Local Affine Transformation Research Articles

Crop Water Status Analysis from Complex Agricultural Data Using UMAP-Based Local Biplot

To optimize growth and management, precision agriculture relies on a deep understanding of agricultural dynamics, particularly crop water status analysis. Leveraging unmanned aerial vehicles, we can efficiently acquire high-resolution spatiotemporal samples by utilizing remote sensors. However, non-linear relationships among data features, localized within specific subgroups, frequently emerge in agricultural data. Interpreting these complex patterns requires sophisticated analysis due to the presence of noise, high variability, and non-stationarity behavior in the collected samples. Here, we introduce Local Biplot, a methodological framework tailored for discerning meaningful data patterns in non-stationary contexts for precision agriculture. Local Biplot relies on the well-known uniform manifold approximation and projection method, such as UMAP, and local affine transformations to codify non-stationary and non-linear data patterns while maintaining interpretability. This lets us find important clusters for transformation and projection within a single global axis pair. Hence, our framework encompasses variable and observational contributions within individual clusters. At the same time, we provide a relevance analysis strategy to help explain why those clusters exist, facilitating the understanding of data dynamics while favoring interpretability. We demonstrated our method’s capabilities through experiments on both synthetic and real-world datasets, covering scenarios involving grass and rice crops. Moreover, we use random forest and linear regression models to predict water status variables from our Local Biplot-based feature ranking and clusters. Our findings revealed enhanced clustering and prediction capability while emphasizing the importance of input features in precision agriculture. As a result, Local Biplot is a useful tool to visualize, analyze, and compare the intricate underlying patterns and internal structures of complex agricultural datasets.

Local parallel free generation and dynamic affine transformation method for soil three-dimensional pore structure information model

The soil three-dimensional (3D) pore structure information model has become a new hotspot in the research of cross-scale disposal of information such as ecology, engineering, and geology. It can solve problems such as the intelligent evaluation of ecological water–soil–air–plant feedback, intelligent risk control of foundation compression deformation, and multiscale intelligent disaster prediction and prevention. However, the current soil 3D pore structure model primarily draws on the global one-time static generation in simulation software, leading to low reliability, low stability of multiple generations, poor variability, difficulty in real-time transformation, high consumption of computing resources, and long generation time, making it challenging to meet the requirements of the rapid processing of information models. Therefore, this study adopts the 3D Drawing Protocol (WebGL) technology and implements the scaling, rotation, and translation transformation of 3D pore structures based on the principle of dynamic affine transformation. The random generation and distribution of pores are realized using the improved Monte Carlo method, and the loading response efficiency of the system is optimized. The dynamic interactive operation of arbitrary increasing and decreasing of pore model is realized using the ray and plane intersection detection principle. Finally, this information system established a visual correlation between the content and reaction time of water-retaining agents and soil porosity and pore distribution through tests on the impact of water-retaining agents on soil pore changes. The information system achieved the real-time tracking of soil pore changes under the action of water-retaining agents. This research solves the problems of static and low generation efficiency of the soil mesopore structure in traditional models and realizes the real-time characterization and visualization of dynamic changes and the distribution of the soil pore structure under the influence of external conditions, which can provide an intuitive visualization platform for mesogeological structure research.

Feature matching of remote‐sensing images based on bilateral local–global structure consistency

AbstractThe goal of feature matching is to establish accurate correspondences between feature points in different images depicting the same scene. To address the polymorphism of local structures, the authors propose a mismatch removal method using bilateral local–global structural consistency. This method incorporates the problem of mismatch removal into the framework of graph matching, constructs a global affinity matrix using local structural similarity and global affine transformation consistency, and optimizes it using a constrained integer quadratic programming method. To comprehensively describe the local structure, the signature quadratic form distance (SQFD) is used to measure the consistency of the neighbourhood structure. Specifically, the weights of edges are constructed based on the SQFD of the local structure, while the matching correctness of nodes and edges between the two graphs is described using local vector similarity. Furthermore, the consistency of the global affine transformation is evaluated by assessing the consistency of the local neighbourhood affine transformation between different corresponding point pairs. In estimating the local affine transformation, a bilateral correction is performed using a total least‐squares (TLS) algorithm to measure the similarity of nodes between the two different graphs. Experimental results demonstrate that the proposed algorithm outperforms state‐of‐the‐art methods in terms of accuracy and effectiveness.

