Normal Shape Models (DNSM). DNSM is a parametric shape representation and has proven to be successful in several segmentation problems. In this paper, we apply this parametric shape representation as a feature extraction algorithm. Further, we propose a kernel density estimation (KDE) based classification approach for dendritic spine classification. We evaluate our proposed approach on a data set of 242 spines, and observe that it outperforms the classical morphological feature based approach for spine classification. Our probabilistic framework also provides a way to examine the separability of spine shape classes in the likelihood ratio space, which leads to further insights about the nature of the shape analysis problem in this context

Morphological analysis of cells by means of an elastic metric in the shape space

Shape analysis is of great importance in many fields, such as computer vision, medical imaging, and computational biology. This analysis can be performed considering shapes as closed planar curves in the shape space. This approach has been used for the first time to obtain the morphological classification of erythrocytes in digital images of sickle cell disease considering the shape space S1, which has the property of being isometric to an infinite-dimensional Grassmann manifold of two-dimensional subspaces (Younes et al., 2008), without taking advantage of all the features offered by the elastic metric related to the possibility of stretching and bending of the curves. In this paper, we study this deformation in the shape space, S2, which is based on the representation of closed planar curves by means of the square-root velocity function (SRVF) (Srivastava et al., 2011), using the elastic metric of this space to obtain more efficient geodesics and geodesic lengths between planar curves. Supervised classification with this approach achieved an accuracy of 94.3%, classification using templates achieved 94.2% and unsupervised clustering in three groups achieved 94.7%, considering three classes of erythrocytes: normal, sickle, and with other deformations. These results are better than those previously achieved in the morphological analysis of erythrocytes and the method can be used in different applications related to the treatment of sickle cell disease, even in cases where it is necessary to study the process of evolution of the deformation, something that can not be done in a natural way in the feature space

Image morphological processing

Mathematical Morphology with applications in image processing and analysis has been becoming increasingly important in today\u27s technology. Mathematical Morphological operations, which are based on set theory, can extract object features by suitably shaped structuring elements. Mathematical Morphological filters are combinations of morphological operations that transform an image into a quantitative description of its geometrical structure based on structuring elements. Important applications of morphological operations are shape description, shape recognition, nonlinear filtering, industrial parts inspection, and medical image processing. In this dissertation, basic morphological operations, properties and fuzzy morphology are reviewed. Existing techniques for solving corner and edge detection are presented. A new approach to solve corner detection using regulated mathematical morphology is presented and is shown that it is more efficient in binary images than the existing mathematical morphology based asymmetric closing for corner detection. A new class of morphological operations called sweep mathematical morphological operations is developed. The theoretical framework for representation, computation and analysis of sweep morphology is presented. The basic sweep morphological operations, sweep dilation and sweep erosion, are defined and their properties are studied. It is shown that considering only the boundaries and performing operations on the boundaries can substantially reduce the computation. Various applications of this new class of morphological operations are discussed, including the blending of swept surfaces with deformations, image enhancement, edge linking and shortest path planning for rotating objects. Sweep mathematical morphology is an efficient tool for geometric modeling and representation. The sweep dilation/erosion provides a natural representation of sweep motion in the manufacturing processes. A set of grammatical rules that govern the generation of objects belonging to the same group are defined. Earley\u27s parser serves in the screening process to determine whether a pattern is a part of the language. Finally, summary and future research of this dissertation are provided

ECG Beat Representation and Delineation by Means of Variable Projection

Objective: The electrocardiogram (ECG) follows a characteristic shape, which has led to the development of several mathematical models for extracting clinically important information. Our main objective is to resolve limitations of previous approaches, that means to simultaneously cope with various noise sources, perform exact beat segmentation, and to retain diagnostically important morphological information. Methods: We therefore propose a model that is based on Hermite and sigmoid functions combined with piecewise polynomial interpolation for exact segmentation and low-dimensional representation of individual ECG beat segments. Hermite and sigmoidal functions enable reliable extraction of important ECG waveform information while the piecewise polynomial interpolation captures noisy signal features like the baseline wander (BLW). For that we use variable projection, which allows the separation of linear and nonlinear morphological variations of the according ECG waveforms. The resulting ECG model simultaneously performs BLW cancellation, beat segmentation, and low-dimensional waveform representation. Results: We demonstrate its BLW denoising and segmentation performance in two experiments, using synthetic and real data. Compared to state-of-the-art algorithms, the experiments showed less diagnostic distortion in case of denoising and a more robust delineation for the P and T wave. Conclusion: This work suggests a novel concept for ECG beat representation, easily adaptable to other biomedical signals with similar shape characteristics, such as blood pressure and evoked potentials. Significance: Our method is able to capture linear and nonlinear wave shape changes. Therefore, it provides a novel methodology to understand the origin of morphological variations caused, for instance, by respiration, medication, and abnormalities

