Introduction: Accurately detecting cracks is crucial for assessing the health of materials. Manual detection methods are time-consuming, leading to the development of automatic detection techniques based on image processing and machine learning. These methods utilize morphological image processing and material deformation analysis through Digital Image or Volume Correlation techniques (DIC/DVC) to identify cracks. The strain field derived from DIC/DVC tends to be noisy. Traditional denoising methods sacrifice spatial resolution, limiting their effectiveness in capturing abrupt structural deformations such as fractures. Method: In this study, a novel DVC regularization method is proposed to obtain a sharper and less noisy strain field. The method minimizes the total variation of spatial strain field components based on the assumption of approximate strain constancy within material phases. Results: The proposed methodology is validated using simulated data and actual 4D $\mathsf{\mu }$-CT experimental data. Compared to classical denoising methods, the proposed DVC regularization method provides a more reliable crack detection with fewer false positives. Conclusions: These results highlight the possibility of estimating a low-noise strain field without relying on the spatial smoothness assumption, thereby improving accuracy and reliability in crack detection.

Digital volume correlation (DVC) is a 3D image-based technique for displacement and strain computation. Traditionally, both (digital image correlation) DIC and DVC are methods based on two individual time frames; the estimation of the displacement and strain field is done using one reference and one moving frame as input. However, dynamic experiments generate more than two temporal frames. Therefore, with classical DVC techniques, only a subset of the available data is used. In this study, we propose a novel DVC method that can rely on more than two frames for the displacement and strain computation. The proposed method aims to be as general as possible; there is no constraint regarding the nature or the rate of the displacement (e.g., cyclic or linear). The aim of this method is to impose a temporal regularization that improves the self-consistency of the algorithm. The multi-frame DVC improves the quality of the registration in challenging situations. As an example, we investigate the dissolution of a pharmaceutical tablet in water, which undergoes three processes: swelling, gel formation, and material erosion. The accuracy of the registration—quantified by the sum of square differences (SSD)—has improved by 23% on an average with respect to the classical two-frame method. Classical DVC methods fail in registering images with structures that change appearance through time, such as the tablet that, in contact with water, reacts chemically, changing phase and becoming a gel. Moreover, we proved that multi-frame DVC is more robust in registering images with severe but realistic motion artefacts. As an example for this case, we apply the method to a series of μ-CT datasets of aluminum foam during a compression experiment. As seen with the tablets, we are in a situation where the appearance of the structures in the images changes through time, but in this case it is because of motion artefacts. Finally, the use of more than two frames makes the method more robust against noisy images, with an average improvement of 35% in registration accuracy obtained using the three-frame DVC method compared to the classical two-frame DVC method.