Fuzzy Object Skeletonization: Theory, Algorithms, and Applications.

Skeletonization offers a compact representation of an object while preserving important topological and geometrical features. Literature on skeletonization of binary objects is quite mature. However, challenges involved with skeletonization of fuzzy objects are mostly unanswered. This paper presents a new theory and algorithm of skeletonization for fuzzy objects, evaluates its performance, and demonstrates its applications. A formulation of fuzzy grassfire propagation is introduced; its relationships with fuzzy distance functions, level sets, and geodesics are discussed; and several new theoretical results are presented in the continuous space. A notion of collision-impact of fire-fronts at skeletal points is introduced, and its role in filtering noisy skeletal points is demonstrated. A fuzzy object skeletonization algorithm is developed using new notions of surface- and curve-skeletal voxels, digital collision-impact, filtering of noisy skeletal voxels, and continuity of skeletal surfaces. A skeletal noise pruning algorithm is presented using branch-level significance. Accuracy and robustness of the new algorithm are examined on computer-generated phantoms and micro- and conventional CT imaging of trabecular bone specimens. An application of fuzzy object skeletonization to compute structure-width at a low image resolution is demonstrated, and its ability to predict bone strength is examined. Finally, the performance of the new fuzzy object skeletonization algorithm is compared with two binary object skeletonization methods.

Trabecular bone characterization on the continuum of plates and rods using in vivo MR imaging and volumetric topological analysis.

Osteoporosis is associated with increased risk of fractures, which is clinically defined by low bone mineral density. Increasing evidence suggests that trabecular bone (TB) micro-architecture is an important determinant of bone strength and fracture risk. We present an improved volumetric topological analysis algorithm based on fuzzy skeletonization, results of its application on in vivo MR imaging, and compare its performance with digital topological analysis. The new VTA method eliminates data loss in the binarization step and yields accurate and robust measures of local plate-width for individual trabeculae, which allows classification of TB structures on the continuum between perfect plates and rods. The repeat-scan reproducibility of the method was evaluated on in vivo MRI of distal femur and distal radius, and high intra-class correlation coefficients between 0.93 and 0.97 were observed. The method's ability to detect treatment effects on TB micro-architecture was examined in a 2 years testosterone study on hypogonadal men. It was observed from experimental results that average plate-width and plate-to-rod ratio significantly improved after 6 months and the improvement was found to continue at 12 and 24 months. The bone density of plate-like trabeculae was found to increase by 6.5% (p = 0.06), 7.2% (p = 0.07) and 16.2% (p = 0.003) at 6, 12, 24 months, respectively. While the density of rod-like trabeculae did not change significantly, even at 24 months. A comparative study showed that VTA has enhanced ability to detect treatment effects in TB micro-architecture as compared to conventional method of digital topological analysis for plate/rod characterization in terms of both percent change and effect-size.

Characterization of trabecular bone plate-rod microarchitecture using multirow detector CT and the tensor scale: Algorithms, validation, and applications to pilot human studies.