A Mathematical Morphology Approach to Cell Shape Analysis

This contribution aims to apply mathematical morphology operators to quantify the shape of round-objects which present irregularities from an ideal circular pattern. More specifically we illustrate, on the one hand, the application of morphological granulometries for size/shape multi-scale description and on the other hand, the radial/angular decompo- sitions using skeletons in polar-logarithmic representation. We discuss also the aspects related to the properties of invariance of these tools, which is important to describe cell shapes acquired under different magnifications, orientations, etc

Measuring the magnitude of morphological integration: The effect of differences in morphometric representations and the inclusion of size

The magnitude of morphological integration is a major aspect of multivariate evolution, providing a simple measure of the intensity of association between morphological traits. Studies concerned with morphological integration usually translate phenotypes into morphometric representations to quantify how different morphological elements covary. Geometric and classic morphometric representations translate biological form in different ways, raising the question if magnitudes of morphological integration estimates obtained from different morphometric representations are compatible. Here we sought to answer this question using the relative eigenvalue variance of the covariance matrix obtained for both geometric and classical representations of empirical and simulated datasets. We quantified the magnitude of morphological integration for both shape and form and compared results between representations. Furthermore, we compared integration values between shape and form to evaluate the effect of the inclusion or not of size on the quantification of the magnitude of morphological integration. Results show that the choice of morphological representation has significant impact on the integration magnitude estimate, either for shape or form. Despite this, ordination of the integration values within representations is relatively the same, allowing for similar conclusions to be reached using different methods. However, the inclusion of size in the dataset significantly changes the estimates of magnitude of morphological integration, hindering the comparison of this statistic obtained from different spaces. Morphometricians should be aware of these differences and must consider how biological hypothesis translate into predictions about integration in each particular choice of representation.Fil: de Andrade Machado, Fabio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; Argentina. University of Massachussets; Estados UnidosFil: Hubbe, Alex. Universidade Federal da Bahia; BrasilFil: Melo, Diogo. Universidade de Sao Paulo; BrasilFil: Porto, Arthur. University of Oslo; NoruegaFil: Marroig, Gabriel. Universidade de Sao Paulo; Brasi

Dendritic Spine Shape Analysis: A Clustering Perspective

Functional properties of neurons are strongly coupled with their morphology. Changes in neuronal activity alter morphological characteristics of dendritic spines. First step towards understanding the structure-function relationship is to group spines into main spine classes reported in the literature. Shape analysis of dendritic spines can help neuroscientists understand the underlying relationships. Due to unavailability of reliable automated tools, this analysis is currently performed manually which is a time-intensive and subjective task. Several studies on spine shape classification have been reported in the literature, however, there is an on-going debate on whether distinct spine shape classes exist or whether spines should be modeled through a continuum of shape variations. Another challenge is the subjectivity and bias that is introduced due to the supervised nature of classification approaches. In this paper, we aim to address these issues by presenting a clustering perspective. In this context, clustering may serve both confirmation of known patterns and discovery of new ones. We perform cluster analysis on two-photon microscopic images of spines using morphological, shape, and appearance based features and gain insights into the spine shape analysis problem. We use histogram of oriented gradients (HOG), disjunctive normal shape models (DNSM), morphological features, and intensity profile based features for cluster analysis. We use x-means to perform cluster analysis that selects the number of clusters automatically using the Bayesian information criterion (BIC). For all features, this analysis produces 4 clusters and we observe the formation of at least one cluster consisting of spines which are difficult to be assigned to a known class. This observation supports the argument of intermediate shape types.Comment: Accepted for BioImageComputing workshop at ECCV 201