Thin-plate Spline Research Articles

Reading QR Codes on challenging surfaces using thin-plate splines

In real world uses, QR Codes are printed or overlaid on top of complex surfaces, like cylindrical bottles or other daily objects with random topographies that pose big challenges to their readout with the conventional planar algorithms proposed in the standard ISO and implemented in most of the available codes. We propose here a general-purpose method to improve the readability of QR Codes placed on these challenging surfaces, by fitting the topography of the underlying arbitrary surface with thin-plate splines. Then, we compare this new method with other alternatives proposed in the literature, like affine, projective and cylindrical transformations. Results demonstrate that our new approach works well under a variety of arbitrary surface topographies including those assumed in former proposals, and improve their readability by a factor of 4, clearly outperforming state-of-the-art decoders.

Improved automated spot counting and modeling with bias correction

ABSTRACT A complete workflow was presented for estimating the concentration of microorganisms in biological samples by automatically counting spots that represent viral plaque forming units (PFU) bacterial colony forming units (CFU), or spot forming units (SFU) in images, and modeling the counts. The workflow was designed for processing images from dilution series but can also be applied to stand-alone images. The accuracy of the methods was greatly improved by adding a newly developed bias correction method. When the spots in images are densely populated, the probability of spot overlapping increases, leading to systematic undercounting. In this paper, this undercount issue was addressed in an empirical way. The proposed empirical bias correction method utilized synthetic images with known spot sizes and counts as a training set, enabling the development of an effective bias correction function using a thin-plate spline model. Its application focused on the bias correction for the automated spot counting algorithm LoST proposed by Lin et al. Simulation results demonstrated that the empirical bias correction significantly improved spot counts, reducing bias for both fixed and random spot sizes and counts.

Predicting Mortality Risks Using Body Mass Index and Weight Loss at Admission in Patients with Heart Failure.

The association of the combination of body mass index (BMI) and weight change at admission with prognoses in patients with heart failure (HF) is unclear. Therefore, we investigated whether BMI and weight changes at admission affect mortality in patients with HF. This retrospective cohort study lasted 99 months, starting in April 2014, and included 4,862 patients with HF from a Japanese real-world database. Cubic and thin-plate smoothing spline analyses were performed to investigate the association of BMI and weight changes with mortality. The percentage weight change was calculated every 6 months. The study outcome was the presence or absence of death. The patients' mean age was 81.5±9.6 years, and 1,239 (25.5%) patients died. Cubic spline analysis revealed a negative correlation of BMI with mortality hazard ratio (HR) (BMI of 18.5 kg/m2 and 25 kg/m2; HR=1.3 [1.2-1.4] and 0.8 [0.7-0.9], respectively). Cubic spline analysis of weight change showed that weight loss tended to increase the mortality HR (each 6% decrease in weight change rate was associated with a 1.1 times higher mortality risk (95% CI [1.0-1.2]) Thin-plate smoothing spline analysis showed that the odds ratio (OR) negatively correlated with BMI (1-year mortality: BMI of 18.5 kg/m2, 22 kg/m2, and 25 kg/m2; OR at 0% weight change=1.5, 1.0, and 0.7, respectively; 2-year mortality: BMI=18.5 kg/m2, 22 kg/m2, and 25 kg/m2; OR at 0% weight change=1.4, 0.9, and 0.7, respectively). A low BMI in patients with HF was associated with a higher risk of mortality. Weight loss in patients, regardless of BMI, was associated with a higher OR for mortality.

