Optimal Affine Transformation Research Articles

Optimal transport-based machine learning to match specific patterns: application to the detection of molecular regulation patterns in omics data

Abstract We present several algorithms designed to learn a pattern of correspondence between 2 data sets in situations where it is desirable to match elements that exhibit a relationship belonging to a known parametric model. In the motivating case study, the challenge is to better understand micro-RNA regulation in the striatum of Huntington’s disease model mice. The algorithms unfold in 2 stages. First, an optimal transport plan P and an optimal affine transformation are learned, using the Sinkhorn–Knopp algorithm and a mini-batch gradient descent. Second, P is exploited to derive either several co-clusters or several sets of matched elements. A simulation study illustrates how the algorithms work and perform. The real data application further illustrates their applicability and interest.

Slam algorithm for multi-robot communication in unknown environment based on particle filter

To solve the SLAM (simultaneous localization and map building) of mobile robots, a multi-robot SLAM algorithm based on particle filter for communication in unknown environment is proposed. In the standard particle filter, the incremental map construction method based on point-line consistency is introduced to preserve the hypothesis of the line segment feature map in each particle, and the importance function is introduced to the observation information. On this basis, sampling map fusion algorithm extracts ORB (oriented FAST and rotated BRIEF) features of local map constructed by a single robot and finds the optimal matching points, calculates the homography matrix of local map optimal matching point set, determines the optimal affine transformation parameters among point sets, so as to complete the local map fusion, and realize the multi-robot communication based on SLAM in unknown environment. The results show that the algorithm achieves high-precision map fusion and it is an effective SLAM construction algorithm for multiple machines.

Efficient 3D Shape Registration by Using Distance Maps and Stochastic Gradient Descent Method

Abstract This paper presents an efficient 3D shape registration by using distance maps and stochastic gradient descent method. The proposed algorithm aims to find the optimal affine transformation parameters (translation, scaling and rotation) that maps two distance maps to each other. These distance maps represent the shapes as an interface and we apply level sets methods to calculate the signed distance to these interfaces. To maximize the similarity between the two distance maps, we apply sum of squared difference (SSD) optimization and gradient descent methods to minimize it. To address the shortcomings of the standard gradient descent method, i.e., many iterations to compute the minimum, we implemented the stochastic gradient descent method. The outcome of these two methods are compared to show the advantages of using stochastic gradient descent method. In addition, we implement computational optimization’s such as parallelization to speed up the registration process.

3-D Feature Matching for Point Cloud Object Extraction

Effective object extraction plays an important role in many point cloud-based applications. This letter proposes a 3-D feature matching framework for point cloud object extraction. To determine the optimal affine transformation parameters for each template feature point, a convex dissimilarity function and the locally affine-invariant geometric constraints are designed to construct the overall objective function. The 3-D feature matching framework is integrated into a point cloud object extraction workflow. Extraction results on six test data sets show that average completeness, correctness, quality, and $F_{1}$ -measure of 0.96, 0.97, 0.93, and 0.96, respectively, are obtained in extracting light poles, vehicles, and palm trees. Comparative studies also confirm that the proposed method performs effectively and robustly, and exhibits superior or compatible performance over the other compared methods.

Level set based shape prior and deep learning for image segmentation

Deep convolutional neural network can effectively extract hidden patterns in images and learn realistic image priors from the training set. And fully convolutional networks (FCNs) have achieved state-of-the-art performance in the image segmentation. However, these methods have the disadvantages of noise, boundary roughness and no prior shape. Therefore, this study proposes a level set with the deep prior method for the image segmentation based on the priors learned by FCNs. The FCNs can learn high-level semantic patterns from the training set. Also, the output of the FCNs represents the high-level semantic information as a probability map and the global affine transformation can obtain the optimal affine transformation of the intrinsic prior shape. Moreover, the improved level set method integrates the information of the original image, the probability map and the corrected prior shape to achieve the image segmentation. Compared with the traditional level set method of simple scenes, the proposed method solves the disadvantage of FCNs by using the high-level semantic information to segment images of complex scenes. Finally, Portrait data set are used to verify the effectiveness of the proposed method. The experimental results show that the proposed method can obtain more accurate segmentation results than the traditional FCNs.

Accurate registration of in vivo time-lapse images.