Garment image style transfer based on deep learning

Before neural networks, image style transfer procedures had a common idea: analyze images with a certain style, build a mathematical or statistical model for the style, and then change the image to be transferred, so that it better fits the established model. In this paper, k-means and semantic closed natural matting algorithm is combined for image segmentation, the style and content in the image are extracted based on neural network, and the resulting image is synthesized by image reconstruction technology to realize the migration of national costume styles. Due to the serious artifacts of the output image, an improved image style transfer algorithm is adopted to constrain the transformation from the input image to the output image in the local affine transformation of the color space, and this constraint is expressed as a completely differentiable parameter term, image distortion is suppressed effectively. In the process of real photo style transfer, there is also space inconsistency. Smoothing is done to ensure that the space style is consistent after style processing, it greatly speeds up the operation speed. On NVIDIA GTX1080TI graphics card, algorithm is tested with 256×256 resolution images. It includes three indicators of average running time, memory usage and the number of styles generated by a single model, which are 0.06 s, 136.06 MB and 1 respectively. These indicators can reflect the efficiency and flexibility of the algorithm.

Microstructure realization of a lattice-based polar solid for arbitrary elastic waveguiding

The ability to precisely directing and controlling longitudinal (P) and transverse (S) waves in 2D solids along an arbitrary trajectory has attracted significant research interest and is crucial for practical applications such as imaging, cloaking, and wave focusing. Here, we report, design and examine an inhomogeneous lattice-based polar medium for ideal elastic waveguide, whose microstructures are inversely determined by the discrete transformation elasticity (DTE). Microstructures of the suggested medium, which are realized through global linear transformation and local affine transformation, enables arbitrary waveguides to transport elastic waves with minimal energy loss. Numerical simulation is then conducted to demonstrate that the lattice-based polar waveguide can efficiently steer both in-plane P and S wave modes over a broad frequency band. We also leverage the medium for Rayleigh wave control on curved surfaces. The constructed polar surface can break the conventional limit of the Rayleigh wave propagation on both concave and convex surfaces with extreme curvatures. This study is not only a concrete manifestation of the polar material, discrete transform elasticity, and their advantages but also provides a great potential in engineering applications such as signal detection, vibration control, and earthquake protection.

A hybrid hierarchical strategy for registration of 7T TOF-MRI to 7T PC-MRI intracranial vessel data

Purpose7T time-of-flight (TOF) MRI provides high resolution for the evaluation of cerebrovascular vessels and pathologies. In combination with 4D flow fields acquired with phase-contrast (PC) MRI, hemodynamic information can be extracted to enhance the analysis by providing direct measurements in the larger arteries or patient-specific boundary conditions. Hence, a registration between both modalities is required.MethodsTo combine TOF and PC-MRI data, we developed a hybrid registration approach. Vessels and their centerlines are segmented from the TOF data. The centerline is fit to the intensity ridges of the lower resolved PC-MRI data, which provides temporal information. We used a metric that utilizes a scaled sum of weighted intensities and gradients on the normal plane. The registration is then guided by decoupled local affine transformations. It is applied hierarchically following the branching order of the vessel tree.ResultsA landmark validation over Monte Carlo simulations yielded an average mean squared error of 184.73 mm and an average Hausdorff distance of 15.20 mm. The hierarchical traversal that transforms child vessels with their parents registers even small vessels not detectable in the PC-MRI.ConclusionThe presented work combines high-resolution tomographic information from 7T TOF-MRI and measured flow data from 4D 7T PC-MRI scan for the arteries of the brain. This enables usage of patient-specific flow parameters for realistic simulations, thus supporting research in areas such as cerebral small vessel disease. Automatization and free deformations can help address the limiting error measures in the future.

Point cloud classification network based on self-attention mechanism

PointNet makes it possible to process point cloud data directly. However, PointNet only extracts global features and cannot capture fine local features. How to build a refined local feature extractor is the main goal of the research. Recently, Transformer has been used for point cloud processing tasks with better performance than other methods. We refer to Transformer and use the self-attention mechanism to design a refined feature extractor to capture richer feature information. In addition, we get the local geometric information at different scales with a local feature extraction module and use affine transformation to convert the local features to a normal distribution. We report results on the ModelNet40 dataset, new feature extraction network greatly improves classification tasks.

Locality-Guided Global-Preserving Optimization for Robust Feature Matching.