A novel thin plate spline methodology to model tissue surfaces and quantify tumor cell invasion in organ-on-chip models

Organ-on-chip (OOC) models can be useful tools for cancer drug discovery. Advances in OOC technology have led to the development of more complex assays, yet analysis of these systems does not always account for these advancements, resulting in technical challenges. A challenging task in the analysis of these two-channel microfluidic models is to define the boundary between the channels so objects moving within and between channels can be quantified. We propose a novel imaging-based application of a thin plate spline method – a generalized cubic spline that can be used to model coordinate transformations – to model a tissue boundary and define compartments for quantification of invaded objects, representing the early steps in cancer metastasis. To evaluate its performance, we applied our analytical approach to an adapted OOC developed by Emulate, Inc., utilizing a two-channel system with endothelial cells in the bottom channel and colorectal cancer (CRC) patient-derived organoids (PDOs) in the top channel. Initial application and visualization of this method revealed boundary variations due to microscope stage tilt and ridge and valley-like contours in the endothelial tissue surface. The method was functionalized into a reproducible analytical process and web tool – the Chip Invasion and Contour Analysis (ChICA) – to model the endothelial surface and quantify invading tumor cells across multiple chips. To illustrate applicability of the analytical method, we applied the tool to CRC organoid-chips seeded with two different endothelial cell types and measured distinct variations in endothelial surfaces and tumor cell invasion dynamics. Since ChICA utilizes only positional data output from imaging software, the method is applicable to and agnostic of the imaging tool and image analysis system used. The novel thin plate spline method developed in ChICA can account for variation introduced in OOC manufacturing or during the experimental workflow, can quickly and accurately measure tumor cell invasion, and can be used to explore biological mechanisms in drug discovery.

Local Influence for the Thin-Plate Spline Generalized Linear Model

Thin-Plate Spline Generalized Linear Models (TPS-GLMs) are an extension of Semiparametric Generalized Linear Models (SGLMs), because they allow a smoothing spline to be extended to two or more dimensions. This class of models allows modeling a set of data in which it is desired to incorporate the non-linear joint effects of some covariates to explain the variability of a certain variable of interest. In the spatial context, these models are quite useful, since they allow the effects of locations to be included, both in trend and dispersion, using a smooth surface. In this work, we extend the local influence technique for the TPS-GLM model in order to evaluate the sensitivity of the maximum penalized likelihood estimators against small perturbations in the model and data. We fit our model through a joint iterative process based on Fisher Scoring and weighted backfitting algorithms. In addition, we obtained the normal curvature for the case-weight perturbation and response variable additive perturbation schemes, in order to detect influential observations on the model fit. Finally, two data sets from different areas (agronomy and environment) were used to illustrate the methodology proposed here.

Virtual reconstruction and geometric morphometric analysis of the Kocabaş hominin fossil from Turkey: Implications for taxonomy and evolutionary significance

The Kocabaş specimen comes from a travertine quarry near the homonymous village in the Denizli basin (Turkey). The specimen comprises three main fragments: portions of the right and left parietal and left and right parts of the frontal bone. The fossil was assumed to belong to the Homo erectus s.l. hypodigm by some authors, whereas others see similarities with Middle Pleistocene fossils (Broken Hill 1/Kabwe, Bodo, or Ceprano). Here, we present the first attempt to make a complete reconstruction of the missing medial portion of the frontal bone and a comprehensive geometric morphometric analysis of this bone. We restored the calotte by aligning and mirroring the three preserved fragments. Afterward, we restored the missing portion by applying the thin-plate spline interpolation algorithm of target fossils onto the reconstructed Kocabaş specimen. For the geometric morphometric analyses, we collected 80 landmarks on the frontal bone (11 osteometric points, 14 bilateral curve semilandmarks, and 41 surface semilandmarks). The comparative sample includes 21 fossils from different chronological periods and geographical areas and 30 adult modern humans from different populations. Shape analyses highlighted the presence in Kocabaş of features usually related to Middle Pleistocene Homo, such as a developed supraorbital torus associated with a relatively short frontal squama and reduced post-toral sulcus. Cluster analysis and linear discriminant analysis classification procedure suggest Kocabaş being part of the same taxonomic unit of Eurasian and African Middle Pleistocene Homo. In light of our results, we consider that attributing the Kocabaş hominin to H. erectus s.l. may be unwarranted. Results of our analyses are compatible with different evolutionary scenarios, but a more precise chronological framework is needed for a thorough discussion of the evolutionary significance of this specimen. Future work should clarify its geological age, given uncertainties regarding its stratigraphic provenance.

