The authors have no conflict of interest
An Improved Segmentation Method for In Vivo μCT Imaging†
Article first published online: 12 JUL 2004
Copyright © 2004 ASBMR
Journal of Bone and Mineral Research
Volume 19, Issue 10, pages 1640–1650, October 2004
How to Cite
Waarsing, J. H., Day, J. S. and Weinans, H. (2004), An Improved Segmentation Method for In Vivo μCT Imaging. J Bone Miner Res, 19: 1640–1650. doi: 10.1359/JBMR.040705
- Issue published online: 2 DEC 2009
- Article first published online: 12 JUL 2004
- Manuscript Accepted: 21 MAY 2004
- Manuscript Revised: 3 MAY 2004
- Manuscript Received: 19 NOV 2003
Image segmentation methods for μCT can influence the accuracy of bone morphometry calculations. A new automated segmentation method is introduced, and its performance is compared with standard segmentation methods. The new method can improve the results of in vivo μCT, where the need to keep radiation dose low limits scan quality.
Introduction: An important topic for μCT analysis of bone samples is the segmentation of the original reconstructed grayscale data sets to separate bone from non-bone. Problems like noise, resolution limitations, and beam-hardening make this a nontrivial issue. Inappropriate segmentation methods will reduce the potential power of μCT and may introduce bias in the architectural measurements, in particular, when new in vivo μCT with its inherent limitations in scan quality is used. Here we introduce a new segmentation method using local thresholds and compare its performance to standard global segmentation methods.
Material and Methods: The local threshold method was validated by comparing the result of the segmentation with histology. Furthermore, the effect of choosing this new method versus standard segmentation methods using global threshold values was investigated by studying the sensitivity of these methods to signal to noise ratio and resolution.
Results: Using the new method on high-quality scans yielded accurate results and virtually no differences between histology and the segmented data sets could be observed. When prior knowledge about the volume fraction of the bone was available the global threshold also resulted in appropriate results. Degrading the scan quality had only minor effects on the performance of the new segmentation method. Although global segmentation methods were not sensitive to noise, it was not possible to segment both lower mineralized thin trabeculae and the higher mineralized cortex correctly with the same threshold value.
Conclusion: At high resolutions, both the new local and conventional global segmentation methods gave near exact representations of the bone structure. When scanned samples are not homogenous (e.g., thick cortices and thin trabeculae) and when resolution is relatively low, the local segmentation method outperforms global methods. It maximizes the potential of in vivo μCT by giving good structural representation without the need to use longer scanning times that would increase absorption of harmful X-ray radiation by the living tissue.
Diseases like osteoporosis can seriously affect the mechanical integrity of bone. Measuring the BMD alone is not sufficient to understand how bone loss affects fracture risk. It is also important to study the actual structure of the trabecular network, for instance by μCT.(1) Since its introduction by Feldkamp et al.,(2) μCT has become an important tool to quantify the morphometry of the trabecular structure of bone biopsy specimens of humans and of whole bones of small animals like rats or mice. In addition, μCT provides the possibility to set up finite element (FE) models to determine the strength and stiffness of the bone sample based solely on the trabecular architecture.(3), (4) Furthermore, the 3D representations of bone can be used as the input for computer simulations of bone remodeling.(5) Recent advances in technology have made in vivo μCT possible; increasing the value of μCT as a research tool by enabling the design of longitudinal studies to follow changes in trabecular structure.(6), (7)
A number of studies have validated the accuracy of μCT. Comparison with histology showed relative small to rather high deviations in 2D morphometric parameters depending on scan resolution and especially on which segmentation method was used.(8–11) Other studies on the effects of scanning resolution and segmentation methods on morphometric parameters support and stress the importance of choosing an appropriate segmentation technique to separate bone from non-bone.(12–15) The demands on segmentation techniques become even more stringent when the quality of the scans is limited, as is the case for in vivo scanning, where scanning time should be as short as possible to limit radiation dose absorbed by the living tissue.