Feature matching is a fundamental problem in many computer vision tasks. This paper proposes a novel effective framework for mismatch removal, named LOcality-guided Global-preserving Optimization (LOGO). To identify inliers from a putative matching set generated by feature descriptor similarity, we introduce a fixed-point progressive approach to optimize a graph-based objective, which represents a two-class assignment problem regarding an affinity matrix containing global structures. We introduce a strategy that a small initial set with a high inlier ratio exploits the topology of the affinity matrix to elicit other inliers based on their reliable geometry, which enhances the robustness to outliers. Geometrically, we provide a locality-guided matching strategy, i.e., using local topology consensus as a criterion to determine the initial set, thus expanding to yield the final feature matching set. In addition, we apply local affine transformations based on reference points to determine the local consensus and similarity scores of nodes and edges, ensuring the validity and generality for various scenarios including complex nonrigid transformations. Extensive experiments demonstrate the effectiveness and robustness of the proposed LOGO, which is competitive with the current state-of-the-art methods. It also exhibits favorable potential for high-level vision tasks, such as essential and fundamental matrix estimation, image registration and loop closure detection.

A novel geometry image to accurately represent a surface by preserving mesh topology

Geometry images parameterise a mesh with a square domain and store the information in a single chart. A one-to-one correspondence between the 2D plane and the 3D model is convenient for processing 3D models. However, the parameterised vertices are not all located at the intersection of the gridlines the existing geometry images. Thus, errors are unavoidable when a 3D mesh is reconstructed from the chart. In this paper, we propose parameterise surface onto a novel geometry image that preserves the constraint of topological neighbourhood information at integer coordinate points on a 2D grid and ensures that the shape of the reconstructed 3D mesh does not change from supplemented image data. We find a collection of edges that opens the mesh into simply connected surface with a single boundary. The point distribution with approximate blue noise spectral characteristics is computed by capacity-constrained delaunay triangulation without retriangulation. We move the vertices to the constrained mesh intersection, adjust the degenerate triangles on a regular grid, and fill the blank part by performing a local affine transformation between each triangle in the mesh and image. Unlike other geometry images, the proposed method results in no error in the reconstructed surface model when floating-point data are stored in the image. High reconstruction accuracy is achieved when the xyz positions are in a 16-bit data format in each image channel because only rounding errors exist in the topology-preserving geometry images, there are no sampling errors. This method performs one-to-one mapping between the 3D surface mesh and the points in the 2D image, while foldovers do not appear in the 2D triangular mesh, maintaining the topological structure. This also shows the potential of using a 2D image processing algorithm to process 3D models.

Fast Fractal Coding of MRI Images using Deep Reinforcement Learning

This paper presents an algorithm based on Fractal theory by using Iterated Function Systems (IFS). An efficient and fast coding mechanism is proposed by exploiting the self similarity nature in the Brain MRI images. The proposed algorithm utilizes Deep Reinforcement Learning (DRL) technique to learn the transformations required to recreate the original image. We avail of the Adaptive Iterated Function System (AIFS) as the encoding scheme. The proposed algorithm is trained and customized to compress the Medical images, especially Magnetic Resonance Imaging (MRI). The algorithm is tested and evaluated by using the original MR head scan test images. It learns from an existing biomedical dataset viz The Internet Brain Segmentation Repository (IBSR) to predict the new local affine transformations. The empirical analysis shows that the proposed algorithm is at least 4 times faster than the competitive methods and the decoding quality is far distinct with a reduction in the bit rate.

Remote Sensing Image Registration Based on Local Affine Constraint With Circle Descriptor

Many methods have been developed to improve the performance of image registration. In this letter, we introduce a novel method based on a local affine constraint for remote sensing image registration, which can be widely used in image processing and pattern recognition. Our algorithm has three components. First, we exploit the scale invariant feature transform (SIFT) method to extract feature points and calculate the gradient magnitude to establish feature descriptors with a circular instead of square neighborhood. Second, an initial matching is implemented by the nearest neighbor distance ratio (NNDR) and the fast sample consensus (FSC) algorithm. Finally, fine registration is established using more correct matches obtained by the local affine transformation circular region search algorithm. Experimental results show that the proposed method achieves subpixel accuracy. In addition, both the correct matching rate and registration demonstrate the effectiveness and efficiency of our method.