A note on polynomial-free unisolvence of polyharmonic splines at random points

In this note we prove almost sure unisolvence of RBF interpolation on randomly distributed sequences by a wide class of polyharmonic splines (including Thin-Plate Splines), without polynomial addition.

Geodetic innovation in Chilean mining: The evolution from static to kinematic reference frame in seismic zones

Abstract The use of regional kinematic reference frames (mRFs) in seismic zones is uncommon worldwide. This article proposes a solution implemented for Chilean mining, whose current projects are based on the classic reference frames (PSAD56 and SAD69). The approach is to move from a classic reference frame to an mRF in seismic countries where earthquakes constantly alter the frame. Our research group calculated an mRF (REDGEOMIN) that includes interseismic, coseismic, and postseismic deformation using CORS with open data from 2009 to 2022 and processed with scientific standards global navigation satellite system. REDGEOMIN consists of a deformation model (ADELA) with an interpolation approach through thin plate spline, allowing the greatest deformation to be modelled at campaign points. The relationship between classical and modern systems was explored with conformal transformations and NTv2 grids to include deformations, especially coming from PSAD56 and SAD69. The results demonstrate that REDGEOMIN aligns with the IGb14 reference frame (<1.0 mm), SIRGAS (ENU = 1.0, 1, 0, 2.0 mm), and the Chilean national reference frame SIRGASChile@2021.00 (ENU = 1, 2, 1, 6, 4.3 mm) aligns with millimetric precision. ADELA deformation model accurately models period locations to within 5 mm. Densification of REDGEOMIN@2022.00 at passive points PSAD56/SAD69 shows centimetric precision. PSAD56/SAD69, adjusted in the 1970s, are outdated due to crustal movement and seismic events and have metric errors. Therefore, different types of transformations were evaluated between PSAD56/SAD69 and REDGEOMIN@2022, whose RMS is between 1.57 and 1.69 m, and national grid transformations (NTv2) with an RMS of 0.23 and 0.16 m for PSAD56 and SAD69, respectively. The relationship between the classic systems and REDGEOMIN allows the transformation of the entire Chilean mining cadastre to epoch 2022.00. Starting in 2022.00, REDGEOMIN/ADELA offers millimetre precision, which is crucial in seismic zones. Furthermore, it paves the way to implement an updated national-level mRF in case of seismic events. Currently, Chilean mining laws are rigid, geodesically speaking. Therefore, legal-technical suggestions for implementing REDGEOMIN are also included in this article.

Data-based adaptive refinement of finite element thin plate spline

The thin plate spline, as introduced by Duchon, interpolates a smooth surface through scattered data. It is computationally expensive when there are many data points. The finite element thin plate spline (TPSFEM) possesses similar smoothing properties and is efficient for large data sets. Its efficiency is further improved by adaptive refinement that adapts the precision of the finite element grid. Adaptive refinement processes and error indicators developed for partial differential equations may not apply to the TPSFEM as it incorporates information about the scattered data. This additional information results in features not evident in partial differential equations. An iterative adaptive refinement process and five error indicators were adapted for the TPSFEM. We give comprehensive depictions of the process in this article and evaluate the error indicators through a numerical experiment with a model problem and two bathymetric surveys in square and L-shaped domains.

Quantitative morphological analysis framework of infant cranial sutures and fontanelles based on CT images.

Characterizing the suture morphological variation is a crucial step to investigate the influence of sutures on infant head biomechanics. This study aimed to establish a comprehensive quantitative framework for accurately capturing the cranial suture and fontanelle morphologies in infants. A total of 69 CT scans of 2-4 month-old infant heads were segmented to identify semilandmarks at the borders of cranial sutures and fontanelles. Morphological characteristics, including length, width, sinuosity index (SI), and surface area, were measured. For this, an automatic method was developed to determine the junction points between sutures and fontanelles, and thin-plate-spline (TPS) was utilized for area calculation. Different dimensionality reduction methods were compared, including nonlinear and linear principal component analysis (PCA), as well as deep-learning-based variational autoencoder (VAE). Finally, the significance of various covariates was analyzed, and regression analysis was performed to establish a statistical model relating morphological parameters with global parameters. This study successfully developed a quantitative morphological framework and demonstrate its application in quantifying morphologies of infant sutures and fontanelles, which were shown to significantly relate to global parameters of cranial size, suture SI, and surface area for infants aged 2-4 months. The developed framework proved to be reliable and applicable in extracting infant suture morphology features from CT scans. The demonstrated application highlighted its potential to provide valuable insights into the morphologies of infant cranial sutures and fontanelles, aiding in the diagnosis of suture-related skull fractures. Infant suture, Infant fontanelle, Morphological variation, Morphology analysis framework, Statistical model.