The most widely used segmentation techniques use global thresholds; a single CT number is chosen, above which all voxels (3D pixels) are marked as bone and below which all remaining voxels are marked as non-bone. The value that is used as a threshold is selected either visually, by analyzing the histogram of CT numbers or by forcing the resulting binary data set to have the same volume as the original bone sample as determined by doing an Archimedes test.(15)
Despite the ease and speed of using a global threshold, serious problems such as beam hardening, noise, and partial volume effects can considerably reduce the quality of the segmentation. The effect of beam hardening can be reduced by using a physical filter during scanning and by using corrective algorithms during reconstruction. Partial volume effects (a voxel that contains both bone and non-bone has a lower CT number than a bone voxel, but a higher CT number than a non-bone voxel) will limit the frequency content of the reconstructed images. This will “smear out” the bone around its real edge in a reconstructed data set. Trabeculae that are thin relative to the resolution can even be smeared out such that the CT number of the trabeculae does not reach the CT number that would represent the true density of the material.(16) The combination of these effects causes the optimal threshold value for a certain part of the reconstruction to be different from the optimal value in other parts. In general, using a single global threshold value will result in the loss of thin trabeculae and oversizing of thicker trabeculae.
Segmentation can be improved by using local threshold values rather than a single global threshold value such that each voxel can be thresholded optimally within its neighborhood. Dufresne(17) has developed a local threshold algorithm for CT scans to compensate for beam-hardening effects based on the analysis of the histogram of the local neighborhood of a voxel. The efficiency of this method will decrease when the resolution is limited and tissues are not homogenous. Kuhn et al.(16) and Elmoutaouakkil et al.(18) proposed more general local segmentation methods, both based on the so-called one-half maximum height (HMH) protocol. Summarized, voxels are considered bone if their CT number is higher than one-half the difference between local minima (background) and local maxima (bone). The more rigorously validated method of Kuhn et al. gives very accurate results for structures much thicker than the resolution of the μCT system; however, structures that are thin relative to the resolution are still oversized.
Segmentation techniques have been studied more extensively for in vivo imaging of human bone by μMRI(19–23) and pQCT.(24–28) Because of their relatively low resolutions (∼150 μm), these systems lack the ability to accurately resolve individual trabeculae. Hence, most studies have focused on parameter extraction techniques that indirectly estimate properties of the trabecular bone. These methods have only been validated by assessing the reproducibility and by showing that they could discriminate between populations.
In this paper, we introduce an automated segmentation method using local threshold values obtained by applying standard edge detection algorithms, while compensating for smeared out thin trabeculae. The method was validated by comparing segmented data sets with traditional histological sections. Furthermore, the consequences of choosing a local versus a global threshold method were investigated by studying the behavior of these methods at different scan qualities and resolutions.
MATERIALS AND METHODS
Before applying the segmentation algorithm, noise was reduced by filtering the data sets with a 3D Gaussian smoothing function. Each voxel in the data set was replaced by the weighted average of the voxels in its 5 × 5 × 5 neighborhood. The weights were functions of the distance of each voxel to the central voxel in the 5 × 5 × 5 neighborhood, according to the Gaussian function of which the SD or radius was a parameter (GaussRadius) that was set by the user.
A standard edge detection algorithm, extended to 3D, was used to find the surface of the bone in the smoothed data set (Fig. 1A). The edges were detected by calculating the 3D spatial gradient of the reconstructed data using three orthogonal 3 × 3 Sobel operators(29) that favor localization of edges above (noise sensitive) detection of edges(30) (Figs. 1B and 2B). The ridges in the gradient field are the edges, indicating the transition from bone to non-bone and correspond to the HMH points. The ridges were detected by finding local maxima in the direction of the gradient. To prevent detection of false (noisy) edges and streaking (breaking up of an edge contour because of noise), only local maxima that were above a high threshold were kept (strong edges), together with smaller maxima that were connected to these high maxima but were still above a low threshold (weak edges; Figs. 1C and 2C).(30) The values of the high- and low-threshold values that define the strong and weak edges were set by the user (GradientCutOffHigh, GradientCutOffLow). The possible values for these parameters ranged between 1 (strongest edges) and 0 (no edge). These values are obtained by normalizing the cumulative histogram of the gradient values in a data set. A parameter value of 0.9 would refer to that gradient value where the cumulative histogram is at 90% of its maximum value.