PURPOSE: Osteoporosis is a common bone disease associated with increased risk of low-trauma fractures leading to substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density (BMD); however, increasing evidence suggests that trabecular bone (TB) microarchitectural quality is an important determinant of bone strength and fracture risk. A tensor scale based algorithm for in vivo characterization of TB plate-rod microarchitecture at the distal tibia using multirow detector CT (MD-CT) imaging is presented and its performance and applications are examined. METHODS: The tensor scale characterizes individual TB on the continuum between a perfect plate and a perfect rod and computes their orientation using optimal ellipsoidal representation of local structures. The accuracy of the method was evaluated using computer-generated phantom images at a resolution and signal-to-noise ratio achievable in vivo. The robustness of the method was examined in terms of stability across a wide range of voxel sizes, repeat scan reproducibility, and correlation between TB measures derived by imaging human ankle specimens under ex vivo and in vivo conditions. Finally, the application of the method was evaluated in pilot human studies involving healthy young-adult volunteers (age: 19 to 21 yr; 51 females and 46 males) and patients treated with selective serotonin reuptake inhibitors (SSRIs) (age: 19 to 21 yr; six males and six females). RESULTS: An error of (3.2% ± 2.0%) (mean ± SD), computed as deviation from known measures of TB plate-width, was observed for computer-generated phantoms. An intraclass correlation coefficient of 0.95 was observed for tensor scale TB measures in repeat MD-CT scans where the measures were averaged over a small volume of interest of 1.05 mm diameter with limited smoothing effects. The method was found to be highly stable at different voxel sizes with an error of (2.29% ± 1.56%) at an in vivo voxel size as compared to the original ex vivo voxel size. Tensor scale measures derived from imaging under in vivo and ex vivo conditions with significantly different modulation transfer function, i.e., difference in "true resolution," showed strong linear correlation (r = 0.92). The study of healthy volunteers shows that, after adjustment for height and weight, males have a 14% higher mean TB plate-width as compared to females (p < 0.05). SSRI-treated patients have 12.5% lower mean TB plate-width (p = 0.052) as compared to age-similar and sex-, height-, and weight-matched healthy controls. In contrast, the observed group difference in dual-energy x-ray absorptiometry (DXA)-derived hip BMD was 10.5% between males and females and only 5.04% between healthy controls and patients on SSRIs. CONCLUSIONS: Tensor scale analysis of MD-CT images yields accurate and reproducible characterization of TB plate-rod microarchitecture that may be more sensitive than DXA-derived BMD to sex differences and to the skeletal changes associated with medical conditions or their treatments.

7 Tesla MRI of bone microarchitecture discriminates between women without and with fragility fractures who do not differ by bone mineral density.

Osteoporosis is a disease of poor bone quality. Bone mineral density (BMD) has limited ability to discriminate between subjects without and with poor bone quality, and assessment of bone microarchitecture may have added value in this regard. Our goals were to use 7 T MRI to: (1) quantify and compare distal femur bone microarchitecture in women without and with poor bone quality (defined clinically by presence of fragility fractures); and (2) determine whether microarchitectural parameters could be used to discriminate between these two groups. This study had institutional review board approval, and we obtained written informed consent from all subjects. We used a 28-channel knee coil to image the distal femur of 31 subjects with fragility fractures and 25 controls without fracture on a 7 T MRI scanner using a 3-D fast low angle shot sequence (0.234 mm × 0.234 mm × 1 mm, parallel imaging factor = 2, acquisition time = 7 min 9 s). We applied digital topological analysis to quantify parameters of bone microarchitecture. All subjects also underwent standard clinical BMD assessment in the hip and spine. Compared to controls, fracture cases demonstrated lower bone volume fraction and markers of trabecular number, plate-like structure, and plate-to-rod ratio, and higher markers of trabecular isolation, rod disruption, and network resorption (p < 0.05 for all). There were no differences in hip or spine BMD T-scores between groups (p > 0.05). In receiver-operating-characteristics analyses, microarchitectural parameters could discriminate cases and controls (AUC = 0.66-0.73, p < 0.05). Hip and spine BMD T-scores could not discriminate cases and controls (AUC = 0.58-0.64, p ≥ 0.08). We conclude that 7 T MRI can detect bone microarchitectural deterioration in women with fragility fractures who do not differ by BMD. Microarchitectural parameters might some day be used as an additional tool to detect patients with poor bone quality who cannot be detected by dual-energy X-ray absorptiometry (DXA).

A robust algorithm for thickness computation at low resolution and its application to in vivo trabecular bone CT imaging.

