Multiscale analysis of tortuosity in retinal images using wavelets and fractal methods

Slope Chain Code-based scale-independent tortuosity measurement on retinal vessels

Retinal vascular tortuosity presents valuable potential as a clinical biomarker for many relevant vascular and systemic diseases. Our work exhibits twofold: first, the definition of a novel scale-invariant metric to measure retinal blood vessel tortuosity; and second, the generation of a local database, called SCALE-TORT, with the intention of providing a means to test the scale invariance property on real retinal vessels rather than on synthetic data. The proposed scale invariant tortuosity metric is based on the Extended Slope Chain Code which uses variable straight-line segments for describing curves. It is focused on the representation of high-definition curves, the length of the segments is a function of the slope changes of the curve. Scale invariance is an important property when several different retinal image settings or different acquisition sources are used during a particular study or in clinical practice. The database SCALE-TORT, introduced herein, was built semi-automatically from digital images containing the coordinates of blood vessel central lines (curves) taken from images of the same eye obtained by two different imaging methodologies: retinal fundus camera and scanning laser ophthalmoscope. The vessel curves extracted from the same eye are paired for images acquired by the fundus camera and those acquired by the scanning laser ophthalmoscope to evaluate the scale invariance of the metric. Ten different tortuosity metrics were implemented and compared including our proposed metric. Three experiments were conducted to test the metrics and their properties. The first aimed to determine which tortuosity metrics possess the following properties: scale invariance, sensitivity to sudden tortuosity changes when the curve remains constant in size, and how they behave when curves are concatenated. In the second experiment, all reviewed metrics were tested on the publicly available RET-TORT database, to compare the results of the specific metric with the tortuosity classification provided by their experts and in comparison with other authors. Finally, in the third experiment, the behavior of different metrics, including those which are scale-invariant, were tested by utilizing the paired retinal vessel curves from our new SCALE-TORT database. In comparison with other tortuosity metrics, we show that the metric Extended Slope Chain Code proposed in this work optimally complies with scale invariance, in addition to having sufficient sensitivity to detect abrupt changes in tortuosity. Easy implementation being a further plus. Furthermore, we present a new and valuable database for scale property evaluation on images of retinal blood vessels called SCALE-TORT. As far as we are aware, there is no public database with these characteristics.

Four Severity Levels for Grading the Tortuosity of a Retinal Fundus Image

Hypertensive retinopathy severity classification is proportionally related to tortuosity severity grading. No tortuosity severity scale enables a computer-aided system to classify the tortuosity severity of a retinal image. This work aimed to introduce a machine learning model that can identify the severity of a retinal image automatically and hence contribute to developing a hypertensive retinopathy or diabetic retinopathy automated grading system. First, the tortuosity is quantified using fourteen tortuosity measurement formulas for the retinal images of the AV-Classification dataset to create the tortuosity feature set. Secondly, a manual labeling is performed and reviewed by two ophthalmologists to construct a tortuosity severity ground truth grading for each image in the AV classification dataset. Finally, the feature set is used to train and validate the machine learning models (J48 decision tree, ensemble rotation forest, and distributed random forest). The best performance learned model is used as the tortuosity severity classifier to identify the tortuosity severity (normal, mild, moderate, and severe) for any given retinal image. The distributed random forest model has reported the highest accuracy (99.4%) compared to the J48 Decision tree model and the rotation forest model with minimal least root mean square error (0.0000192) and the least mean average error (0.0000182). The proposed tortuosity severity grading matched the ophthalmologist’s judgment. Moreover, detecting the tortuosity severity of the retinal vessels’, optimizing vessel segmentation, the vessel segment extraction, and the created feature set have increased the accuracy of the automatic tortuosity severity detection model.

Multifractal-based lacunarity analysis of trabecular bone in radiography

This study presents textural characterization techniques for effective osteoporosis diagnosis using bone radiograph images. The automatic classification of osteoporosis and healthy (control) cases using bone radiograph images in this work presents a major challenge as the images show no visual differences for both cases. The proposed work utilizes multifractals to characterize the trabecular bone texture in the radiographs. Initially, Holder exponents are computed, then Hausdorff dimensions are determined, which quantify the global regularity of the pixels. Finally, lacunarity is computed from the Hausdorff dimensions. Performance metrics show that estimating lacunarity from the Hausdorff dimensions, rather than the input image, directly helps in achieving better textural characterization of bone radiographs, leading to better performance in osteoporosis classification. The proposed lacunarity-based trabecular bone textural characterization method is compared with other multifractal-based methods for trabecular bone textural characterization, such as box-counting and regularization dimensions. The proposed method is also evaluated with the textural characterization of a bone radiograph challenge dataset to demonstrate its effectiveness compared to the other methods used in the challenge.

Pyramidal fractal dimension for high resolution images

Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images.