The set of edges that resulted from the edge detection step was used to obtain local threshold values spanning the surface of the bone. The CT number of a voxel that is part of the set of edges served as a local threshold value for its neighborhood. The total set of local thresholds was obtained by dilating the local-threshold surface in 3D iteratively until it filled a matrix of local threshold values, giving each voxel its own local threshold. During a dilation step, a voxel was included into the set of local thresholds if it had neighboring voxels in a 3 × 3 × 3 neighborhood that were included in previous steps. The local threshold value for the to-be-included voxel was calculated by taking the Gaussian weighted average of the threshold values of the voxels in the 3 × 3 × 3 neighborhood. The dilation process was continued until all voxels in the data set had been appointed a local threshold value (Fig. 2D).
The last step of the algorithm consisted of comparing the gray value of each voxel with its local threshold value and marking it as bone when it was higher than this value and marking it as non-bone otherwise, resulting in a binary data set (Figs. 1D and 2E). An extra condition was included here to decrease the effect of smearing out trabeculae that were thin relative to the resolution. The maximal CT numbers of such a thin trabecula will be lower than the CT number corresponding to the average density of the material. For rod-shaped trabeculae, this decrease in CT number is proportional to the decrease in radius.(31) By assuming all trabeculae have approximately the same BMD, thin trabeculae could be identified by comparing a local threshold value to the average threshold value; when it was lower, a thin trabecula was identified. To reduce the risk of false positives, that is, classifying a thick trabecula as being thin, a minimal difference of 1 SD between the local and the average threshold value was required before a trabecula was identified as being thin. The local threshold value was adjusted upward proportional to the difference between the original local threshold value (TL) and the average threshold value (TL,mean), scaled by the difference between the average threshold value and the average CT number of the background (CTbackground).
The average CT number of the background was a parameter that was set by the user (BackgroundValue). As a consequence of the adjustment, the resulting trabecula was slightly thinner than when the local threshold would not have been adjusted.
If not stated differently, the value for the radius of the Gauss filter (GaussRadius) was determined by trial and error, as was the GradientCutOffLow parameter. The GaussRadius had values ranging from 0.4 for scans with low noise content to 1.0 for scans with high noise content. GradientCutOffHigh was held constant for all segmentations and was set to 0.99. The value of BackGroundValue, needed for the compensation of smeared out thin trabeculae was set equal to the average CT value of the background material, which is air in clean and dry samples and marrow or soft tissue in whole bones and in vivo scanning.
Decreasing the value of GradientCutOffLow resulted in the inclusion of thinner trabeculae and eventually in the inclusion of noise, but did not influence the thickness of the trabeculae. The value for this parameter was chosen just above the level where noisy structures started to seem in the data sets. Increasing GaussRadius decreased the noise in the data sets, but also smeared out trabeculae, which could result in thickening of trabeculae. This value was adjusted in conjunction with GradientCutOffLow such that the lowest values possible for both parameters could be used.
Validation: comparison with histological sections
Two rat tibias were scanned in a Skyscan-1072 MicroCT scanner (Skyscan, Antwerp, Belgium), yielding reconstructed data sets with a voxel size of 11 μm. The system had an actual resolution of 8 μm specified by the manufacturer (10%MTF). The data sets were segmented both by using the local threshold method and by applying a global threshold such that the resulting data sets had the same volume fraction as the data sets obtained from the local threshold method.
After scanning, the bones were embedded in methyl methacrylate (MMA). Serial sections were obtained by repeatedly slicing 30-μm-thick sections off the MMA block. After each cut, the bone at the surface of the block was stained with alizarine red, coloring the calcium red, and a microphotograph with a pixel size of 2 μm was taken of the block surface. Processing the sample en block prevented geometrical distortion that occurs when processing thin sections.
Registration software from the University of Leuven(32) was used to automatically reposition the segmented data sets such that they optimally matched the set of histological microphotographs.
The cross-sections of the scan data were compared with the histological data by overlaying the segmented serial microphotographs with the registered scan data and calculating the difference in bone area.
Comparing segmentation methods at different resolutions
To obtain data sets with different scan resolutions, but with equal noise content, scanning was simulated using a real scan as input. To serve as input data sets, six pieces of trabecular bone from core biopsy specimens of canine distal femora, embedded in MMA, were scanned in a Skyscan-1076 μCT scanner. The system resolution, as specified by the manufacturer, was 15 μm (10% MTF). The resulting data sets had a voxel size of 18 μm. Before embedding, the volumes of the core biopsy specimens were measured using Archimedes' principle.(15)
To simulate scanning at different resolutions, the radon transform of the original scan was calculated resulting in virtual shadow projections. These shadow projections were resampled to pixel sizes of 35 and 53 μm by selecting a random voxel in a 2 × 2 × 2 neighborhood in case of the 35-μm samples and in a 3 × 3 × 3 neighborhood in case of the 53-μm samples. By resampling, the noise levels remained constant. The inverse radon transform was calculated for the original sets of virtual shadow projections and the two sets of resampled shadow projections, giving reconstructed data sets with voxel sizes of 18, 35, and 53 μm. The calculations were performed using Matlab (The Mathworks).
