A semi-supervised multiview-MRI network for the detection of Knee Osteoarthritis.

Knee OsteoArthritis (OA) is a prevalent chronic condition, affecting a significant proportion of the global population. Detecting knee OA is crucial as the degeneration of the knee joint is irreversible. In this paper, we introduce a semi-supervised multi-view framework and a 3D CNN model for detecting knee OA using 3D Magnetic Resonance Imaging (MRI) scans. We introduce a semi-supervised learning approach combining labeled and unlabeled data to improve the performance and generalizability of the proposed model. Experimental results show the efficacy of our proposed approach in detecting knee OA from 3D MRI scans using a large cohort of 4297 subjects. An ablation study was conducted to investigate the contributions of various components of the proposed model, providing insights into the optimal design of the model. Our results indicate the potential of the proposed approach to improve the accuracy and efficiency of OA diagnosis. The proposed framework reported an AUC of 93.20% for the detection of knee OA.

A highly generalized classifier for osteoporosis radiography based on multiscale fractal, lacunarity, and entropy distributions.

Background: Osteoporosis is a common degenerative disease with high incidence among aging populations. However, in regular radiographic diagnostics, asymptomatic osteoporosis is often overlooked and does not include tests for bone mineral density or bone trabecular condition. Therefore, we proposed a highly generalized classifier for osteoporosis radiography based on the multiscale fractal, lacunarity, and entropy distributions. Methods: We collected a total of 104 radiographs (92 for training and 12 for testing) of lumbar spine L4 and divided them into three groups (normal, osteopenia, and osteoporosis). In parallel, 174 radiographs (116 for training and 58 for testing) of calcaneus from health and osteoporotic fracture groups were collected. The texture feature data of all the radiographs were pulled out and analyzed. The Davies-Bouldin index was applied to optimize hyperparameters of feature counting. Neighborhood component analysis was performed to reduce feature dimension and increase generalization. A support vector machine classifier was trained with only the most effective six features for each binary classification scenario. The accuracy and sensitivity performance were estimated by calculating the area under the curve. Results: Interpretable feature trends of osteoporotic pathological changes were depicted. On the spine test dataset, the accuracy and sensitivity of binary classifiers were 0.851 (95% CI: 0.730-0.922), 0.813 (95% CI: 0.718-0.878), and 0.936 (95% CI: 0.826-1) for osteoporosis diagnosis; 0.721 (95% CI: 0.578-0.824), 0.675 (95% CI: 0.563-0.772), and 0.774 (95% CI: 0.635-0.878) for osteopenia diagnosis; and 0.935 (95% CI: 0.830-0.968), 0.928 (95% CI: 0.863-0.963), and 0.910 (95% CI: 0.746-1) for osteoporosis diagnosis from osteopenia. On the calcaneus test dataset, they were 0.767 (95% CI: 0.629-0.879), 0.672 (95% CI: 0.545-0.793), and 0.790 (95% CI: 0.621-0.923) for osteoporosis diagnosis. Conclusion: This method showed the capacity of resisting disturbance on lateral spine radiographs and high generalization on the calcaneus dataset. Pixel-wise texture features not only helped to understand osteoporosis on radiographs better but also shed new light on computer-aided osteopenia and osteoporosis diagnosis.

A discriminative shape-texture convolutional neural network for early diagnosis of knee osteoarthritis from X-ray images.

Knee Osteoarthritis (OA) is one of the most common causes of physical disability worldwide associated with a significant personal and socioeconomic burden. Deep Learning approaches based on Convolutional Neural Networks (CNNs) achieved remarkable improvements in knee OA detection. Despite this success, the problem of early knee OA diagnosis from plain radiographs remains a challenging task. This is due to the high similarity between the X-ray images of OA and non-OA subjects and the disappearance of texture information regarding bone microarchitecture changes in the top layers during the learning process of the CNN models. To address these issues, we propose a Discriminative Shape-Texture Convolutional Neural Network (DST-CNN), which automatically diagnoses early knee OA from X-ray images. The proposed model incorporates a discriminative loss to improve class separability and deal with high inter-class similarities. In addition, a new Gram Matrix Descriptor (GMD) block is embedded in the CNN architecture to compute texture features from several intermediate layers and combine them with the shape features in the top layers. We show that merging texture features with deep ones leads to better prediction of the early stages of OA. Comprehensive experimental results on two large public databases, Osteoarthritis Initiative (OAI) and Multicenter Osteoarthritis Study (MOST) demonstrate the potential of the proposed network. Ablation studies and visualizations are provided for a detailed understanding of our proposed approach.