Image rectangling network based on reparameterized transformer and assisted learning

Stitched images can offer a broader field of view, but their boundaries can be irregular and unpleasant. To address this issue, current methods for rectangling images start by distorting local grids multiple times to obtain rectangular images with regular boundaries. However, these methods can result in content distortion and missing boundary information. We have developed an image rectangling solution using the reparameterized transformer structure, focusing on single distortion. Additionally, we have designed an assisted learning network to aid in the process of the image rectangling network. To improve the network’s parallel efficiency, we have introduced a local thin-plate spline Transform strategy to achieve efficient local deformation. Ultimately, the proposed method achieves state-of-the-art performance in stitched image rectangling with a low number of parameters while maintaining high content fidelity. The code is available at https://github.com/MelodYanglc/TransRectangling.

Continuous Piecewise-Affine Based Motion Model for Image Animation

Image animation aims to bring static images to life according to driving videos and create engaging visual content that can be used for various purposes such as animation, entertainment, and education. Recent unsupervised methods utilize affine and thin-plate spline transformations based on keypoints to transfer the motion in driving frames to the source image. However, limited by the expressive power of the transformations used, these methods always produce poor results when the gap between the motion in the driving frame and the source image is large. To address this issue, we propose to model motion from the source image to the driving frame in highly-expressive diffeomorphism spaces. Firstly, we introduce Continuous Piecewise-Affine based (CPAB) transformation to model the motion and present a well-designed inference algorithm to generate CPAB transformation from control keypoints. Secondly, we propose a SAM-guided keypoint semantic loss to further constrain the keypoint extraction process and improve the semantic consistency between the corresponding keypoints on the source and driving images. Finally, we design a structure alignment loss to align the structure-related features extracted from driving and generated images, thus helping the generator generate results that are more consistent with the driving action. Extensive experiments on four datasets demonstrate the effectiveness of our method against state-of-the-art competitors quantitatively and qualitatively. Code will be publicly available at: https://github.com/DevilPG/AAAI2024-CPABMM.

Spatial landmark detection and tissue registration with deep learning

Spatial landmarks are crucial in describing histological features between samples or sites, tracking regions of interest in microscopy, and registering tissue samples within a common coordinate framework. Although other studies have explored unsupervised landmark detection, existing methods are not well-suited for histological image data as they often require a large number of images to converge, are unable to handle nonlinear deformations between tissue sections and are ineffective for z-stack alignment, other modalities beyond image data or multimodal data. We address these challenges by introducing effortless landmark detection, a new unsupervised landmark detection and registration method using neural-network-guided thin-plate splines. Our proposed method is evaluated on a diverse range of datasets including histology and spatially resolved transcriptomics, demonstrating superior performance in both accuracy and stability compared to existing approaches.

Ultra-dense Motion Capture: An exploratory full-automatic approach for dense tracking of breast motion in 4D.