All reconstructed data sets were segmented in three different ways. One set of data were obtained by applying the automatic local threshold algorithm with adjustment for smeared out trabeculae (LocalAuto). A second data set was obtained by applying a global threshold value that was chosen such that the volume of the resulting data set was equal to the volume of the original sample as determined using Archimedes' principle (GlobalArch). The third set was obtained by setting the global threshold at a value where the sensitivity of the volume to changes in threshold value was smallest, as determined after analysis of the density histogram(15) (GlobalHist). The study set-up is summarized in Table 1.
For the LocalAuto method, the parameters GaussRadius and GradientCutOffLow were determined by trial and error for the data sets with 18-μm voxel size. The GaussRadius for the data sets with voxel sizes of 35 and 53 μm were, respectively, scaled to one-half and one-third of the GaussRadius of the data sets with the highest resolution. GradientCutOffLow was adjusted to get the lowest acceptable value.
All samples in the same group were segmented with the same parameter values. To ascertain that only the segmentation methods themselves were compared, the Gaussian smoothing was also applied to all data sets before global segmentation. The same value for GaussRadius was used as for the local threshold algorithm.
For all resulting data sets, volume fraction and 3D-direct thickness(33) were calculated, as well as connectivity(34) and structure model index (SMI).(35) The first two parameters are representations of the bone mass and its distribution, and the last two parameters characterize geometry and topology of the bone sample. The parameters were calculated using the freely available software of the 3D-Calculator project (www.eur.nl/fgg/orthopaedics/Downloads.html). The effects of scanning resolution and the addition of noise on each segmentation method were assessed by analyzing the relative change of the morphometric parameters.
A reliable segmentation method maintains the ability to detect group differences at decreased scan qualities. The method should be reliable in the sense that the way samples relate to each other when scanning at different resolutions should not change. In other words, if sample A has a volume fraction that is slightly higher than the volume fraction of sample B at high resolution, it should still have a higher volume fraction when the samples are scanned at a lower resolution. In this paper, we will refer to this quality of segmentation algorithms with the term “reliability,” which was assessed by using regression analysis. If the way in which samples relate to each other is the same at different resolutions, the variation between samples at a low resolution is explained completely by the variation at a high resolution, which is expressed by the R2 value. R2 was assessed for each parameter and each thresholding method by regressing the outcomes for the data sets with 35 and 53 μm on the outcomes of the 18-μm data sets.
Finally, the different segmentation methods were analyzed visually by overlaying the cross-sections for the different methods.
Comparing the influence of noise on the different segmentation methods
The effect of noise on the segmentation methods was investigated by adding noise to the 35-μm data sets described in the previous section. The original 35-μm data sets served as the low-noise reference. Data sets with medium and high noise levels were created by adding Gaussian-distributed noise with an SD of 0.005 (medium) and 0.01 (high) to the virtual shadow projections of the 35-μm data sets.
After reconstruction, all data sets were segmented using the three different methods described above (GlobalArch, GlobalHisto, and LocalAuto).
The LocalAuto parameter settings for the low noise data sets as determined in the previous section were taken as a reference for the data sets with higher noise levels. GradientCutOffLow was kept constant for these data sets, whereas GaussRadius was increased until no more noisy structures were present in the data sets.
The segmented data sets were analyzed in the same way as in the study of the effects of decreasing resolution.
Comparing segmentation methods for whole bone scans at different scan qualities
The tibia of a rat was scanned in vivo using the Skyscan 1076 in vivo system. Scanning time was kept short (20 minutes) to limit radiation dose absorbed by the living tissue, resulting in a data set with high noise levels. The resulting data set had a voxel size of 18 μm. After death, the tibia of the rat was dissected and scanned in vitro in a Skyscan 1072 μCT system. A long scan was made (3 h) to obtain a high signal-to-noise ratio.
