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Image Registration
Published in R. Suganya, S. Rajaram, A. Sheik Abdullah, Big Data in Medical Image Processing, 2018
R. Suganya, S. Rajaram, A. Sheik Abdullah
The choice of the geometric transformation model is crucial to the success of a registration algorithm and is highly dependent on the nature of the data to be registered. Usually the geometric transformation is divided into rigid and non-rigid classes. The rigid transformation is the simplest one, and it can be defined by 6 parameters or degrees of freedom: 3 translation and 3 rotational parameters. In rigid transformations, the distance between corresponding points are preserved. The non-rigid transformation class includes the similarity transformation (translation, rotation and scaling), affine transformation map straight lines to straight lines while the parallelism is preserved. Projective transformations map straight lines to straight lines but parallelism is in general not preserved and the curved transformation is also commonly referred to as deformable, elastic or fluid transformation (Francisco et al. 2012). A rigid transformation involves only rotation and translation. It is the most important geometric transformation among all registration techniques. This has supported the work using MI based registration followed by rigid body transformation.
Image Registration
Published in Elizabeth Berry, A Practical Approach to Medical Image Processing, 2007
There are four types of geometrical transformation, and these are shown in Figure 8.4: Rigid—In a rigid transformation all parts of the object are assumed to move as a whole, and there is no movement of one part of the object relative to any other. This may be appropriate to a solid object like the human skull, but not a deformable one such as the liver. A rigid transformation could be a translation (linear movement) as indicated in Figure 8.5b, where the initial position is shown dashed, or a rotation as seen in Figures 8.5c and d. Affine—In an affine transformation, straight lines remain straight and parallel lines remain parallel. Angles can change, too, as happens in a scaling (Figure 8.6b) or shearing (Figure 8.6c) deformation. Note that the rigid transformation is a subset of the affine transformation. Projective—Projective transformations (Figure 8.7) include further deformation. Straight lines remain straight but in projective transformations parallel lines need not remain parallel. Curved or elastic—Curved or elastic transformations (Figure 8.8) are most appropriate for deformable tissue. In contrast with all the other transformations, straight lines need not remain straight. The curved or elastic transformation is the most general case of transformation. It should be used with care, and never applied to structures known to be rigid.
Grid graph-based large-scale point clouds registration
Published in International Journal of Digital Earth, 2023
Yi Han, Guangyun Zhang, Rongting Zhang
Points-based registration uses mathematical rules instead of feature descriptor to identify corresponding pairs. There are some point-based methods in the literature which do not follow the paradigm of feature descriptors calculation and feature matching. For example, iterative closest point (ICP) (Besl and McKay 1992) is the most extensively used point cloud registration approach. ICP heuristically chooses the closest point in Euclidean space as a correspondence; then, a rigid transformation is fitted by using these correspondences. Thus, ICP searches for local optimum of initial transformation by alternating between finding the correspondences and computing the best transformation given these correspondences. Many variants, such as point-to-plane, plane-to-plane and normal, are proposed to improve one or more constraints of ICP. ICP is still sensitive to partial overlaps, and ICP will almost always fail in 3D scan sequences with partial overlaps. Many methods introduce robust transformation estimation technique to improve the robustness of ICP, such as Trimmed ICP (Chetverikov, Stepanov, and Krsek 2005), and Go-ICP (Yang, Li et al. 2016). ICP and its variant high relies on the initial transformation parameter.
Anomaly detection for fabricated artifact by using unstructured 3D point cloud data
Published in IISE Transactions, 2023
Chengyu Tao, Juan Du, Tzyy-Shuh Chang
Under this setting, the projection of on the parametric base plane is where and are the coordinates of the u-axis and v-axis in respectively, and Notably, R and t are the rotation and translation of the rigid transformation from the coordinate frame to the frame
Fast Robust Location and Scatter Estimation: A Depth-based Method
Published in Technometrics, 2023
Maoyu Zhang, Yan Song, Wenlin Dai
Affine equivariance makes the analysis independent of any affine transformation of the data. For any nonsingular p × p matrix A and vector v, the estimators and are affine equivariant if they satisfy where . The projection depth has been shown affine equivariant (Zuo and Serfling 2000a; Zuo 2006), that is the depth value does not vary through affine transformation for any sample, and hence the indexes of samples forming the trimmed region remain the same. Consequently, is obviously affine equivariant. For , a similar property holds for rigid transformation (Mosler and Mozharovskyi 2022), which is a bit more restrictive than the affine transformation. For high dimensional situations, the affine equivariance may be less important under nonstandard data contamination such as componentwise outliers (Alqallaf et al. 2009).