This paper presents two new 3D curvelet transforms which are built as extensions of the 2D first

generation curvelet transform. The first one, called the RidCurvelet, is especially well designed

for representing 2D surfaces in a 3D space while the second one, the BeamCurvelet, is better

adapted to represent 1D filaments in 3D space. We show that these 3D curvelet transforms can

be built using existing 3D transforms, the 3D wavelet transform, the 3D ridgelet transform,

and the 3D beamlet transform. We illustrate the applicability of these transforms on various

examples such as the detection of linear structures and planar surfaces, as well as on denoising

and inpainting.