Both the high-quality (in vitro) and low-quality (in vivo) scans were segmented using both the automated local threshold algorithm and by using the most optimal global threshold value. When the global threshold was chosen too high, no trabecular bone was included in the segmentation. On the other hand, when the global threshold was chosen too low, all trabecular bone was included, but cortical bone was oversized. For a range of threshold values, the difference in volume estimates between the globally and locally segmented data sets for cortical and trabecular bone was calculated as a percentage of the cortical and trabecular bone volume, respectively, in the locally segmented data set. The minimum in total difference was chosen as the most optimal global threshold value.
Animal procedures formed part of a larger experiment for which approval was obtained from the Animal Ethics Committee.
Comparison with histological sections
Using the local threshold method as well as applying the global threshold, set at a threshold value that resulted in the same volume fraction as with the local method, resulted in very good representations of the bone. For both thicker and thinner structures, the histological images were nearly identical to the segmented cross-sections obtained with the local threshold method (Fig. 3). Quantitative analysis of bone area showed an average difference of −0.5% between the corresponding locally and globally thresholded cross-sections and the histological sections. Where the locally thresholded cross-sections gave differences in bone area compared with the histological sections that varied between −0.4% and −0.6%, the globally thresholded cross-sections gave differences that varied between −1% and 1%. Detailed examination showed that the most negative differences of the globally thresholded cross-sections were measured in sections that contained thin structures that were less well detected by the global method than by the local method (Fig. 3).
Influence of a reduction in resolution on segmentation methods
When resolution of the data sets was decreased from 18 to 35 μm, the local segmentation method (LocalAuto) gave the least change in parameter values. Parameters changed on average by about 7% for the local method, whereas the global methods resulted in changes of 12% and 13%. Reliability was very high for all methods, with R2 values ranging from 0.96 to 0.98. Changes in parameter values and the results of the reliability test are summarized in Tables 2 and 3. When resolution was further decreased to 53 μm, the performance of all methods deteriorated strongly, resulting in changes of ∼30%.
At high resolution, the LocalAuto method resulted in a slightly higher value for volume fraction than the two global methods (Fig. 4). When resolution was decreased, the volume fraction for the GlobalHist method increased rapidly and rose above values for the LocalAuto method. For all resolutions, the LocalAuto segmentation method gave thinner trabeculae and a more plate-like structure, indicated by SMI values close to one. In absolute values, connectivity density did not show much difference between the segmentation methods.
Visual inspection of the segmented data sets showed that, in general, both global methods resulted in more bone on the outside of the core samples, whereas the LocalAuto method resulted in more bone at the inside of the core sample (Fig. 5). This difference became stronger as resolution decreased.
Influence of noise on segmentation methods
Adding noise had the least effect on the parameter values estimated with the GlobalArch method. On average, the values changed 6% when medium noise levels were added and 7% when high noise levels were added. The GlobalAuto method gave changes of 8% and 10%, respectively, for the addition of medium and high noise, and the LocalAuto method gave changes of 10% and 17% (Table 4). GlobalArch gave similar results for reliability as LocalAuto, with R2 values of about 0.97 for addition of medium noise levels and 0.94 for addition of high noise levels. GlobalHist gave the least reliable results, with R2 values of 0.87 for addition of medium noise levels and 0.84 for addition of high noise levels (Table 5).
The effects on the various parameters showed strong differences between the segmentation methods. The GlobalArch method had problems with representing connectivity: the reliability went down to 0.82 for the highest noise level. GlobalHist had problems with estimating the volume (BV) and especially with SMI (R2 as low as 0.56 for the addition of the highest noise level). The LocalAuto method gave strong increases in the absolute value for SMI and had problems with trabecular thickness, where reliability decreased to 0.86 when high noise levels were added.
Comparison of the segmentation methods for whole bone scans
Applying the local threshold algorithm to the high-quality in vitro scan of a whole rat tibia resulted in a visually convincing segmentation. The local segmentation of the lower-quality in vivo scan showed only minor differences compared with the high-quality data set; metaphysial trabeculae were slightly thicker (Figs. 6B2 and 6C2).
For high global threshold values, the cortical bone in the globally segmented data set resembled the cortical bone in the locally segmented data set. However, no trabecular bone was included in the data set. Adjusting the global threshold value downward resulted in the inclusion of more trabecular bone, but this was accompanied by a strong increase in cortical bone volume. Setting the global threshold at the value where there was no difference in total bone volume with the locally segmented data set would still result in a trabecular bone volume that was >40% less than the trabecular bone volume resulting from the local segmentation algorithm (Fig. 6A).
