In the last decade, the fractal dimension has become a popular parameter to characterize image textures. Also in radiographs, various procedures have been used to estimate the fractal dimension. However, certain characteristics of the radiographic process, e.g., noise and blurring, interfere with the straightforward application of these estimation methods. In this study, the influence of quantum noise and image blur on several estimation methods was quantified by simulating the effect of quantum noise and the effect of modulation transfer functions, corresponding with different screen-film combinations, on computer generated fractal images. The results are extrapolated to explain the effect of film-grain noise on fractal dimension estimation. The effect of noise is that, irrespective of the noise source, the fractal dimension is overestimated, especially for lower fractal dimensions. On the other hand, blurring results in an underestimation of the dimensions. The effect of blurring is dependent on the estimation method used; the dimension estimates by the power spectrum method are lowered with a constant value, whereas the underestimation by the methods working in the spatial domain is dependent on the given dimension. The influence of the MTF and noise on fractal dimension estimation seriously limits the comparability of fractal dimensions estimated from radiographs which differ in noise content or MTF. Only when the power spectrum method is used, it is possible to correct for the influence of different MTFs of screen-film combinations. It is concluded that only when using the same object-focus distance, the same exposure conditions, the same digitizer at the same resolution, can fractal dimensions as estimated in radiographs be reliably compared.

This paper outlines a strategy to validate multiple imputation methods. Rubin's criteria for proper multiple imputation are the point of departure. We describe a simulation method that yields insight into various aspects of bias and efficiency of the imputation process. We propose a new method for creating incomplete data under a general Missing At Random (MAR) mechanism. Software implementing the validation strategy is available as a SAS/IML module. The method is applied to investigate the behavior of polytomous regression imputation for categorical data.

Tissue structures, represented by textures in radiographs, can be quantified using texture analysis methods. Different texture analysis methods have been used to discriminate between different aspects of various diseases in primarily x rays of chest, bone, and breasts. However, most of these methods have not specifically been developed for use on radiographs. Certain characteristics of the radiographic process, e.g., noise and blurring, influence the visible texture. In order for a texture analysis method to be able to discriminate between different underlying textures, it should not be too sensitive for such processes as image noise and blur. In this study, we investigated the sensitivity of four different texture analysis methods for image noise and blur. First, a baseline measurement was performed of the discriminative performance of the Spatial Gray-Level Dependence method, the Fourier Power Spectrum, the Fractal Dimension, and the Morphological Gradient Method on images, which were not affected by radiographic noise and blur. Two types of images were used: fractal and Brodatz. Whereas the Brodatz images represent very different textures, the differences between the fractal images are more gradual. We assume that the behavior of the different texture analysis methods on the fractal images is representative for their performance on radiologic textures. On these types of images we simulated the effect of four different noise levels and the effect of two different modulation transfer functions, corresponding with different screenfilm combinations. The influence on the discriminative performance of the four texture analysis methods was evaluated. The influence of noise on the discriminative performance is, as expected, dependent on the image type used; the discrimination of more gradually different images, such as the fractal images, is already lowered for relatively low noise levels. In contrast, when the images are more different, only high noise levels decrease the discriminative performance. The discriminative power of the Morphological Gradient Method is least affected by image blur. We conclude that the discriminative performance of the Morphological Gradient Method is superior to that of other methods in circumstances which mimic the conditions prevailing in radiographs.

No abstract

The strength of bone is determined not only by bone density but also by structure. Therefore, quantification of the structure in radiographs by texture parameters may result in a better prediction of fracture risk. Since in radiographs density and structure are strongly correlated, the predictive power of texture parameters should be corrected for the influence of BMD to determine the additional information conveyed by these parameters. In this study, we evaluated the predictive power of various texture parameters based on the Grey-Level Dependence Method and the Morphological Gradient Method. This study was performed on 67 vertebrae obtained from 20 male and 12 female human cadaver thoracolumbar spines. BMD and area of the vertebral body were determined from QCT images and texture parameters were derived from direct magnification (DIMA) radiographs. The fracture force, measured under conditions simulating the in vivo situation, was corrected with the area of the vertebra to yield the fracture stress (FS). Results of the study indicate that BMD correlates significantly with FS r = 0.82 (P < 0. 001, n = 24) and r = 0.94 (P < 0.001, n = 43) for female and male vertebrae, respectively. Correlation coefficients of the investigated texture parameters were as high as 0.80 (P < 0.001) and 0.67 (P < 0.001) for the female and male vertebrae, respectively. Multiple regression analysis showed that in female vertebrae, the addition of one texture parameter to BMD results in a better prediction of strength. The multiple correlation coefficient was 0. 87 (P < 0.001) in this case. In male vertebrae, BMD was the best predictor of fracture stress. These results suggest that texture parameters, as measured in magnification radiographs, can predict bone strength. Whereas in all cases BMD is the best single predictor of bone strength, for women texture parameters contain useful additional information.