Prediction of knee osteoarthritis progression using radiological descriptors obtained from bone texture analysis and Siamese neural networks: data from OAI and MOST cohorts.

BACKGROUND: Trabecular bone texture (TBT) analysis has been identified as an imaging biomarker that provides information on trabecular bone changes due to knee osteoarthritis (KOA). In parallel with the improvement in medical imaging technologies, machine learning methods have received growing interest in the scientific osteoarthritis community to potentially provide clinicians with prognostic data from conventional knee X-ray datasets, in particular from the Osteoarthritis Initiative (OAI) and the Multicenter Osteoarthritis Study (MOST) cohorts. PATIENTS AND METHODS: This study included 1888 patients from OAI and 683 patients from MOST cohorts. Radiographs were automatically segmented to determine 16 regions of interest. Patients with an early stage of OA risk, with Kellgren and Lawrence (KL) grade of 1 < KL < 4, were selected. The definition of OA progression was an increase in the OARSI medial joint space narrowing (mJSN) grades over 48 months in OAI and 60 months in MOST. The performance of the TBT-CNN model was evaluated and compared to well-known prediction models using logistic regression. RESULTS: The TBT-CNN model was predictive of the JSN progression with an area under the curve (AUC) up to 0.75 in OAI and 0.81 in MOST. The predictive ability of the TBT-CNN model was invariant with respect to the acquisition modality or image quality. The prediction models performed significantly better with estimated KL (KLprob) grades than those provided by radiologists. TBT-based models significantly outperformed KLprob-based models in MOST and provided similar performances in OAI. In addition, the combined model, when trained in one cohort, was able to predict OA progression in the other cohort. CONCLUSION: The proposed combined model provides a good performance in the prediction of mJSN over 4 to 6 years in patients with relevant KOA. Furthermore, the current study presents an important contribution in showing that TBT-based OA prediction models can work with different databases.

Trabecular bone texture analysis of conventional radiographs in the assessment of knee osteoarthritis: review and viewpoint.

BACKGROUND: Trabecular bone texture analysis (TBTA) has been identified as an imaging biomarker that provides information on trabecular bone changes due to knee osteoarthritis (KOA). Consequently, it is important to conduct a comprehensive review that would permit a better understanding of this unfamiliar image analysis technique in the area of KOA research. We examined how TBTA, conducted on knee radiographs, is associated to (i) KOA incidence and progression, (ii) total knee arthroplasty, and (iii) KOA treatment responses. The primary aims of this study are twofold: to provide (i) a narrative review of the studies conducted on radiographic KOA using TBTA, and (ii) a viewpoint on future research priorities. METHOD: Literature searches were performed in the PubMed electronic database. Studies published between June 1991 and March 2020 and related to traditional and fractal image analysis of trabecular bone texture (TBT) on knee radiographs were identified. RESULTS: The search resulted in 219 papers. After title and abstract scanning, 39 studies were found eligible and then classified in accordance to six criteria: cross-sectional evaluation of osteoarthritis and non-osteoarthritis knees, understanding of bone microarchitecture, prediction of KOA progression, KOA incidence, and total knee arthroplasty and association with treatment response. Numerous studies have reported the relevance of TBTA as a potential bioimaging marker in the prediction of KOA incidence and progression. However, only a few studies have focused on the association of TBTA with both OA treatment responses and the prediction of knee joint replacement. CONCLUSION: Clear evidence of biological plausibility for TBTA in KOA is already established. The review confirms the consistent association between TBT and important KOA endpoints such as KOA radiographic incidence and progression. TBTA could provide markers for enrichment of clinical trials enhancing the screening of KOA progressors. Major advances were made towards a fully automated assessment of KOA.

Integrative blockwise sparse analysis for tissue characterization and classification.