In vivo imaging experiments often require automated detection and tracking of changes in the specimen. These tasks can be hindered by variations in the position and orientation of the specimen relative to the microscope, as well as by linear and nonlinear tissue deformations. We propose a feature-based registration method, coupled with optimal transformations, designed to address these problems in 3D time-lapse microscopy images. Features are detected as local regions of maximum intensity in source and target image stacks, and their bipartite intensity dissimilarity matrix is used as an input to the Hungarian algorithm to establish initial correspondences. A random sampling refinement method is employed to eliminate outliers, and the resulting set of corresponding features is used to determine an optimal translation, rigid, affine, or B-spline transformation for the registration of the source and target images. Accuracy of the proposed algorithm was tested on fluorescently labeled axons imaged over a 68-day period with a two-photon laser scanning microscope. To that end, multiple axons in individual stacks of images were traced semi-manually and optimized in 3D, and the distances between the corresponding traces were measured before and after the registration. The results show that there is a progressive improvement in the registration accuracy with increasing complexity of the transformations. In particular, sub-micrometer accuracy (2-3 voxels) was achieved with the regularized affine and B-spline transformations.

ARENA: Inter-modality affine registration using evolutionary strategy.

Image fusion of different imaging modalities renders valuable information to clinicians. In this paper, we proposed an automatic multimodal registration method to register intra-operative ultrasound images (US) to preoperative magnetic resonance images (MRI) in the context of image-guided neurosurgery. We employed refined correlation ratio as a similarity metric for our intensity-based image registration method. We deem MRI as the fixed image ([Formula: see text]) and US as the moving image ([Formula: see text]) and then transform [Formula: see text] to align with [Formula: see text]. We utilized the covariance matrix adaptation evolutionary strategy to find the optimal affine transformation in registration of [Formula: see text] to [Formula: see text]. We applied our method on the publicly available retrospective evaluation of cerebral tumors (RESECT) database and Montreal Neurological Institute's brain images of tumors for evaluation (BITE) database. We validated the results qualitatively and quantitatively. Qualitative validation is conducted (by the three authors) through overlaying pre- and post-registration US and MRI to allow visual assessment of the alignment. Quantitative validation is performed by utilizing the corresponding landmarks in the databases for the preoperative MRI and the intra-operative US. Average mean target registration error (mTRE) has been reduced from [Formula: see text] to [Formula: see text] in 22 patients in the RESECT database and from [Formula: see text] to [Formula: see text] in the BITE database. A nonparametric statistical analysis performed using the Wilcoxon rank sum test shows that there is a significant difference between pre- and post-registration mTREs with a p value of [Formula: see text] for the RESECT database and [Formula: see text] for the BITE database. The proposed fully automatic registration method significantly improved the alignment of MRI and US images and can therefore be used to reduce the misalignment of US and MRI caused by brain shift, calibration errors, and patient to MRI transformation matrix.

An Improved Method of Geomagnetic Aided Inertial Navigation Algorithm with Gyro and Accelerometer Error Corrected Online

In consideration of the problem that traditional geomagnetic aided navigation method cannot reduce the scaling error of indication track in inertial navigation system (INS), which will further limit the error correction precision of gyro and accelerometer, an improved geomagnetic matching algorithm based on affine transformation is proposed in this paper. A geomagnetic matching algorithm led to the optimal affine transformation solution by Procrustes analysis is presented and develops latitude and longitude reference information. Then a 13-dimensional-state extended Kalman filter which estimates the attitude misalignment angles, the position error, the velocity error, the Gyro drift, and accelerometer error is introduced to continuously update the output of INS and remove the accumulative error. The results show that geomagnetic aided navigation based on improved algorithm has better location accuracy and correction accuracy of INS than the traditional method.

Trimmed strategy for affine registration of point sets

We propose a trimmed strategy for affine registration of point sets using the Lie group parameterization. All affine transformations form an affine Lie group, thus finding an optimal transformation in registration is reduced to finding an optimal element in the affine group. Given two point sets (with outliers) and an initial element in the transformation group, we seek the optimal group element iteratively by minimizing an energy functional. This is conducted by sequentially finding the closest correspondence of two point sets, estimating the overlap rate of two sets, and finding the optimal affine transformation via the exponential map of the affine group. This method improves the trimmed iterative closest point algorithm (TrICP) in two aspects: (1) We use the Lie group parameterization to implement TrICP. (2) We also extend TrICP to the case of affine transformations. The performance of the proposed algorithm is demonstrated by using the LiDAR data acquired in the Mount St. Helens area. Both visual inspections and evaluation index (root mean trimmed squared distance) indicate that our algorithm performs consistently better than TrICP and other related algorithms, especially in the presence of outliers and missing points.