Understanding the dynamic deformation pattern and biomechanical properties of breasts is crucial in various fields, including designing ergonomic bras and customized prostheses, as well as in clinical practice. Previous studies have recorded and analyzed the dynamic behaviors of the breast surface using 4D scanning, which provides a sequence of 3D meshes during movement with high spatial and temporal resolutions. However, these studies are limited by the lack of robust and automated data processing methods which result in limited data coverage or error-prone analysis results. To address this issue, we identify revealing inter-frame dense correspondence as the core challenge towards conducting reliable and consistent analysis of the 4D scanning data. We proposed a fully-automatic approach named Ulta-dense Motion Capture (UdMC) using Thin-plate Spline (TPS) to augment the sparse landmarks recorded via motion capture (MoCap) as initial dense correspondence and then rectified it with a sophisticated post-alignment scheme. Two downstream tasks are demonstrated to validate its applicability: virtual landmark tracking and deformation intensity analysis. For evaluation, a dynamic 4D human breast anthropometric dataset DynaBreastLite was constructed. The results show that our approach can robustly capture the dynamic deformation characteristics of the breast surfaces, significantly outperforms baselines adapted from previous works in terms of accuracy, consistency, and efficiency. For 10 fps dataset, average error of 0.25 cm on control-landmarks and 0.33 cm on non-control (arbitrary) landmarks were achieved, with 17-70 times faster computation time. Evaluation was also carried out on 60 fps and 120 fps datasets, with consistent and large performance gaining being observed. The proposed method may contribute to advancing research in breast anthropometry, biomechanics, and ergonomics by enabling more accurate tracking of the breast surface deformation patterns and dynamic characteristics.

Geometric morphometric methods for identification of oyster species based on morphology.

Both genetic and environmental factors affect the morphology of oysters. Molecular identification is currently the primary means of species identification, but it is inconvenient and costly. In this research, we evaluated the effectiveness of geometric morphometric (GM) techniques in distinguishing between two oyster species, Crassostreagigas and C.ariakensis. We used traditional morphometric and GM methods, including principal component analysis (PCA), thin-plate spline analysis (TPS) and canonical variable analysis (CVA), to identify specific features that distinguish the two species. We found that differences in shape can be visualised using GM methods. The Procrustes analysis revealed significant differences in shell morphology between C.gigas and C.ariakensis. The shells of C.ariakensis are more prominent at the widest point and are more scattered and have a greater variety of shapes. The shells of C.gigas are more oval in shape. PCA results indicated that PC1 explained 45.22%, PC2 explained 22.09% and PC3 explained 10.98% of the variation between the two species, which suggests that the main morphological differences are concentrated in these three principal components. Combining the TPS analysis function plots showed that the shell shape of C.ariakensis is mainly elongated and spindle-shaped, whereas the shell shape of C.gigas is more oval. The CVA results showed that the classification rate for the two species reached 100% which means that C.ariakensis and C.gigas have distinct differences in shell morphology and can be completely separated, based on morphological characteristics. Through these methods, a more comprehensive understanding of the morphological characteristics of different oyster populations can be obtained, providing a reference for oyster classification and identification.

Geometric Morphometric Research of the Molars in Tree Shrews (Tupaia belangeri) from Different Regions

Background: Biological traits are mainly determined by genotype and are also influenced by environmental factors, especially in the process of adapting to different environments, corresponding phenotypic variations may occur. Even for the same animal, there may be some morphological differences due to its long-term adaptation to different habitat environments. Molar teeth are the direct contact point between animals and the environment, which are of great significance in the study of animal adaptability to different environments. Methods: To explore the relationship between the morphology of the molars (upper molars and lower molars) of tree shrews (Tupaia belangeri) and environmental variations in different regions, we applied geometric morphometric methods to measure the morphological characteristics of the molars of T. belangeri in 12 different regions of China (Hainan, Daxin, Leye, Xingyi, Xichang, Hekou, Kunming, Mengla, Dali, Tengchong, Pianma, Laboratory bred F1 generation). Result: The results showed that the morphological variations of the lower molars of T. belangeri in 12 different regions were larger, which was more suitable and reference valuable for studying the morphological differences among different geographical populations. The Principal component analysis showed that T. belangeri from 12 regions were clustered into 4 branches: Hainan was clustered into one branch, Daxin was clustered into one branch, Pianma and Tengchong were clustered into one branch and Leye, Xingyi, Hekou, Kunming, Xichang, Mengla, Dali and laboratory bred F1 generation were clustered into one branch. The thin plate spline analysis showed that deformations in the upper molars were mostly concentrated in the alveolar and dental margins. The deformations of the lower molars were mainly concentrated in the alveolar, marginal and occlusal surfaces. Multidimensional scaling showed that there were differences in molars morphology among the 12 locations, with significant variations in Hainan, Daxin, Pianma and Tengchong regions, reflecting the adaptive variation of T. belangeri to different ecological environments. The present results can provide a certain basis for the study of phenotypic adaptation in T. belangeri.