A method for local approximation of a planar deformation field

Abstract We present a method of approximation of a deformation field based on the local affine transformations constructed based on n nearest neighbors with respect to points of adopted grid. The local affine transformations are weighted by means of inverse distance squared between each grid point and observed points (nearest neighbors). This work uses a deformation gradient, although it is possible to use a displacement gradient instead – the two approaches are equivalent. To decompose the deformation gradient into components related to rigid motions (rotations, translations are excluded from the deformation gradient through differentiation process) and deformations, we used a polar decomposition and decomposition into a sum of symmetric and an anti-symmetric matrices (tensors). We discuss the results from both decompositions. Calibration of a local affine transformations model (i.e., number of nearest neighbors) is performed on observed points and is carried out in a cross-validation procedure. Verification of the method was conducted on simulated data-grids subjected to known (functionally generated) deformations, hence, known in every point of a study area.

LAM: Locality affine-invariant feature matching

False match removal is a crucial and fundamental task in photogrammetry and computer vision. This paper proposes a robust and efficient mismatch-removal algorithm based on the concepts of local barycentric coordinate (LBC) and matching coordinate matrices (MCMs), called locality affine-invariant matching (LAM). LAM is suitable for both rigid and nonrigid image matching problems. We define a novel LBC system based on area ratios, which is invariant to local affine transformations. We also present the MCMs based on the coordinates of matches, whose degeneracy is able to indicate the correctness of correspondences. Our LAM method first builds a mathematical model based on the LBCs to extract good matches that preserve local neighborhood structures. Then, LAM constructs local MCMs using the extracted reliable correspondences and identifies the correctness for the remaining matches via minimizing the rank of the MCMs. LAM has linear space and linearithmic time complexities. Extensive experiments on both rigid and nonrigid real datasets demonstrate the power of the proposed method; i.e., LAM is more robust to complex transformations compared to other methods and is two orders of magnitude faster than RANSAC under low inlier rates. The source code of the proposed LAM method will be publicly available in http://www.escience.cn/people/lijiayuan/index.html.

BALG: An alternative for fast and robust feature matching

Robust feature matcher is usually inapplicable to real time computer vision applications as its high computational complexity, while fast feature matcher is short of robustness to geometric transformations. By studying the sampling pattern of binary descriptor and local geometric statistics of features, this paper proposes a fast and robust feature matching method with binary affine invariant descriptor and local geometric consistency check (BALG). The sampling pattern is adaptively adjusted according local affine transformation that can be effectively estimated from the local intensity moments. The affine sampling pattern improves the affine invariance of binary descriptor while enable fast processing. Furthermore, candidate matches are sorted into local groups along different orientations with sequence order constraint, and then followed by local geometric consistency check. False matches are efficiently filtered out with high recall. Extensive experiments on four publicly benchmark datasets prove the proposed method to be an alternative for time critical feature matcher.

Non-rigid point cloud registration based lung motion estimation using tangent-plane distance.

Accurate estimation of motion field in respiration-correlated 4DCT images, is a precondition for the analysis of patient-specific breathing dynamics and subsequent image-supported treatment planning. However, the lung motion estimation often suffers from the sliding motion. In this paper, a novel lung motion method based on the non-rigid registration of point clouds is proposed, and the tangent-plane distance is used to represent the distance term, which describes the difference between two point clouds. Local affine transformation model is used to express the non-rigid deformation of the lung motion. The final objective function is expressed in the Frobenius norm formation, and matrix optimization scheme is carried out to find out the optimal transformation parameters that minimize the objective function. A key advantage of our proposed method is that it alleviates the requirement that the source point cloud and the reference point cloud should be in one-to-one corresponding relationship, and the requirement is difficult to be satisfied in practical application. Furthermore, the proposed method takes the sliding motion of the lung into consideration and improves the registration accuracy by reducing the constraint of the motion along the tangent direction. Non-rigid registration experiments are carried out to validate the performance of the proposed method using popi-model data. The results demonstrate that the proposed method outperforms the traditional method with about 20% accuracy increase.

Registration of Dynamic Thermography Data of the Abdomen of Pregnant and Non-Pregnant Women.

