AbstractThe computational complexity of wave-based image ultrasound transmission reconstructionsis very high especially in 3D. Hence, ray-based approximations are often used. Bent rayapproaches like the fast marching method are time-consuming in comparison to the straightray approximation. The B ́ezier curve technique for refraction approximation, introduced byPerez-Liva et al., could be a compromise between computational effort and image quality. Inthis work, the method was extended to 3D and an evaluation on two 3D datasets was carriedout. The first dataset was simulated with the k-wave toolbox, with hemispherically arrangedemitters and receivers and a sound speed inhomogeneity. With a mean squared error of 9.98m/s the method produces similar results as the fast marching method (11.85 m/s). The objectsize is represented better in comparison to the straight ray method. Applied to real data ofthe KIT 3D USCT both methods performed similarly. The object size was better preservedusing bent ray methods. The B ́ezier bent ray method shows first promising results in 3D asit leads to similar results than the fast marching method