The topic of sparse representation of samples in high dimensional spaces has attracted growing interest during the past decade. In this work, we develop sparse representation-based methods for classification of clinical imaging patterns into healthy and diseased states. We propose a spatial block decomposition method to address irregularities of the approximation problem and to build an ensemble of classifiers that we expect to yield more accurate numerical solutions than conventional sparse analyses of the complete spatial domain of the images. We introduce two classification decision strategies based on maximum a posteriori probability (BBMAP), or a log likelihood function (BBLL) and an approach to adjusting the classification decision criteria. To evaluate the performance of the proposed approach we used cross-validation techniques on imaging datasets with disease class labels. We first applied the proposed approach to diagnosis of osteoporosis using bone radiographs. In this problem we assume that changes in trabecular bone connectivity can be captured by intensity patterns. The second application domain is separation of breast lesions into benign and malignant categories in mammograms. The object classes in both of these applications are not linearly separable, and the classification accuracy may depend on the lesion size in the second application. Our results indicate that the proposed integrative sparse analysis addresses the ill-posedness of the approximation problem and produces very good class separation for trabecular bone characterization and for breast lesion characterization. Our approach yields higher classification rates than conventional sparse classification and previously published convolutional neural networks (CNNs) that we fine-tuned for our datasets, or utilized for feature extraction. The BBLL technique also produced higher classification rates than learners using hand-crafted texture features, and the Bag of Keypoints, which is a sophisticated patch-based method. Furthermore, our comparative experiments showed that the BBLL function may yield more accurate classification than BBMAP, because BBLL accounts for possible estimation bias.

Discriminative Regularized Auto-Encoder for Early Detection of Knee OsteoArthritis: Data from the Osteoarthritis Initiative.

OsteoArthritis (OA) is the most common disorder of the musculoskeletal system and the major cause of reduced mobility among seniors. The visual evaluation of OA still suffers from subjectivity. Recently, Computer-Aided Diagnosis (CAD) systems based on learning methods showed potential for improving knee OA diagnostic accuracy. However, learning discriminative properties can be a challenging task, particularly when dealing with complex data such as X-ray images, typically used for knee OA diagnosis. In this paper, we introduce a Discriminative Regularized Auto Encoder (DRAE) that allows to learn both relevant and discriminative properties that improve the classification performance. More specifically, a penalty term, called discriminative loss is combined with the standard Auto-Encoder training criterion. This additional term aims to force the learned representation to contain discriminative information. Our experimental results on data from the public multicenter OsteoArthritis Initiative (OAI) show that the developed method presents potential results for early knee OA detection.

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.

A decision support tool for early detection of knee OsteoArthritis using X-ray imaging and machine learning: Data from the OsteoArthritis Initiative.

This paper presents a fully developed computer aided diagnosis (CAD) system for early knee OsteoArthritis (OA) detection using knee X-ray imaging and machine learning algorithms. The X-ray images are first preprocessed in the Fourier domain using a circular Fourier filter. Then, a novel normalization method based on predictive modeling using multivariate linear regression (MLR) is applied to the data in order to reduce the variability between OA and healthy subjects. At the feature selection/extraction stage, an independent component analysis (ICA) approach is used in order to reduce the dimensionality. Finally, Naive Bayes and random forest classifiers are used for the classification task. This novel image-based approach is applied on 1024 knee X-ray images from the public database OsteoArthritis Initiative (OAI). The results show that the proposed system has a good predictive classification rate for OA detection (82.98% for accuracy, 87.15% for sensitivity and up to 80.65% for specificity).

Ischemic stroke enhancement using a variational model and the expectation maximization method.