Spherical interpolation of scattered data using least squares thin-plate spline and inverse multiquadric functions

Spherical interpolation of scattered data using least squares thin-plate spline and inverse multiquadric functions

Smooth digital terrain modeling in irregular domains using finite element thin plate splines and adaptive refinement

<p>Digital terrain models (DTMs) are created using elevation data collected in geological surveys using varied sampling techniques like airborne lidar and depth soundings. This often leads to large data sets with different distribution patterns, which may require smooth data approximations in irregular domains with complex boundaries. The thin plate spline (TPS) interpolates scattered data and produces visually pleasing surfaces, but it is too computationally expensive for large data sizes. The finite element thin plate spline (TPSFEM) possesses smoothing properties similar to those of the TPS and interpolates large data sets efficiently. This article investigated the performance of the TPSFEM and adaptive mesh refinement in irregular domains. Boundary conditions are critical for the accuracy of the solution in domains with arbitrary-shaped boundaries and were approximated using the TPS with a subset of sampled points. Numerical experiments were conducted on aerial, terrestrial, and bathymetric surveys. It was shown that the TPSFEM works well in square and irregular domains for modeling terrain surfaces and adaptive refinement significantly improves its efficiency. A comparison of the TPSFEM, TPS, and compactly supported radial basis functions indicates its competitiveness in terms of accuracy and cost.</p>

NeuralTPS: Learning Signed Distance Functions without Priors from Single Sparse Point Clouds.

Surface reconstruction for point clouds is one of the important tasks in 3D computer vision. The latest methods rely on generalizing the priors learned from large scale supervision. However, the learned priors usually do not generalize well to various geometric variations that are unseen during training, especially for extremely sparse point clouds. To resolve this issue, we present a neural network to directly infer SDFs from single sparse point clouds without using signed distance supervision, learned priors or even normals. Our insight here is to learn surface parameterization and SDFs inference in an end-to-end manner. To make up the sparsity, we leverage parameterized surfaces as a coarse surface sampler to provide many coarse surface estimations in training iterations, according to which we mine supervision for our thin plate splines (TPS) based network to infer smooth SDFs in a statistical way. Our method significantly improves the generalization ability and accuracy on unseen point clouds. Our experimental results show our advantages over the state-of-the-art methods in surface reconstruction for sparse point clouds under synthetic datasets and real scans.

Inverse-Like Antagonistic Scene Text Spotting via Reading-Order Estimation and Dynamic Sampling.

Scene text spotting is a challenging task, especially for inverse-like scene text, which has complex layouts, e.g., mirrored, symmetrical, or retro-flexed. In this paper, we propose a unified end-to-end trainable inverse-like antagonistic text spotting framework dubbed IATS, which can effectively spot inverse-like scene texts without sacrificing general ones. Specifically, we propose an innovative reading-order estimation module (REM) that extracts reading-order information from the initial text boundary generated by an initial boundary module (IBM). To optimize and train REM, we propose a joint reading-order estimation loss ( LRE ) consisting of a classification loss, an orthogonality loss, and a distribution loss. With the help of IBM, we can divide the initial text boundary into two symmetric control points and iteratively refine the new text boundary using a lightweight boundary refinement module (BRM) for adapting to various shapes and scales. To alleviate the incompatibility between text detection and recognition, we propose a dynamic sampling module (DSM) with a thin-plate spline that can dynamically sample appropriate features for recognition in the detected text region. Without extra supervision, the DSM can proactively learn to sample appropriate features for text recognition through the gradient returned by the recognition module. Extensive experiments on both challenging scene text and inverse-like scene text datasets demonstrate that our method achieves superior performance both on irregular and inverse-like text spotting.