Medical Image Segmentation Using Multifractal Analysis

Image segmentation plays a key role in image analysis processes. The operations performed on a segmented image tend to affect it differently than if they were performed on the original image; therefore, segmenting an image can show radically different results from the original image and successfully doing so can yield features and other important information about the image. Proper image analysis is of high importance to the medical community as accurately classifying different conditions and diseases can be facilitated with excellent patient imaging. Multifractal analysis can be leveraged for performing texture classification and image segmentation. In this paper, we propose fusion-based algorithms utilizing multifractal analysis for medical image segmentation. We use two specific multifractal masks: square and quincunx. Our techniques show new insights by using methods such as histogram decomposition in conjunction with new techniques, such as fusion. By fusing different slope images, we can extract more features thus making our proposed algorithms more robust and accurate than traditional multifractal analysis techniques. These methods are further capable of reliably segmenting medical images by implementing multifractal analysis techniques in coordination with methods such as gaussian blurring and morphological operations. The resulting image can then be easily analyzed by medical professionals for diagnosing medical conditions. The outcomes show that the proposed algorithms extract dominant features that are more encompassing and powerful than classical techniques

A multifractal approach to space-filling recovery for PET quantification.

Purpose: A new image-based methodology is developed for estimating the apparent space-filling properties of an object of interest in PET imaging without need for a robust segmentation step and used to recover accurate estimates of total lesion activity (TLA). Methods: A multifractal approach and the fractal dimension are proposed to recover the apparent space-filling index of a lesion (tumor volume, TV) embedded in nonzero background. A practical implementation is proposed, and the index is subsequently used with mean standardized uptake value (SUVmean) to correct TLA estimates obtained from approximate lesion contours. The methodology is illustrated on fractal and synthetic objects contaminated by partial volume effects (PVEs), validated on realistic 18F-fluorodeoxyglucose PET simulations and tested for its robustness using a clinical 18F-fluorothymidine PET test-retest dataset. Results: TLA estimates were stable for a range of resolutions typical in PET oncology (4-6 mm). By contrast, the space-filling index and intensity estimates were resolution dependent. TLA was generally recovered within 15% of ground truth on postfiltered PET images affected by PVEs. Volumes were recovered within 15% variability in the repeatability study. Results indicated that TLA is a more robust index than other traditional metrics such as SUVmean or TV measurements across imaging protocols. Conclusions: The fractal procedure reported here is proposed as a simple and effective computational alternative to existing methodologies which require the incorporation of image preprocessing steps (i.e., partial volume correction and automatic segmentation) prior to quantification

Classification of pathology in diabetic eye disease

Proliferative diabetic retinopathy is a complication of diabetes that can eventually lead to blindness. Early identification of this complication reduces the risk of blindness by initiating timely treatment. We report the utility of pattern analysis tools linked with a simple linear discriminant analysis that not only identifies new vessel growth in the retinal fundus but also localises the area of pathology. Ten fluorescein images were analysed using seven feature descriptors including area, perimeter, circularity, curvature, entropy, wavelet second moment and the correlation dimension. Our results indicate that traditional features such as area or perimeter measures of neovascularisation associated with proliferative retinopathy were not sensitive enough to detect early proliferative retinopathy (SNR = 0.76, 0.75 respectively). The wavelet second moment provided the best discrimination with a SNR of 1.17. Combining second moment, curvature and global correlation dimension provided a 100% discrimination (SNR = 1)

Computer-aided detection and diagnosis of breast cancer in 2D and 3D medical imaging through multifractal analysis

This Thesis describes the research work performed in the scope of a doctoral research program and presents its conclusions and contributions. The research activities were carried on in the industry with Siemens S.A. Healthcare Sector, in integration with a research team. Siemens S.A. Healthcare Sector is one of the world biggest suppliers of products, services and complete solutions in the medical sector. The company offers a wide selection of diagnostic and therapeutic equipment and information systems. Siemens products for medical imaging and in vivo diagnostics include: ultrasound, computer tomography, mammography, digital breast tomosynthesis, magnetic resonance, equipment to angiography and coronary angiography, nuclear imaging, and many others. Siemens has a vast experience in Healthcare and at the beginning of this project it was strategically interested in solutions to improve the detection of Breast Cancer, to increase its competitiveness in the sector. The company owns several patents related with self-similarity analysis, which formed the background of this Thesis. Furthermore, Siemens intended to explore commercially the computer- aided automatic detection and diagnosis eld for portfolio integration. Therefore, with the high knowledge acquired by University of Beira Interior in this area together with this Thesis, will allow Siemens to apply the most recent scienti c progress in the detection of the breast cancer, and it is foreseeable that together we can develop a new technology with high potential. The project resulted in the submission of two invention disclosures for evaluation in Siemens A.G., two articles published in peer-reviewed journals indexed in ISI Science Citation Index, two other articles submitted in peer-reviewed journals, and several international conference papers. This work on computer-aided-diagnosis in breast led to innovative software and novel processes of research and development, for which the project received the Siemens Innovation Award in 2012. It was very rewarding to carry on such technological and innovative project in a socially sensitive area as Breast Cancer.No cancro da mama a deteção precoce e o diagnóstico correto são de extrema importância na prescrição terapêutica e caz e e ciente, que potencie o aumento da taxa de sobrevivência à doença. A teoria multifractal foi inicialmente introduzida no contexto da análise de sinal e a sua utilidade foi demonstrada na descrição de comportamentos siológicos de bio-sinais e até na deteção e predição de patologias. Nesta Tese, três métodos multifractais foram estendidos para imagens bi-dimensionais (2D) e comparados na deteção de microcalci cações em mamogramas. Um destes métodos foi também adaptado para a classi cação de massas da mama, em cortes transversais 2D obtidos por ressonância magnética (RM) de mama, em grupos de massas provavelmente benignas e com suspeição de malignidade. Um novo método de análise multifractal usando a lacunaridade tri-dimensional (3D) foi proposto para classi cação de massas da mama em imagens volumétricas 3D de RM de mama. A análise multifractal revelou diferenças na complexidade subjacente às localizações das microcalci cações em relação aos tecidos normais, permitindo uma boa exatidão da sua deteção em mamogramas. Adicionalmente, foram extraídas por análise multifractal características dos tecidos que permitiram identi car os casos tipicamente recomendados para biópsia em imagens 2D de RM de mama. A análise multifractal 3D foi e caz na classi cação de lesões mamárias benignas e malignas em imagens 3D de RM de mama. Este método foi mais exato para esta classi cação do que o método 2D ou o método padrão de análise de contraste cinético tumoral. Em conclusão, a análise multifractal fornece informação útil para deteção auxiliada por computador em mamogra a e diagnóstico auxiliado por computador em imagens 2D e 3D de RM de mama, tendo o potencial de complementar a interpretação dos radiologistas