OBJECTIVES: In order to enable less experienced physicians to reliably detect early signs of stroke, A novel approach was proposed to enhance the visual perception of ischemic stroke in non-enhanced CT. METHODS: A set of 39 retrospective CT scans were used, divided into 23 cases of acute ischemic stroke and 16 normal patients. Stroke cases were obtained within 4.5 h of symptom onset and with a mean NIHSS of 12.9±7.4. After selection of adjunct slices from the CT exam, image averaging was performed to reduce the noise and redundant information. This was followed by a variational decomposition model to keep the relevant component of the image. The expectation maximization method was applied to generate enhanced images. RESULTS: We determined a test to evaluate the performance of observers in a clinical environment with and without the aid of enhanced images. The overall sensitivity of the observer's analysis was 64.5 % and increased to 89.6 % and specificity was 83.3 % and increased to 91.7 %. CONCLUSION: These results show the importance of a computational tool to assist neuroradiology decisions, especially in critical situations such as the diagnosis of ischemic stroke. KEY POINTS: • Diagnosing patients with stroke requires high efficiency to avoid irreversible cerebral damage. • A computational algorithm was proposed to enhance the visual perception of stroke. • Observers' performance was increased with the aid of enhanced images.

Classification of the trabecular bone structure of osteoporotic patients using machine vision.

Osteoporosis is a common bone disease which often leads to fractures. Clinically, the major challenge for the automatic diagnosis of osteoporosis is the complex architecture of bones. The clinical diagnosis of osteoporosis is conventionally done using Dual-energy X-ray Absorptiometry (DXA). This method has specific limitations, however, such as the large size of the instrument, a relatively high cost and limited availability. The method proposed here is based on the automatic processing of X-ray images. The bone X-ray image was statistically processed and strategically reformed to extract discriminatory statistical features of different orders. These features were used for machine learning for the classification of two populations composed of osteoporotic and healthy subjects. Four classifiers - support vector machine (SVM), k-nearest neighbors, Naïve Bayes and artificial neural network - were used to test the performance of the proposed method. Tests were performed on X-ray images of the calcaneus bone collected from the hospital of Orleans. The results are significant in terms of accuracy and time complexity. Experimental results indicate a classification rate of 98% using an SVM classifier which is encouraging for automatic osteoporosis diagnosis using bone X-ray images. The low time complexity of the proposed method makes it suitable for real time applications.

Anisotropic Discrete Dual-Tree Wavelet Transform for Improved Classification of Trabecular Bone.

This paper deals with a new anisotropic discrete dual-tree wavelet transform (ADDTWT) to characterize the anisotropy of bone texture. More specifically, we propose to extend the conventional discrete dual-tree wavelet transform (DDTWT) by using the anisotropic basis functions associated with the hyperbolic wavelet transform instead of isotropic spectrum supports. A texture classification framework is adopted to assess the performance of the proposed transform. The generalized Gaussian distribution is used to model the distribution of the sub-band coefficients. The estimated vector of parameters for each image is then used as input for the support vector machine classifier. Experiments were conducted on synthesized anisotropic fractional Brownian motion fields and on a real database composed of osteoporotic patients and control cases. Results show that the ADDTWT outperforms most of the competing anisotropic transforms with an area under curve rate of 93%.

Fractional Brownian Motion and Rao Geodesic Distance for Bone X-Ray Image Characterization.

Osteoporosis diagnosis has attracted particular attention in recent decades. Textured images from the microarchitecture of osteoporotic and healthy subjects show a high degree of similarity, increasing the difficulty of classifying such textures. Thus, the evaluation of osteoporosis from the bone X-ray images presents a major challenge for pattern recognition and medical applications. The purpose of this paper is to use the fractional Brownian motion (fBm) model and the probability density function of its increments to compute a similarity measure with the Rao geodesic distance to classify trabecular bone X-ray images. When evaluated on synthetic fBm images (test vectors) with the well-known Hurst parameter H, the proposed method met our expectations in which a good classification of the synthetic images was achieved. A clinical study was conducted on textured bone X-ray images from two different female populations of osteoporotic patients (fracture cases) and control subjects. Using the proposed method, an area under curve rate of 97% was achieved.

Application of chemometric algorithms to MALDI mass spectrometry imaging of pharmaceutical tablets.