A general purpose sampling algorithm for continuous distributions (the t-walk)

We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning. We call this MCMC the t-walk. The t-walk maintains two independent points in the sample space, and all moves are based on proposals that are then accepted with a standard Metropolis-Hastings acceptance probability on the product space. Hence the t-walk is provably convergent under the usual mild requirements. We restrict proposal distributions, or `moves', to those that produce an algorithm that is invariant to scale, and approximately invariant to affine transformations of the state space. Hence scaling of proposals, and effectively also coordinate transformations, that might be used to increase efficiency of the sampler, are not needed since the t-walk's operation is identical on any scaled version of the target distribution. Four moves are given that result in an effective sampling algorithm. We use the simple device of updating only a random subset of coordinates at each step to allow application of the t-walk to high-dimensional problems. In a series of test problems across dimensions we find that the t-walk is only a small factor less efficient than optimally tuned algorithms, but significantly outperforms general random-walk M-H samplers that are not tuned for specific problems. Further, the t-walk remains effective for target distributions for which no optimal affine transformation exists such as those where correlation structure is very different in differing regions of state space. Several examples are presented showing good mixing and convergence characteristics, varying in dimensions from 1 to 200 and with radically different scale and correlation structure, using exactly the same sampler. The t-walk is available for R, Python, MatLab and C++ at http://www.cimat.mx/~jac/twalk/

A general purpose sampling algorithm for continuous distributions (the t-walk)

We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning. We call this MCMC the t-walk. The t-walk maintains two independent points in the sample space, and all moves are based on proposals that are then accepted with a standard Metropolis-Hastings acceptance probability on the product space. Hence the t-walk is provably convergent under the usual mild requirements. We restrict proposal distributions, or `moves', to those that produce an algorithm that is invariant to scale, and approximately invariant to affine transformations of the state space. Hence scaling of proposals, and effectively also coordinate transformations, that might be used to increase efficiency of the sampler, are not needed since the t-walk's operation is identical on any scaled version of the target distribution. Four moves are given that result in an effective sampling algorithm. We use the simple device of updating only a random subset of coordinates at each step to allow application of the t-walk to high-dimensional problems. In a series of test problems across dimensions we find that the t-walk is only a small factor less efficient than optimally tuned algorithms, but significantly outperforms general random-walk M-H samplers that are not tuned for specific problems. Further, the t-walk remains effective for target distributions for which no optimal affine transformation exists such as those where correlation structure is very different in differing regions of state space. Several examples are presented showing good mixing and convergence characteristics, varying in dimensions from 1 to 200 and with radically different scale and correlation structure, using exactly the same sampler. The t-walk is available for R, Python, MatLab and C++ at http://www.cimat.mx/~jac/twalk/

Multifrequency eddy current testing of steam generator tubes using optimal affine transformation : Review of progress in quantitative nondestructive evaluation, Williamsburg, Virginia (United States), 22–26 Jun. 1987. Vol. 7A, pp. 821–830. Edited by D.D. Thompson and D.E. Chimenti, Plenum Press, 1988.

Multifrequency eddy current testing of steam generator tubes using optimal affine transformation : Review of progress in quantitative nondestructive evaluation, Williamsburg, Virginia (United States), 22–26 Jun. 1987. Vol. 7A, pp. 821–830. Edited by D.D. Thompson and D.E. Chimenti, Plenum Press, 1988.

Multifrequency eddy current testing of steam generator tubes using optimal affine transformation Review of progress in quantitative nondestructive evaluation, Williamsburg, Virginia (United States), 22–26 Jun. 1987. Vol. 7A, pp. 821–830. Edited by D.D. Thompson and D.E. Chimenti, Plenum Press, 1988.

Multifrequency eddy current testing of steam generator tubes using optimal affine transformation Review of progress in quantitative nondestructive evaluation, Williamsburg, Virginia (United States), 22–26 Jun. 1987. Vol. 7A, pp. 821–830. Edited by D.D. Thompson and D.E. Chimenti, Plenum Press, 1988.