Adult bone diseases, especially osteoporosis, lead to increased risk of fracture which in turn is associated with substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density; however, increasing evidence suggests that the microarchitectural quality of trabecular bone (TB) is an important determinant of bone strength and fracture risk. Accurate measures of TB thickness and marrow spacing is of significant interest for early diagnosis of osteoporosis or treatment effects. Here, we present a new robust algorithm for computing TB thickness and marrow spacing at a low resolution achievable in vivo. The method uses a star-line tracing technique that effectively deals with partial voluming effects of in vivo imaging with voxel size comparable to TB thickness. Also, the method avoids the problem of digitization associated with conventional algorithms based on sampling distance transform along skeletons. Accuracy of the method was examined using computer-generated phantom images, while the robustness of the method was evaluated on human ankle specimens in terms of stability across a wide range of voxel sizes, repeat scan reproducibility under in vivo conditions, and correlation between thickness values computed at ex vivo and in vivo imaging resolutions. Also, the sensitivity of the method was examined by evaluating its ability to predict the bone strength of cadaveric specimens. Finally, the method was evaluated in a human study involving 40 healthy young-adult volunteers (age: 19-21 years; 20 males and 20 females) and ten athletes (age: 19-21 years; six males and four females). Across a wide range of voxel sizes, the new method is significantly more accurate and robust as compared to conventional methods. Both TB thickness and marrow spacing measures computed using the new method demonstrated strong associations (R2 ∈ [0.83, 0.87]) with bone strength. Also, the TB thickness and marrow spacing measures allowed discrimination between male and female volunteers (p ∈ [0.01, 0.04]) as well as between athletes and nonathletes (p ∈ [0.005, 0.03]).

High bone density masks architectural deficiencies in an individual with spinal cord injury.

Context Spinal cord injury (SCI) causes a decline of bone mineral density (BMD) in the paralyzed extremities via the gradual degradation and resorption of trabecular elements. Clinical tools that report BMD may not offer insight into trabecular architecture flaws that could affect bone's ability to withstand loading. We present a case of a woman with a 30-year history of SCI and abnormally high distal femur BMD. Findings Peripheral quantitative-computed tomography-based BMD for this subject was ∼20% higher than previously published non-SCI values. Computed tomography (CT) revealed evidence of sclerotic bone deposition in the trabecular envelope, most likely due to glucocorticoid-induced osteonecrosis. Volumetric topologic analysis of trabecular architecture indicated that the majority of the bone mineral was organized into thick, plate-like structures rather than a multi-branched trabecular network. Visual analysis of the CT stack confirmed that the sclerotic bone regions were continuous with the cortex at only a handful of points. Conclusions Conventional clinical BMD analysis could have led to erroneous assumptions about this subject's bone quality. CT-based analysis revealed that this subject's high BMD masked underlying architectural flaws. For patients who received prolonged glucocorticoid therapy, excessively high BMD should be viewed with caution. The ability of this subject's bone to resist fracture is, in our view, extremely suspect. A better understanding of the mechanical competency of this very dense, but architecturally flawed bone would be desirable before this subject engaged in activities that load the limbs.

Application of fuzzy skeletonization ot quantitatively assess trabecular bone micro-architecture.

Adult bone diseases, especially osteoporosis, lead to increased risk of fracture associated with substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density; however, increasing evidence suggests that the micro-architectural quality of trabecular bone (TB) is an important determinant of bone strength and fracture risk. Skeletonization plays an important role providing a compact representation of TB network that allows computation of several quantitative parameters relating to TB micro-architecture. Literature of three-dimensional skeletonization is quite matured for binary digital objects. However, the challenges of skeletonization for fuzzy objects are mostly unanswered. Here, an algorithm for fuzzy skeletonization is presented using fuzzy grassfire propagation and a branch-level noise pruning strategy and, finally, its application to TB micro-architectural assessment is investigated. Specifically, the fuzzy skeletonization algorithm is applied to compute TB plateness, plate/rod ratio, thickness, and spacing. Finally, the effectiveness of these measures to predict experimental bone strength is investigated on twelve cadaveric specimens and the results are encouraging with the R(2) value of linear correlation with bone strength being as high as 0.93, 0.88, 0.85 and 0.86, respectively.

Integrated spatiotemporal analysis for automatic contrast agent inflow detection on angiography and fluoroscopy during transcatheter aortic valve implantation.

