Contourlet-based active contour model for PET image segmentation.

PURPOSE: PET-guided radiation therapy treatment planning, clinical diagnosis, assessment of tumor growth, and therapy response rely on the accurate delineation of the tumor volume and quantification of tracer uptake. Most PET image segmentation techniques proposed thus far are suboptimal in the presence of heterogeneity of tracer uptake within the lesion. This work presents an active contour model approach based on the method of Chan and Vese ["Active contours without edges," IEEE Trans. Image Process. 10, 266-277 (2001)] designed to take into account the high level of statistical uncertainty (noise) and to handle the heterogeneity of tumor uptake typically present in PET images. METHODS: In the proposed method, the fitting terms in the Chan-Vese formulation are modified by introducing new input images, including the smoothed version of the original image using anisotropic diffusion filtering (ADF) and the contourlet transform of the image. The advantage of utilizing ADF for image smoothing is that it avoids blurring the object's edges and preserves the average activity within a region, which is important for accurate PET quantification. Moreover, incorporating the contourlet transform of the image into the fitting terms makes the energy functional more effective in directing the evolving curve toward the object boundaries due to the enhancement of the tumor-to-background ratio (TBR). The proper choice of the energy functional parameters has been formulated by making a clear consensus based on tumor heterogeneity and TBR levels. This cautious parameter selection leads to proper handling of heterogeneous lesions. The algorithm was evaluated using simulated phantom and clinical studies, where the ground truth and histology, respectively, were available for accurate quantitative analysis of the segmentation results. The proposed technique was also compared to a number of previously reported image segmentation techniques. RESULTS: The results were quantitatively analyzed using three evaluation metrics, including the spatial overlap index (SOI), the mean relative error (MRE), and the mean classification error (MCE). Although the performance of the proposed method was analogous to other methods for some datasets, overall the proposed algorithm outperforms all other techniques. In the largest clinical group comprising nine datasets, the proposed approach improved the SOI from 0.41±0.14 obtained using the best-performing algorithm to 0.54±0.12 and reduced the MRE from 54.23±103.29 to 0.19±16.63 and the MCE from 112.86±69.07 to 60.58±18.43. CONCLUSIONS: The proposed segmentation technique is superior to other representative segmentation techniques in terms of highest overlap between the segmented volume and the ground truth∕histology and minimum relative and classification errors. Therefore, the proposed active contour model can result in more accurate tumor volume delineation from PET images.

An efficient piecewise modeling of ECG signals based on Hermitian basis functions.

In this paper, a new piecewise modeling for approximation of ECG signal is presented. Most of the modeling methods are focused to obtain the best approximation of the entire ECG signal. The proposed method exploits the importance of different intervals of ECG signals, in particular QRS complex, by performing a segmented based modeling using Hermitian basis functions. This yields to weighting the approximation error of each segment based on its importance throughout the ECG complex. As the result shows the total error obtained in this method is almost halved in comparison with similar non-segmented method. This has a great impact in modeling the heart arrhythmias where a small error could mislead the diagnosis. The presented method uses only the 5th order Hermitian basis functions which considerably reduce the total parameters needed to represent the ECG signal in comparison with other Hermitian based methods.