There is often no readily available geometric model for non-destructive testing of samples with complex geometries, such as a CAD model or a surface representation. Photogrammetry or laser scanning allows recovering this information by generating point clouds that describe the geometry. With immersed boundary methods, particularly the finite cell method (FCM), it is possible to overcome the tedious task of surface reconstruction and mesh generation by enabling direct simulations on geometries defined by point clouds [1]. Nevertheless, information about the material of the sample and possible defects or anomalies still needs to be discovered. For detecting defects characterized by a high contrast in the impedance, such as cracks or voids, the density scaling version of the full waveform inversion has proven to be particularly successful [2]. We extend our framework for full waveform inversion to directly incorporate geometries defined by point clouds and iteratively reveals the internal structure of a sample. To this end, we use the spectral cell method (SCM), a combination of the FCM and the spectral element method [3], and implicit-explicit time integration [4] to efficiently solve the forward and backward wave problems in the corresponding adjoint optimization. We will demonstrate the proposed approach's applicability, efficiency, and accuracy on various 2D and 3D examples in non-destructive testing for the acoustic and elastic wave equations. [1] Kudela, László & Kollmannsberger, Stefan & Almac, Umut & Rank, Ernst (2020) Direct Structural Analysis of Domains Defined by Point Clouds, Computer Methods in Applied Mechanics and Engineering, 10.1016/j.cma.2019.112581 [2] Bürchner, Tim & Kopp, Philipp & Kollmannsberger, Stefan & Rank, Ernst (2023) Immersed boundary parameterizations for full waveform inversion, Computer Methods in Applied Mechanics and Engineering, 10.1016/j.cma.2023.115893 [3] Joulaian, Meysam & Eisenträger, Sascha & Gabbert, Ulrich & Düster, Alexander (2014) Finite and spectral cell method for wave propagation in heterogeneous materials, Computational Mechanics, 10.1007/s00466-014-1019-z [4] Faßbender, Christian & Bürchner, Tim & Kopp, Philipp & Rank, Ernst & Kollmannsberger, Stefan, (2023) Implicit-Explicit Time Integration for the Immersed Wave Equation, preprint submitted to Computers and Mathematics with Applications, 10.48550/arXiv.2310.14712