To date the use of thermography in the context of obstetrics has been primarily limited to the acquisition and analysis of static thermal images. In contrast, dynamic thermography involves the acquisition of a sequence of thermal images, taking into account temporal variations that would otherise be overlooked. However, dynamic recordings of regions of interest in human participants are likely to be affected by unavoidable participant movement due to breathing and other involuntary movements. In this work, a triangulation-based video registration technique using local affine transformations is proposed to register the abdominal region in dynamic thermal sequences. The proposed method is tested on one hour recordings of thermal data obtained from 10 pregnant and 10 non-pregnant female participants. The results obtained show that the proposed approach can compensate for movements and significantly improve region alignment throughout the thermal image sequence, thereby facilitating subsequent analysis of spatiotemporal temperature data in the considered image sequence.

Efficient Recovery of Essential Matrix From Two Affine Correspondences.

We propose a method to estimate the essential matrix using two affine correspondences for a pair of calibrated perspective cameras. Two novel, linear constraints are derived between the essential matrix and a local affine transformation. The proposed method is also applicable to the over-determined case. We extend the normalization technique of Hartley to local affinities and show how the intrinsic camera matrices modify them. Even though perspective cameras are assumed, the constraints can straightforwardly be generalized to arbitrary camera models since they describe the relationship between local affinities and epipolar lines (or curves). Benefiting from the low number of exploited points, it can be used in robust estimators, e.g. RANSAC, as an engine, thus leading to significantly less iterations than the traditional point-based methods. The algorithm is validated both on synthetic and publicly available data sets and compared with the state-of-the-art. Its applicability is demonstrated on two-view multi-motion fitting, i.e., finding multiple fundamental matrices simultaneously, and outlier rejection.

Robust Non-rigid Registration Based on Affine ICP Algorithm and Part-Based Method

The classical affine iterative closest point (ICP) algorithm is fast and accurate for affine registration between two point sets, but it is easy to fall into a local minimum. As an extension of the classical affine registration algorithm, this paper first proposes an affine ICP algorithm based on control point guided, and then applies this new method to establish a robust non-rigid registration algorithm based on local affine registration. The algorithm uses a hierarchical iterative method to complete the point set non-rigid registration from coarse to fine. In each iteration, the sub data point sets and sub model point sets are divided, meanwhile, the shape control points of each sub point set are updated. Then we use the control point guided affine ICP algorithm to solve the local affine transformation between the corresponding sub point sets. Next, the local affine transformation obtained by the previous step is used to update the sub data point sets and their shape control point sets. Experimental results demonstrate that the accuracy and convergence of our algorithm are greatly improved compared with the traditional point set non-rigid registration algorithms.

Robust feature matching via support-line voting and affine-invariant ratios

Robust image matching is crucial for many applications of remote sensing and photogrammetry, such as image fusion, image registration, and change detection. In this paper, we propose a robust feature matching method based on support-line voting and affine-invariant ratios. We first use popular feature matching algorithms, such as SIFT, to obtain a set of initial matches. A support-line descriptor based on multiple adaptive binning gradient histograms is subsequently applied in the support-line voting stage to filter outliers. In addition, we use affine-invariant ratios computed by a two-line structure to refine the matching results and estimate the local affine transformation. The local affine model is more robust to distortions caused by elevation differences than the global affine transformation, especially for high-resolution remote sensing images and UAV images. Thus, the proposed method is suitable for both rigid and non-rigid image matching problems. Finally, we extract as many high-precision correspondences as possible based on the local affine extension and build a grid-wise affine model for remote sensing image registration. We compare the proposed method with six state-of-the-art algorithms on several data sets and show that our method significantly outperforms the other methods. The proposed method achieves 94.46% average precision on 15 challenging remote sensing image pairs, while the second-best method, RANSAC, only achieves 70.3%. In addition, the number of detected correct matches of the proposed method is approximately four times the number of initial SIFT matches.

A theory of point-wise homography estimation

We propose a method, called HAF, to estimate planar homography from an affine correspondence satisfying the epipolar constraint in an image pair. An affine correspondence consists of a point pair and the related local affine transformation mapping the pixels infinitely close to the point locations from the first to the second images. As a minimal solver, it estimates the homography from only one correspondence, however, it is generalized for the over-determined case as well. The required local affinities are obtained by affine-covariant feature detectors accurately. As a side-effect of the tests, the state-of-the-art affine-covariant detectors are compared to each other w.r.t. the accuracy of the estimated point-wise homographies. The proposed method is validated both on the publicly available AdelaideRMF dataset and in a synthetic testing environment.