Comparison of Ventricular Geometry for Two Real-Time 3D Ultrasound Machines with Three-dimensional Level Set Elsa D. Angelini, Rio Otsuka, Shunishi Homma, Andrew F. Laine The Heffner Biomedical Imaging Lab Department of Biomedical Engineering, Columbia University, New York, NY, USA Average error (1) = 0.86%, (2) = 1%. Gaussian kernel for (3) lead to the smallest error (0.03%). Anisotropic diffusion (3-4) reduces measurement errors for first-order interpolation kernels.RESULTS Computation Times Measurements of cylinder diameter were performed manually by a user on B-scan slices for different data processing: (1) Original data (scale=1); (2) Original data (scale=2); (3) Original data (scale=2 with smoothing);(4) Diffused data (thresholds=5, 10 iterations) (scale=1); (5) Diffused data (variable threshold, 10 iterations) (scale=1). INTRODUCTION Three-dimensional ultrasound machines based on matrix phased-array transducers are gaining predominance for real-time dynamic screening in cardiac and obstetric practice. Comparison of the quantification of cardiac function from two matrix-phased array 3D ultrasound machines: RT3D machine from Volumetrics Medical Imaging. Entire cardiac volume is acquired with an array of 64  64 elements and a downsampling factor of 4 between receive/transmit modes. Sonos 7500 machine from Philips Medical Systems. Four cardiac sub-volumes and no downsampling.DATA RT3D data were acquired by a RT3D Volumetrics© machine using acquisition parameters identical to clinical settings. Phantom object: Two cylinders (diameter = 10 mm) with different signal-to-noise ratios (SNR). Our experiments focused on a SNR of 2dB. In-vitro phantom: myocardium muscle sample in a water tank. Clinical data: Echocardiographic volume of a healthy volunteer. DISCUSSIO N Downscaling with smoothing and anisotropic diffusion can efficiently reduce speckle noise and sampling artifacts. Anisotropic diffusion with variable gradient threshold significantly improves image quality. Manual tracing on denoised RT3D data showed high spatial measurement accuracy for scales 1 and 2 on phantom data. Anisotropic diffusion is less computational expensive than spatial Brushlet denoising and provided similar visual improvement of image quality. Anisotropic diffusion lowers the order of the interpolation kernels for scan conversion enabling optimization of data processing for real-time denoising and visualization. SEGMENTATION Homogeneity-based Implicit Deformable Model Segmentation algorithm: Initially proposed by Chan and Vese [1], and derived from the Mumford- Shah functional [2]. The segmentation of a volume data I is performed via deformation of an initial curve C to minimize the following energy functional: REFERENC ES 1.O. V. Ramm and S. W. Smith, "Real time volumetric ultrasound imaging system." Journal of Digital Imaging, Vol. 3, No. 4, pp , Q. Duan, E. D. Angelini, T. Song and A. Laine, "Fast interpolation algorithms for real-time three-dimensional cardiac ultrasound", IEEE EMBS Annual International Conference, pp , Cancun, Mexico, Y. Yu and S. T. Acton, "Speckle reducing anisotropic diffusion." IEEE Transactions on Image Processing, Vol. 11, No. 11, pp , P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion." IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 12, No. 7, pp , J. Weickert, B. M. t. H. Romeny and M. A. Viergever, "Efficient and reliable schemes for nonlinear diffusion filtering." IEEE Transactions on Image Processing, Vol. 7, No. 3, pp , E. Angelini, A. Laine, S. Takuma, J. Holmes and S. Homma, "LV volume quantification via spatio-temporal analysis of real-time 3D echocardiography." IEEE Transactions on Medical Imaging, Vol. 20, No. 6, pp , CONCLUSI ON A fast 3D scan conversion algorithm combined with smoothing and anti-aliasing was introduced for RT3D ultrasound. A fast denoising method based on anisotropic diffusion with varying gradient threshold was described for RT3D ultrasound. Quantitative assessment was performed, showing high spatial accuracy of RT3D ultrasound. Cylindrical phantom object. (a) Anisotropic diffusion with a fixed gradient threshold. (b) Anisotropic diffusion with a variable gradient threshold. Scan conversion result of Phantom (a) Scale =1 (b) Scale =2 (c) Scale=2 with smoothing. Endocardiographic data (a) Original data. (b) Anisotropic diffusion with a variable gradient threshold. (c) Brushlet threshold in transform space. in-vitro myocardium tissue sample. (a) Original data. (b) Data after anisotropic diffusion with a variable gradient threshold. RESULTS METHODOLOGY 2.2 Anisotropic Filtering Original framework of Perona and Malik with the diffusion function proposed by Weickert. The parameter λ serves as a gradient threshold. A linear model is proposed for iterative adaptivity: ACKNOWLEDGEMENTS The authors would like to thank to Dr. Homma, Dr. Hirata and Dr. Otsuka from the Echocardiography Laboratories at Columbia Presbyterian Hospital for providing the ultrasound data sets. Data Matrix size in spherical coordinate s Scale of scan conversio n Smoothin g option for scan conversio n Matrix size in Cartesian coordinates Diffusion computati on time for one iteration (seconds) Scan conversio n computati on time (seconds) Phantom object 64x64x3731No389x389x Cardiac tissue 64x64x2581No274x274x Clinical exam 64x64x4381No454x454x Clinical exam 64x64x4382No228x228x Clinical exam 64x64x4382Yes228x228x Clinical exam 64x64x4381No454x454x Measurements of Object Dimensions of a Cylinder Numerical implementation: Implementation with a 3D level set framework. implicit numerical scheme for unconditional stability. Parameters controlled and optimized: Smoothness: Yes/No Scale: [original voxel size: (0.308 mm) 3 ] Filter width (1/2/3) (optimized in previous studies) - c 0 and c 1 = average of the volume data I inside and outside of the curve C. - L(C) = length of the curve. - A(C) = area of the curve.