Jorge J. G. Leandro

Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification

We present a method for automated segmentation of the vasculature in retinal images. The method produces segmentations by classifying each image pixel as vessel or nonvessel, based on the pixels feature vector. Feature vectors are composed of the pixels intensity and two-dimensional Gabor wavelet transform responses taken at multiple scales. The Gabor wavelet is capable of tuning to specific frequencies, thus allowing noise filtering and vessel enhancement in a single step. We use a Bayesian classifier with class-conditional probability density functions (likelihoods) described as Gaussian mixtures, yielding a fast classification, while being able to model complex decision surfaces. The probability distributions are estimated based on a training set of labeled pixels obtained from manual segmentations. The methods performance is evaluated on publicly available DRIVE (Staal et al.,2004) and STARE (Hoover et al.,2000) databases of manually labeled images. On the DRIVE database, it achieves an area under the receiver operating characteristic curve of 0.9614, being slightly superior than that presented by state-of-the-art approaches. We are making our implementation available as open source MATLAB scripts for researchers interested in implementation details, evaluation, or development of methods

Automated segmentation of retinal blood vessels and identification of proliferative diabetic retinopathy

Proliferative diabetic retinopathy can lead to blindness. However, early recognition allows appropriate, timely intervention. Fluorescein-labeled retinal blood vessels of 27 digital images were automatically segmented using the Gabor wavelet transform and classified using traditional features such as area, perimeter, and an additional five morphological features based on the derivatives-of-Gaussian wavelet-derived data. Discriminant analysis indicated that traditional features do not detect early proliferative retinopathy. The best single feature for discrimination was the wavelet curvature with an area under the curve (AUC) of 0.76. Linear discriminant analysis with a selection of six features achieved an AUC of 0.90 (0.73-0.97, 95% confidence interval). The wavelet method was able to segment retinal blood vessels and classify the images according to the presence or absence of proliferative retinopathy.

Blood vessels segmentation in retina: preliminary assessment of the mathematical morphology and of the wavelet transform techniques

The article reports on the development of a system for automatic analysis of retinal angiographic images. Particularly, we focus on the segmentation of the blood vessels in these images. We started by implementing a previously known technique based on mathematical morphology. Due to some shortcomings of this method for our data, we have developed a new approach based on the continuous wavelet transform using the Morlet wavelet. The main advantage of the latter with respect to our images lies in its capabilities in tuning to specific frequencies, thus allowing noise filtering and blood vessel enhancement in a single step. Furthermore, as we intend to use shape analysis techniques for the detection and quantitative characterisation of the vascular branching pattern in the retina, the wavelets will also be important with respect to performing fractal and multifractal image analysis. Nevertheless, it is worth mentioning that the mathematical morphology method was able to detect finer detail more precisely. Our present results suggest that an interesting direction to be investigated is how to use both approaches together in order to obtain better results and apply this as a diagnostic tool.

Evolution of Retinal Blood Vessel Segmentation Methodology Using Wavelet Transforms for Assessment of Diabetic Retinopathy

Diabetes is a chronic disease that affects the body’s capacity to regulate the amount of sugar in the blood. One in twenty Australians are affected by diabetes, but this figure is conservative, due to the presence of subclinical diabetes, where the disease is undiagnosed, yet is already damaging the body without manifesting substantial symptoms. This incidence rate is not confined to Australia, but is typical of developed nations, and even higher in developing nations. Excess sugar in the blood results in metabolites that cause vision loss, heart failure and stroke, and damage to peripheral blood vessels.These problems contribute significantly to the morbidity and mortality of the Australian population, so that any improvement in early diagnosis would therefore represent a significant gain. The incidence is projected to rise, and has already become a major epidemic [16].

Blood vessels segmentation in nonmydriatic images using wavelets and statistical classifiers

This work describes a new framework for automatic analysis of optic fundus nonmydriatic images, focusing on the segmentation of the blood vessels by using pixel classification based on pattern recognition techniques. Each pixel is represented by a feature vector composed of color information and measurements at different scales taken from the continuous wavelet (Morlet) transform as well as from mean and order filtering applied to the green channel. The major benefit resulting from the wavelet application to the optic fundus images is its multiscale analysing capability in tuning to specific frequencies, thus allowing noise filtering and blood vessel enhancement in a single step. Supervised classifiers are then applied to label each pixel as either a vessel or a nonvessel. Two different strategies to select the training set have been devised: (1) the blood vessels of a sample image are completely drawn by hand, leading to a labeled image (i.e. vessels /spl times/ nonvessel pixels) which is used to train the classifier, to be applied to other images; (2) the vessels located in a given small portion of the target image are drawn by hand and the remaining fundus image is segmented by a classifier trained using the hand-drawn portion to define the training set. The latter strategy is particularly suitable for the implementation of a semiautomated software to be used by health workers in order to avoid the need of setting imaging parameters such as thresholds. Both strategies have been extensively assessed and several successful experimental results using real-case images have been obtained.

Automatic contour extraction from 2D neuron images.