PURPOSE: In this paper, the authors propose an integrated spatial and temporal analysis for automatic detection of contrast agent inflow at the aortic root on fluoroscopic and angiographic sequences during transcatheter aortic valve implantation procedures as a means to automatically trigger registration of 3D aortic models. METHODS: The proposed contrast agent inflow detection method is based on a contrast feature curve, calculated using histogram analysis and a likelihood ratio test. Several image preprocessing steps are performed to enhance the properties of the contrast feature curve. For sequences with a dominant peak on its contrast feature curve, a cascaded classifier is then applied to differentiate the contrast-enhanced aorta from contrast-enhanced balloons. Finally, a multilayer classifier based on sparse Gabor features is used to recognize sequences containing a faint contrast-enhanced aorta. RESULTS: The algorithm was evaluated using 105 sequences consisting of more than 12,000 frames, and achieved a detection accuracy of 99.1% (100% sensitivity and 98.5% specificity). The computation time for a typical sequence of 150 frames was ≈ 1 s on a single-core Dell PC with a 1 GHz Intel Xeon processor and 2 GB of RAM. CONCLUSIONS: The authors developed a novel, automatic method for contrast agent inflow detection on x-ray sequences. With the achieved efficiency and accuracy, the proposed method is potentially feasible for clinical use as it facilitates a seamless workflow in utilizing patient-specific 3D models to provide anatomical details during transcatheter aortic valve implantation procedures.

A NEW ALGORITHM FOR TRABECULAR BONE THICKNESS COMPUTATION AT LOW RESOLUTION ACHIEVED UNDER IN VIVO CONDITION.

Adult bone diseases, especially osteoporosis, lead to increased risk of fracture associated with substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density (BMD); however, increasing evidence suggests that the micro-architectural quality of trabecular bone (TB) is an important determinant of bone strength and fracture risk. Accurate measurement of trabecular thickness and marrow spacing is of significant interest for early diagnosis of osteoporosis or treatment effects. Here, we present a new robust algorithm for computing TB thickness and marrow spacing at a low resolution achievable in vivo. The method uses a star-line tracing technique that effectively deals with partial voluming effects of in vivo imaging where voxel size is comparable to TB thickness. Experimental results on cadaveric ankle specimens have demonstrated the algorithm's robustness (ICC>0.98) under repeat scans of multi-row detector computed tomography (MD-CT) imaging. It has been observed in experimental results that TB thickness and marrow spacing measures as computed by the new algorithm have strong association (R2 ∈{0.85, 0.87}) with TB's experimental mechanical strength measures.

A new multi-object image thresholding method based on correlation between object class uncertainty and intensity gradient.

PURPOSE: Image thresholding and gradient analysis have remained popular image preprocessing tools for several decades due to the simplicity and straight-forwardness of their definitions. Also, optimum selection of threshold and gradient strength values are hidden steps in many advanced medical imaging algorithms. A reliable method for threshold optimization may be a crucial step toward automation of several medical image based applications. Most automatic thresholding and gradient selection methods reported in literature primarily focus on image histograms ignoring a significant amount of information embedded in the spatial distribution of intensity values forming visible features in an image. Here, we present a new method that simultaneously optimizes both threshold and gradient values for different object interfaces in an image that is based on unification of information from both the histogram and spatial image features; also, the method works for unknown number of object regions. METHODS: A new energy function is formulated by combining the object class uncertainty measure, a histogram-based feature, of each pixel with its image gradient measure, a spatial contextual feature in an image. The energy function is designed to measure the overall compliance of the theoretical premise that, in a probabilistic sense, image intensities with high class uncertainty are associated with high image gradients. Finally, it is expressed as a function of threshold and gradient parameters and optimum combinations of these parameters are sought by locating pits and valleys on the energy surface. A major strength of the algorithm lies in the fact that it does not require the number of object regions in an image to be predefined. RESULTS: The method has been applied on several medical image datasets and it has successfully determined both threshold and gradient parameters for different object interfaces even when some of the thresholds are almost impossible to locate in the histogram. Both accuracy and reproducibility of the method have been examined on several medical image datasets including repeat scan 3D multidetector computed tomography (CT) images of cadaveric ankles specimens. Also, the new method has been qualitatively and quantitatively compared with Otsu's method along with three other algorithms based on minimum error thresholding, maximum segmented image information and minimization of homogeneity- and uncertainty-based energy and the results have demonstrated superiority of the new method. CONCLUSIONS: We have developed a new automatic threshold and gradient strength selection algorithm by combining class uncertainty and spatial image gradient features. The performance of the method has been examined in terms of accuracy and reproducibility and the results found are better as compared to several popular automatic threshold selection methods.

Quantitative characterization of trabecular bone micro-architecture using tensor scale and multi-detector CT imaging.