During drug product development, the nature and distribution of the active substance have to be controlled to ensure the correct activity and the safety of the final medication. Matrix assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI), due to its structural and spatial specificities, provides an excellent way to analyze these two critical parameters in the same acquisition. The aim of this work is to demonstrate that MALDI-MSI, coupled with four well known multivariate statistical analysis algorithms (PCA, ICA, MCR-ALS and NMF), is a powerful technique to extract spatial and spectral information about chemical compounds from known or unknown solid drug product formulations. To test this methodology, an in-house manufactured tablet and a commercialized Coversyl(®) tablet were studied. The statistical analysis was decomposed into three steps: preprocessing, estimation of the number of statistical components (manually or using singular value decomposition), and multivariate statistical analysis. The results obtained showed that while principal component analysis (PCA) was efficient in searching for sources of variation in the matrix, it was not the best technique to estimate an unmixing model of a tablet. Independent component analysis (ICA) was able to extract appropriate contributions of chemical information in homogeneous and heterogeneous datasets. Non-negative matrix factorization (NMF) and multivariate curve resolution-alternating least squares (MCR-ALS) were less accurate in obtaining the right contribution in a homogeneous sample but they were better at distinguishing the semi-quantitative information in a heterogeneous MALDI dataset.

Changes in prevalence of calcaneal spurs in men & women: a random population from a trauma clinic.

BACKGROUND: This study reports the changing prevalence of ankle (Achilles and plantar) spurs with age, in order to comment on their significance to rheumatologists. METHODS: 1080 lateral ankle radiographs from each of 9 (50 men and 50 women) age cohorts from 2 to 96 years old of patients attending a trauma clinic were examined and spurs classified as small or large. RESULTS: The prevalence of both Achilles and plantar spurs in relation to the age categories and sex was variable. Overall, there was 38% of the population who had a spur (Achilles or plantar) and only third (11%) with spurs at both sites (Achilles and plantar). Large spurs were more prevalent in older individuals (40 to 79 years). There were no large plantar spurs in individuals <40 years of age and only 2% for the Achilles. The prevalence of spurs (Achilles and plantar) was significantly higher for woman than men in individuals <50 years of age. There was a notable moderate positive correlation (r = 0.71) between both plantar and Achilles spurs for women <30 years of age but no correlation for men (r = -0.03). CONCLUSION: Plantar and Achilles spurs are highly prevalent in older people and the radiographic appearance of spurs differs between men and women. In individuals < 50 years of age, spur (Achilles and plantar) formation is more common in women than in men. Additionally, there was a notable moderate positive correlation between Achilles and plantar spurs for women <30 years of age.

3D shape-dependent thinning method for trabecular bone characterization.

PURPOSE: Curve and surface thinning are widely-used skeletonization techniques for modeling objects in three dimensions. In the case of trabecular bone analysis, however, neither curve nor surface thinning is really efficient since the internal geometry of the object is usually composed of both rod and plate shapes. The purpose of this paper is to propose an original method called hybrid skeleton which better matches the geometry of the data compared to curve and surface skeletons. In the hybrid skeleton algorithm, 1D curves represent rod-shaped zones whereas 2D surfaces represent plate-shaped elements. METHODS: The proposed hybrid skeleton algorithm is based on a combination of three methods. (1) A new variant of the method proposed by Bonnassie et al. for the classification of voxels as belonging to plate-like or rod-like structures, where the medial axis (MA) algorithm is replaced by a fast and connected skeletonization algorithm. In addition, the reversibility of the MA algorithm is replaced by an isotropic region-growth method to spread the rod and plate labels back to the original object. (2) A well chosen surface thinning method applied on the plate voxels set. (3) A well chosen curve skeleton thinning method applied on the rod voxels set. The efficiency and the robustness of the proposed algorithm were evaluated using synthesis test vectors. A clinical study was led on micro-CT (computed tomography) images of two different populations of osteoarthritic and osteoporotic trabecular bone samples. The morphological and topological characteristics of the two populations were evaluated using the proposed hybrid skeleton as well as the classification algorithm. RESULTS: When evaluated on test vectors and compared to Bonnassie's algorithm, the proposed classification algorithm gives a slightly better rate of classification. The hybrid skeleton preserves the shape information of the processed objects. Interesting morphological and topological features as well as volumetric ones were extracted from the skeleton and from the classified volumes, respectively. The extracted features enable the two populations of osteoarthritic and osteoporotic trabecular bone samples to be distinguished. CONCLUSIONS: Compared to curve-based or surface-based skeletons, the hybrid skeleton better matches the geometry of the data. Each rod is represented by a one-voxel-thick arc and each plate is represented by a one-voxel-thick surface. The hybrid skeleton as well as the proposed classification algorithm introduce relevant parameters linked to the presence of plates in the trabecular bone data, showing that rods and plates contain independent information about trabeculae. The hybrid skeleton offers a new opportunity for precise studies of porous media such as trabecular bone.

