IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE. VOL. II. NO. 6. JUNE 1989 567 Principal Warps: Thin-Plate Splines and the Decomposition of Deformations

Citations in the corpus

• All You Need Is Boundary: Toward Arbitrary-Shaped Text Spotting (2019, background): “(Liu et al. 2018; Li, Wang, and Shen 2017; He et al. 2018; Busta et al. 2017) share a common idea: text region features are extracted for subsequent recognizer.”
• Spatial Transformer Networks (2015, methodology): “ all use bilinear sampling, but variants use different transformation functions: an affine transformation (Aff), projective transformation (Proj), and a 16-point thin plate spline transformation (TPS) [2]. The CNN models include two max-pooling layers. All networks have approximately the same number ”
• Bird Species Categorization Using Pose Normalized Deep Convolutional Nets (2014, neutral): “The above transformations Name W (y,w) Solve w∗t p # Pts Translation y = yt +T T = µi−µt |S| ≥ 1 2D Similarity y = sRyt + t R =V diag(1,det(VU>))U>, s = tr(M̄>i RM̄t) tr(M̄>t M̄t) , T = µi− sRµt |S| ≥ 2 2D Affine y = Ayht A = MiM h> t (M h t M h> t ) −1 |S| ≥ 3 Table 1: Computation of warping…”
• Learning Video Object Segmentation from Static Images (2016, positive): “To simulate the noise of the previous frame output, during offline training, we generate input masks by deforming the annotations via affine transformation as well as non-rigid deformations via thin-plate splines [4], followed by a coarsening step (dilation morphological operation) to remove details”
• Automatic construction of 3-D statistical deformation models of the brain using nonrigid registration (2003, methodology): “used deformation maps based on thin-plate splines to study the shape variability in patients with schizophrenia and normal controls [30], [31].”
• Iris Segmentation Using Geodesic Active Contours (2009, methodology): “In the future, the center of the iris and its radius can be coarsely estimated using a faster technique and the GAC may be initialized near the estimated iris boundary to determine the exact shape of the iris.”
• Thin-Plate Spline Motion Model for Image Animation (2022, methodology): “According to the derivation in [2] , the k TPS transformation is obtained as follows:”
• A Multi-Object Rectified Attention Network for Scene Text Recognition (2019, methodology): “Using thin-plate-spline [4] to back propagate the gradients, RARE is end-to-end optimized.”
• Efficient shape matching using shape contexts (2005, methodology): “The thin plate spline (TPS) model [ 32 ] is used to create these distortions.”
• Trajectory-Based Skill Learning Using Generalized Cylinders (2018, methodology): “Their proposed trajectory transfer method is based on the classic Thin Plate Splines (TPS) registration algorithm (Bookstein, 1989) extended to 3D Cartesian space, which we also utilize here.”
• Active Contours (2000, background): “Splines, common in computer graphics, have also been used in computer vision for some years, for shape-warping (Bookstein, 1988), representing corners and edges in static scenes (Medioni and Yasumoto, 1986; Arbogast and Mohr, 1990) and for shape approximation (Menet et al.”
• A new point matching algorithm for non-rigid registration (2003, methodology): “Furthermore, we develop a specific algorithm—TPS– RPM—wherein we adopt the thin-plate spline (TPS) [7,43] as the non-rigid mapping.”
• Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling (2010, methodology): “One popular spline-based method is the Thin-Plate Spline (TPS) transformation (Bookstein, 1989).”
• Large Scale 3D Morphable Models (2017, methodology): “To overcome this limitation, Patel and Smith (2009) proposed to manually annotate the cylindrical face projections with a set of sparse annotations, employing a thin plate splines (TPS) warp (Bookstein 1989) to register the UV images of the meshes into a common reference frame.”
• Visualizations in geometric morphometrics: How to read and how to make graphs showing shape changes (2013, methodology): “…shape changes into different geometric components: a component of uniform (or affine) shape change that is the same throughout the entire configuration and a nonuniform component of shape change that is localized to various degrees (Bookstein, 1989, 1991, 1996c; Rohlf and Bookstein, 2003).”
• Survey of Medical Image Registration (2013, background): “The „„thin-plate‟‟ spline [52,53] has been used extensively to investigate subtle morphometric variation in schizophrenia [54].”