The fractal heart — embracing mathematics in the cardiology clinic

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care

Fractal-based analysis of optical coherence tomography data to quantify retinal tissue damage

BACKGROUND: The sensitivity of Optical Coherence Tomography (OCT) images to identify retinal tissue morphology characterized by early neural loss from normal healthy eyes is tested by calculating structural information and fractal dimension. OCT data from 74 healthy eyes and 43 eyes with type 1 diabetes mellitus with mild diabetic retinopathy (MDR) on biomicroscopy was analyzed using a custom-built algorithm (OCTRIMA) to measure locally the intraretinal layer thickness. A power spectrum method was used to calculate the fractal dimension in intraretinal regions of interest identified in the images. ANOVA followed by Newman-Keuls post-hoc analyses were used to test for differences between pathological and normal groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of each parameter to discriminate between eyes of pathological patients and normal healthy eyes. RESULTS: Fractal dimension was higher for all the layers (except the GCL + IPL and INL) in MDR eyes compared to normal healthy eyes. When comparing MDR with normal healthy eyes, the highest AUROC values estimated for the fractal dimension were observed for GCL + IPL and INL. The maximum discrimination value for fractal dimension of 0.96 (standard error =0.025) for the GCL + IPL complex was obtained at a FD <= 1.66 (cut off point, asymptotic 95% Confidence Interval: lower-upper bound = 0.905-1.002). Moreover, the highest AUROC values estimated for the thickness measurements were observed for the OPL, GCL + IPL and OS. Particularly, when comparing MDR eyes with control healthy eyes, we found that the fractal dimension of the GCL + IPL complex was significantly better at diagnosing early DR, compared to the standard thickness measurement. CONCLUSIONS: Our results suggest that the GCL + IPL complex, OPL and OS are more susceptible to initial damage when comparing MDR with control healthy eyes. Fractal analysis provided a better sensitivity, offering a potential diagnostic predictor for detecting early neurodegeneration in the retina

Exploration of the Relationship Between the Fractal Dimension of Microcalcification Clusters and the Hurst Exponent of Background Tissue Disruption in Mammograms

Breast cancer is one of the most frequent cancers among women worldwide and holds the second place in cancer-related death. Mammography is the most commonly used screening technique, however, the dense nature of some breasts makes the analysis of mammograms challenging for radiologists. The 2D Wavelet Transform Modulus Maxima (WTMM) is one mathematical approach that is used to for the analysis of mammograms. In 2014, a team from the CompuMAINE Lab characterized differences between benign microcalcification clusters (MC) from malignant MC by calculating their fractal dimension, D, with the aid of the 2D WTMM method. In a different implementation of the 2D WTMM method, this same team did research in 2017 where they quantified tissue disruption in breast tissue microenvironment using the Hurst exponent, H. The goal of this study was to further explore the potential relationship between the fractality of MC clusters and tissue disruption in the microenvironment surrounding these clusters. Statistical relationships are explored between the fractal dimension, D, of MC clusters and the Hurst exponent, H measuring tissue disruption. A “2D fractal dimension vs. Hurst exponent plot” was graphed to show this relationship used to distinguish between benign and malignant cases. In the graph, a quadrilateral region extending horizontally from Hurst value of (0.2,0.8) centered at 0.5 and stretching vertically from fractal dimension value of (1.2,1.8) centered 1.5 was identified. Analysis of this region has showed that the 60% of the malignant cases and 21% benign cases are found inside the quadrilateral for CC view and 68% of the malignant cases and 12% of benign cases are found inside the region for MLO view. As a conclusion, based on the outcomes of this study one can hypothesize that with further analyses, loss of tissue homeostasis describing the state of the microenvironment of a breast tissue and the fractal nature of MC clusters have a quantifiable relationship to distinguish benign cases from malignant cases in mammogram analysis

Provably scale-covariant networks from oriented quasi quadrature measures in cascade

This article presents a continuous model for hierarchical networks based on a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed and it is shown that the resulting representation allows for provable scale and rotation covariance. A prototype application to texture analysis is developed and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.Comment: 12 pages, 3 figures, 1 tabl