At the optimal global threshold, where the summed difference in cortical and trabecular volume between globally and locally segmented data sets was smallest, the globally segmented data set showed a cortex that was thicker than the cortex of the locally segmented data set while less trabecular bone was detected. Compared with the globally segmented data set of the high-quality scan, the globally segmented data set of the in vivo scan showed few differences. The trabecular structure seemed slightly more fragmented (Figs. 6B3 and 6C3).
Segmentation of μCT data sets is not a trivial issue, and its complexity is often neglected or underestimated. In this paper, we have tried to clarify this issue by comparing different segmentation techniques and by introducing a new segmentation algorithm using local threshold values.
Applying this local threshold method gave very accurate results. For high-quality scans, the segmented data set was a nearly exact representation of the real bone, as could be seen by comparison with histological sections (Fig. 3). All trabeculae, both thick and thin, were represented with the correct thickness. The structural integrity of the trabecular network was represented correctly as well, and no connections between trabeculae were missed. Applying a global threshold performed almost equally, but some of the thinner connections between trabeculae were lost. These connections could be recovered by adjusting the global threshold value, but this would result in thickening of the trabeculae and thus in an overestimation of the bone volume.
The global segmentation method could only give such a good result given prior knowledge about the real volume of the bone, a prerequisite that is not needed for the automatic local threshold algorithm. In many situations, information about the volume of a bone sample is not present or is difficult to get. When scanning core biopsy specimens, the bone volume can only be obtained after a cumbersome measurement procedure based on Archimedes' principle. For entire bones, it is even practically impossible to get the real volume of the bone, which excludes the global segmentation method based on knowledge about bone volume.
Another situation in which it is impossible to obtain the real volume of a bone is when animals are scanned in vivo. The added value of scanning living animals lies in the fact that the longitudinal study design allows comparison of scans of different time-points of the same animal, such that temporal changes in bone architecture can be followed at the level of single trabeculae.(6) Because radiation load on living tissues should be as small as possible, the quality of the scans are limited. The resulting images contain more noise and have a lower resolution than in conventional μCT. This situation places high demands on the method of thresholding. Although the influence of noise seems rather small on both local and global segmentation methods, global thresholding methods fail to give a good representation of the bone. This is partly caused by the relative low resolution of the system that makes thin structures appear less dense. Besides, the result of global thresholding will also be affected by differences in mineralization between cortical and trabecular bone (Fig. 6). Thus, in vivo scanning is more powerful when combined with local segmentation techniques.
This study indicates that when good-quality scans are made at high resolution and the samples have a homogenous structure, a global threshold performs just as well as the local threshold method. A typical situation that satisfies these conditions is when studies are undertaken in which bone biopsy specimens are scanned at high resolution and compared. The convenience and speed of applying a global threshold makes using this method very tempting. However, the implications of the choice of global threshold value should not be underestimated. In most studies, bone biopsy specimens of subjects with a certain pathological condition or biopsy specimens resulting from some intervention study are compared with controls. The possible changes in bone morphology and bone mineralization caused by these pathologies or interventions will affect the distribution of densities of the scans and thus might interact with the choice of threshold value. This problem can be reduced when the real volume of the samples are known. However, often this volume is not known. In general, using a global threshold might result in uncertainties about which part of the measured difference between groups are caused by the choice of threshold value. Because the result of the local threshold method is not influenced by changes in mineralization and is less sensitive to changes in architecture (especially to changes in the amount of thick versus thin trabeculae), using this method could reduce the uncertainty about measured differences between groups. Although the results presented in this study supports this assumption, more tests are needed to see if the local segmentation method is truly better at predicting group differences.