This work describes a novel methodology for automatic contour extraction from 2D images of 3D neurons (e.g. camera lucida images and other types of 2D microscopy). Most contour-based shape analysis methods cannot be used to characterize such cells because of overlaps between neuronal processes. The proposed framework is specifically aimed at the problem of contour following even in presence of multiple overlaps. First, the input image is preprocessed in order to obtain an 8-connected skeleton with one-pixel-wide branches, as well as a set of critical regions (i.e., bifurcations and crossings). Next, for each subtree, the tracking stage iteratively labels all valid pixel of branches, up to a critical region, where it determines the suitable direction to proceed. Finally, the labeled skeleton segments are followed in order to yield the parametric contour of the neuronal shape under analysis. The reported system was successfully tested with respect to several images and the results from a set of three neuron images are presented here, each pertaining to a different class, i.e. alpha, delta and epsilon ganglion cells, containing a total of 34 crossings. The algorithms successfully got across all these overlaps. The method has also been found to exhibit robustness even for images with close parallel segments. The proposed method is robust and may be implemented in an efficient manner. The introduction of this approach should pave the way for more systematic application of contour-based shape analysis methods in neuronal morphology.

Exploring wavelet transforms for morphological differentiation between functionally different cat retinal ganglion cells

Cognition or higher brain activity is sometimes seen as a phenomenon greater than the sum of its parts. This viewpoint however is largely dependent on the state of the art of experimental techniques that endeavor to characterize morphology and its association to function. Retinal ganglion cells are readily accessible for this work and we discuss recent advances in computational techniques in identifying novel parameters that describe structural attributes possibly associated with specific function. These parameters are based on calculating wavelet gradients from cell images followed by the extraction of meaningful measures including 2nd wavelet moment, entropy of orientation, and curvature. For the three cell types analyzed, the mean 2nd wavelet moment, which relates to the field of influence of the dendritic-tree segments was significantly different. β cells had the highest mean 2nd wavelet moment, followed by the α and δ cells (134 ± 22, 93 ± 19 and 63 ± 12, respectively). There was no significant difference between cells for entropy of orientation, indicating no class with a preferential orientation of their dendritic tree. Curvature provided similar results to the 2nd wavelet moment with β cells having the highest curvature followed by α and the δ cells (mean ± SD: 161 ± 15; 134 ± 22; 121 ± 15). Our feature space analysis also indicated a difference between these cell types. No difference was found between the α and β cell types and their physiological counterparts the Y and X cells based on wavelet analysis. Both the X and Y cells can be divided into two subtypes, the ON- and OFF-center cells based on the stratification level of the dendritic tree within the retina. Using 2nd wavelet moment, a difference in their morphological attributes, not reported previously, was noted for these subtypes. The 2nd wavelet moment and curvature are further discussed with respect to explaining regularity of spacing and coverage associated with retinal ganglion cell mosaics.

AUTOMATED MORPHOMETRIC ANALYSIS OF THE CAT RETINAL α/Y, β/X AND δ GANGLION CELLS USING WAVELET STATISTICAL MOMENT AND CLUSTERING ALGORITHMS

Computational morphological analysis comprises the development of measures (indicators) that describe different form attributes of a neuron and provides additional parameters for classification algorithms. Our work addressed the problem of small group sizes often encountered in neuromorphological and neurophysiological research, automated classification tasks (unsupervised learning) and introduced a new morphological measure: the wavelet statistical moment. We analysed cat α/Y, β/X and δ Golgi-stained retinal ganglion cells using six different shape features (circularity, 2nd statistical moment and entropy of Gaussian blurred images, wavelet statistical moment, number of terminations and the fractal dimension). This allowed us to compare the sensitivity of the methods in uniquely describing morphological attributes of these cells.

Shape Analysis Using the Spectral Graph Wavelet Transform

The present work describes a framework for morphological characterization of galaxies based on the Spectral Graph Wavelet Transform. A galaxy image is sampled with a number of points randomly chosen, whose Delaunay triangulation results in an arbitrary graph. The average intensity value in a 5 × 5 vicinity of a pixel related to a graph vertex is assigned to the corresponding graph vertex. A weight inversely proportional to the photometric distance between each pair of vertices is assigned to the respective graph edge. The Spectral Graph Wavelet Transform is computed from this weighted graph with real-valued vertices yielding a high-dimensional feature vector, which is reduced to a two dimensional vector through Principal Component Analysis. The proposed framework has been assessed through two case studies, namely, the case study of analyzing (i) 2D binary images from shapes and preliminary results of (ii) 2D gray tone images from galaxies. The obtained results imply the suitability of this framework for the characterization of galaxies images.

Automated Spatial Pattern Analysis for Identification of Foot Arch Height From 2D Foot Prints

Arch height is an important determinant for the risk of foot pathology, especially in an aging population. Current methods for analyzing footprints require substantial manual processing time. The current research investigated automated determination of foot type based on features derived from the Gabor wavelet utilizing digitized footprints to allow timely assessment of foot type and focused intervention. Two hundred and eighty footprints were collected, and area, perimeter, curvature, circularity, 2nd wavelet moment, mean bending energy (MBE), and entropy were determined using in house developed MATLAB codes. The results were compared to the gold standard using Spearman’s Correlation coefficient and multiple linear regression models with significance set at 0.05. The proposed approach found MBE combined with foot perimeter to give the best results as shown by ANOVA (F(2,211) = 10.18, p < 0.0001) with the mean ±SD of low, normal, and high arch being, respectively, 0.26 ± 0.025,.24 ± 0.021, and 0.23 ± 0.024. A clinical review of the new cut off values, as set by the first and the third quartiles of our sample, lead to reliability up to 87%. Our results suggest that automated wavelet-based foot type classification of 2D binary images of the plantar surface of the foot is comparable to current state-of-the-art methods providing a cost and time effective tool suitable for clinical diagnostics.