A new method for 3D thinning of hybrid shaped porous media using artificial intelligence. Application to trabecular bone.

Curve and surface thinning are widely-used skeletonization techniques for modeling objects in three dimensions. In the case of disordered porous media analysis, however, neither is really efficient since the internal geometry of the object is usually composed of both rod and plate shapes. This paper presents an alternative to compute a hybrid shape-dependent skeleton and its application to porous media. The resulting skeleton combines 2D surfaces and 1D curves to represent respectively the plate-shaped and rod-shaped parts of the object. For this purpose, a new technique based on neural networks is proposed: cascade combinations of complex wavelet transform (CWT) and complex-valued artificial neural network (CVANN). The ability of the skeleton to characterize hybrid shaped porous media is demonstrated on a trabecular bone sample. Results show that the proposed method achieves high accuracy rates about 99.78%-99.97%. Especially, CWT (2nd level)-CVANN structure converges to optimum results as high accuracy rate-minimum time consumption.

Modeling of biological doses and mechanical effects on bone transduction.

Shear stress, hormones like parathyroid and mineral elements like calcium mediate the amplitude of stimulus signal, which affects the rate of bone remodeling. The current study investigates the theoretical effects of different metabolic doses in stimulus signal level on bone. The model was built considering the osteocyte as the sensing center mediated by coupled mechanical shear stress and some biological factors. The proposed enhanced model was developed based on previously published works dealing with different aspects of bone transduction. It describes the effects of physiological doses variations of calcium, parathyroid hormone, nitric oxide and prostaglandin E2 on the stimulus level sensed by osteocytes in response to applied shear stress generated by interstitial fluid flow. We retained the metabolic factors (parathyroid hormone, nitric oxide and prostaglandin E2) as parameters of bone cell mechanosensitivity because stimulation/inhibition of induced pathways stimulates osteogenic response in vivo. We then tested the model response in terms of stimulus signal variation versus the biological factors doses to external mechanical stimuli. Despite the limitations of the model, it is consistent and has physiological bases. Biological inputs are histologically measurable. This makes the model amenable to experimental verification.

3D image analysis and artificial intelligence for bone disease classification.

In order to prevent bone fractures due to disease and ageing of the population, and to detect problems while still in their early stages, 3D bone micro architecture needs to be investigated and characterized. Here, we have developed various image processing and simulation techniques to investigate bone micro architecture and its mechanical stiffness. We have evaluated morphological, topological and mechanical bone features using artificial intelligence methods. A clinical study is carried out on two populations of arthritic and osteoporotic bone samples. The performances of Adaptive Neuro Fuzzy Inference System (ANFIS), Support Vector Machines (SVM) and Genetic Algorithm (GA) in classifying the different samples have been compared. Results show that the best separation success (100 %) is achieved with Genetic Algorithm.

Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection.

It has been shown that the analysis of two dimensional (2D) bone X-ray images based on the fractional Brownian motion (fBm) model is a good indicator for quantifying alterations in the three dimensional (3D) bone micro-architecture. However, this 2D measurement is not a direct assessment of the 3D bone properties. In this paper, we first show that S(3D), the self-similarity parameter of 3D fBm, is linked to S(2D), that of its 2D projection, by S(3D)=S(2D)-0.5. In the light of this theoretical result, we have experimentally examined whether this relation holds for trabecular bone. Twenty one specimens of trabecular bone were derived from frozen human femoral heads. They were digitized using a high resolution mu-CT. Their projections were simulated numerically by summing the data in the three orthogonal directions and both 3D and 2D self-similarity parameters were measured. Results show that the self-similarity of the 3D bone volumes and that of their projections are linked by the previous equation. This demonstrates that a simple projection provides 3D information about the bone structure. This information can be a valuable adjunct to the bone mineral density for the early diagnosis of osteoporosis.