Local segmentation of high-resolution scans resulted in accurate representations of the volume. However, when resolution was decreased, the local segmentation method started to overestimate the volume of the scan. This phenomenon is related to the smearing out of thin structures. The lower the resolution, the more trabeculae are smeared out around their real edge, and compensation starts to become problematic. Global methods were also affected by this phenomenon, resulting in a strong increase in trabecular thickness with decreasing resolution (Fig. 4B). The average increase in trabecular thickness resulted in extra volume being added to the thickened trabeculae. For the GlobalArch method, in which the volume of the data sets was fixed, this extra volume was balanced by an equal decrease in the volume of thinner trabeculae and thus to changes in structure. This is clearly reflected in the change of structural parameters like connectivity density and especially SMI for this method (Fig. 4). As indicated by the less severe changes in SMI and connectivity, the GlobalHist method favored structural integrity above volume. As a consequence, there was a strong rise in trabecular thickness and especially in volume fraction. The local segmentation combined the strong points of both global threshold methods, because it combined preservation of structural integrity with good representation of bone volume.
A further decrease in resolution to a voxel size of 53 μm resulted in unreliable results for all segmentation methods. At this resolution, average trabeculae have a real thickness of less than two or three voxels, which is not sufficient for good representation of the bone. Still the results show that the LocalAuto method gave better volume estimates than the GlobalHist method and a better structural integrity than the GlobalArch method. A study by Laib and Ruegsegger(27) tried to extract volume-related parameters from human in vivo scans at much lower resolutions than were used in this study (165 μm voxel size). Their methods gave surprisingly good reliability values for the measured parameters, comparable with the global methods in this paper. However, the low resolution made it impossible to extract the exact structure.
The effects of noise on the different segmentation methods could mostly be explained by the effects of the smoothing filter needed to remove this noise. Filtering the noisy data sets blurred out the smallest details and thinnest trabeculae. Logically, this had the greatest influence on those methods that were most sensitive to thin structures. Blurring the thinnest structures did not influence the GlobalArch method, which favored the detection of thick trabeculae above the detection of thin trabeculae, because it already failed to detect the thin trabeculae in the low noise situation. The LocalAuto method on the other hand, detected both thick and thin trabeculae and was therefore very sensitive to blurring of the thin trabeculae. As a result, the thickness of the blurred thin trabeculae was overestimated, and the average thickness increased. The thickness measure was affected less for samples with mainly thick trabeculae than for samples with both thin and thick trabeculae, explaining the decrease in reliability of the trabecular thickness measure for the LocalAuto method when high noise levels were added to the samples (Table 5).
Overlaying the globally thresholded data sets with the data sets obtained with the local threshold algorithm showed an interesting phenomenon (Fig. 5). The local segmentation method detected more bone in the center of the bone sample, whereas the global method resulted in thicker structures on the outside of the bone sample. Imperfect beam hardening correction in a reconstructed data set generally causes the outside of a cylindrical object to appear denser than the inside. Using a global threshold, therefore, resulted in overestimation of the thickness of the trabeculae in the outer section of a bone sample, whereas it underestimated the thickness on the inside of the sample. Because this difference of apparent density did not influence the local edges of the bone in a reconstructed data set, beam hardening artifacts have little influence on the local segmentation algorithm, as is shown with the overlaid cross-sections (Fig. 5).
In conclusion, the local threshold method gives a nearly exact representation of a scanned bone at high resolutions without the need for a priori knowledge about the volume of the bone. When analyzing high-resolution scans of homogenous structures, for example, bone biopsy specimens, the performance of global threshold methods perform similarly to the local threshold method. As soon as the scanned structures are not homogenous and include both thick cortices and thin trabeculae or when scan resolution is relatively low, the local threshold method outperforms the global methods. This makes the local threshold method ideally suited, and perhaps even crucial, for use with in vivo μCT.
This work was supported by European Union Grant QLRT-1999–02024 (MIAB).