Osteoporosis, characterized by low bone mineral density (BMD) and micro-architectural deterioration of trabecular bone (TB), increases risk of fractures associated with substantial morbidity, mortality, and financial costs. A quantitative measure of TB micro-architecture with high reproducibility, large between-subjects variability and strong association with bone strength that may be computed via in vivo imaging would be an important indicator of bone quality for clinical trials evaluating fracture risks under different clinical conditions. Previously, the notion of tensor scale (t-scale) was introduced using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. Here, we develop a new 3-D t-scale algorithm for fuzzy objects and investigate its application to compute quantitative measures characterizing TB micro-architecture acquired by in vivo multi-row detector CT (MD-CT) imaging. Specifically, new measures characterizing individual trabeculae on the continuum of a perfect plate and a perfect rod and their orientation are directly computed in a volumetric BMD representation of a TB network. Reproducibility of these measures is evaluated using repeat MD-CT scans and also by comparing their correlation between MD-CT and micro-CT imaging. Experimental results have demonstrated that the t-scale-based TB micro-architectural measures are highly reproducible with strong association of their values at MD-CT and micro-CT resolutions. Results of an experimental mechanical study have proved these measures' ability to predict TB's bone strength.

Performance of the MRI-based virtual bone biopsy in the distal radius: serial reproducibility and reliability of structural and mechanical parameters in women representative of osteoporosis study populations.

Serial reproducibility and reliability critically determine sensitivity to detect changes in response to intervention and provide a basis for sample size estimates. Here, we evaluated the performance of the MRI-based virtual bone biopsy in terms of 26 structural and mechanical parameters in the distal radius of 20 women in the age range of 50 to 75 years (mean=62.0 years, S.D.=8.1 years), representative of typical study populations in drug intervention trials and fracture studies. Subjects were examined three times at average intervals of 20.2 days (S.D.=14.5 days) by MRI at 1.5 T field strength at a voxel size of 137×137×410 µm(3). Methods involved prospective and retrospective 3D image registration and auto-focus motion correction. Analyses were performed from a central 5×5×5 mm(3) cuboid subvolume and trabecular volume consisting of a 13 mm axial slab encompassing the entire medullary cavity. Whole-volume axial stiffness and sub-regional Young's and shear moduli were computed by finite-element analysis. Whole-volume-derived aggregate mean coefficient of variation of all structural parameters was 4.4% (range 1.8% to 7.7%) and 4.0% for axial stiffness; corresponding data in the subvolume were 6.5% (range 1.6% to 13.0%) for structural, and 5.5% (range 4.6% to 6.5%) for mechanical parameters. Aggregate ICC was 0.976 (range 0.947 to 0.986) and 0.992 for whole-volume-derived structural parameters and axial stiffness, and 0.946 (range 0.752 to 0.991) and 0.974 (range 0.965 to 0.978) for subvolume-derived structural and mechanical parameters, respectively. The strongest predictors of whole-volume axial stiffness were BV/TV, junction density, skeleton density and Tb.N (R(2) 0.79-0.87). The same parameters were also highly predictive of sub-regional axial modulus (R(2) 0.88-0.91). The data suggest that the method is suited for longitudinal assessment of the response to therapy. The underlying technology is portable and should be compatible with all general-purpose MRI scanners, which is appealing considering the very large installed base of this modality.

Graph search with appearance and shape information for 3-D prostate and bladder segmentation.

The segmentation of soft tissues in medical images is a challenging problem due to the weak boundary, large deformation and serious mutual influence. We present a novel method incorporating both the shape and appearance information in a 3-D graph-theoretic framework to overcome those difficulties for simultaneous segmentation of prostate and bladder. An arc-weighted graph is constructed corresponding to the initial mesh. Both the boundary and region information is incorporated into the graph with learned intensity distribution, which drives the mesh to the best fit of the image. A shape prior penalty is introduced by adding weighted-arcs in the graph, which maintains the original topology of the model and constraints the flexibility of the mesh. The surface-distance constraints are enforced to avoid the leakage between prostate and bladder. The target surfaces are found by solving a maximum flow problem in low-order polynomial time. Both qualitative and quantitative results on prostate and bladder segmentation were promising, proving the power of our algorithm.