- 12002 Biaxial failure behavior of bovine tibial trabecular bone. J Biomech Eng 124: 699–705., ,
- 21989 The direct examination of three-dimensional bone architecture in vitro by computed tomography. J Bone Miner Res 4: 3–11., , , ,
- 32003 Trabecular bone tissue strains in the healthy and osteoporotic human femur. J Bone Miner Res 18: 1781–1788., , ,
- 42000 Three-dimensional morphometry of the L6 vertebra in the ovariectomized rat model of osteoporosis: Biomechanical implications. J Bone Miner Res 15: 1981–1991., , , , ,
- 52001 A three-dimensional simulation of age-related remodeling in trabecular bone. J Bone Miner Res 16: 688–696., ,
- 62004 Detecting and tracking local changes in the tibiae of individual rats: A novel method to analyse longitudinal in vivo micro-CT data. Bone 34: 163–169., , , , , , , ,
- 72003 Noninvasive in vivo monitoring of bone architecture alterations in hindlimb-unloaded female rats using novel three-dimensional microcomputed tomography. J Bone Miner Res 18: 1622–1631., , , , , ,
- 82002 Assessing the accuracy of high-resolution X-ray computed tomography of primate trabecular bone by comparisons with histological sections. Am J Phys Anthropol 118: 1–10., ,
- 91998 Morphometric analysis of human bone biopsies: A quantitative structural comparison of histological sections and micro-computed tomography. Bone 23: 59–66., , , , , ,
- 101998 Mechanical properties of ewe vertebral cancellous bone compared with histomorphometry and high-resolution computed tomography parameters. Bone 22: 651–658., , , , , , ,
- 111998 Analysis of trabecular microarchitecture of human iliac bone using microcomputed tomography in patients with hip arthrosis with or without vertebral fracture. Bone 23: 163–169., , , ,
- 122002 The influence of microcomputed tomography threshold variations on the assessment of structural and mechanical trabecular bone properties. Bone 31: 107–109., , ,
- 131996 Resolution dependency of microstructural properties of cancellous bone based on three-dimensional mu-tomography. Technol Health Care 4: 113–119., , , , ,
- 142000 An investigation of segmentation methods and texture analysis applied to tomographic images of human vertebral cancellous bone. J Microsc 197: 305–316., , , , ,
- 151999 Accuracy of cancellous bone volume fraction measured by micro-CT scanning. J Biomech 32: 323–326., ,
- 161990 Evaluation of a microcomputed tomography system to study trabecular bone structure. J Orthop Res 8: 833–842., , , ,
- 171998 Segmentation techniques for analysis of bone by three-dimensional computed tomographic imaging. Technol Health Care 6: 351–359.
- 182002 Segmentation of cancellous bone from high-resolution computed tomography images: Influence on trabecular bone measurements. IEEE Trans Med Imaging 21: 354–362., , ,
- 192003 Topology-based orientation analysis of trabecular bone networks. Med Phys 30: 158–168., ,
- 202002 New model-independent measures of trabecular bone structure applied to in vivo high-resolution MR images. Osteoporos Int 13: 130–136., , ,
- 211997 Correlation of trabecular bone structure with age, bone mineral density, and osteoporotic status: In vivo studies in the distal radius using high resolution magnetic resonance imaging. J Bone Miner Res 12: 111–118., , , , , ,
- 221997 In vivo assessment of trabecular bone structure at the distal radius from high-resolution magnetic resonance images. Med Phys 24: 585–593., , ,
- 232002 Processing and analysis of in vivo high-resolution MR images of trabecular bone for longitudinal studies: Reproducibility of structural measures and micro-finite element analysis derived mechanical properties. Osteoporos Int 13: 278–287., ,
- 241994 Non-invasive bone biopsy: A new method to analyse and display the three-dimensional structure of trabecular bone. Phys Med Biol 39: 145–164., ,
- 251996 In vivo reproducibility of three-dimensional structural properties of noninvasive bone biopsies using 3D-pQCT. J Bone Miner Res 11: 1745–1750., , ,
- 261996 In vivo assessment of trabecular bone structure at the distal radius from high-resolution computed tomography images. Phys Med Biol 41: 495–508., , ,
- 271999 Comparison of structure extraction methods for in vivo trabecular bone measurements. Comput Med Imaging Graph 23: 69–74.,
- 281997 Ridge number density: A new parameter for in vivo bone structure analysis. Bone 21: 541–546., , ,
- 291999 The Image Processing Handbook. CRC Press, Boca Raton, FL, USA.
- 301986 A computational approach to edge detection. IEEE Trans Pattern Analysis Machine Intelligence 8: 679–698.
- 31American Society for Testing and Materials 1997 Standard Guide for Computed Tomography (CT) Imaging: ASTM Standards, vol. E1440–97. American Society for Testing and Materials, Philadelphia, PA, USA.
- 321997 Multimodality image registration by maximization of mutual information. IEEE Trans Med Imaging 16: 187–198., , , ,
- 331997 A new method for the model-independent assessment of thickness in three-dimensional images. J Microsc 185: 67–75.,
- 341993 Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions. Bone 14: 173–182.,
- 351997 Quantification of bone microarchitecture with the structure model index. Comput Methods Biomech Biomed Engin 1: 15–23.,