Image deformation using moving least squares

Schaefer, Scott; McPhail, Travis; Warren, Joe

doi:10.1145/1141911.1141920

Cited by 543 publications

(122 citation statements)

References 15 publications

Supporting

Mentioning

121

Contrasting

Unclassified

Order By: Relevance

“…Evaluation series B consists of 400 serial sections including the signal change induced by the volume (Supplementary Video 3) and as such is a more realistic test case. We have artificially distorted all sections of both series using randomized smooth non-linear transformations using a Moving-Least-Squares affine transformation 18 We report the average scale factor of each section relative to ground truth for all three alignment methods (Supplementary Fig. 7).…”

Section: Artificially Generated Ground Truthmentioning

confidence: 99%

Elastic volume reconstruction from series of ultra-thin microscopy sections

et al. 2012

View full text Add to dashboard Cite

Anatomy of large biological specimens is often reconstructed from serially sectioned volumes imaged by high-resolution microscopy. We developed a method to reassemble a continuous volume from such large section series that explicitly minimizes artificial deformation by applying a global elastic constraint. We demonstrate our method on a series of transmission electron microscopy sections covering the entire 558-cell Caenorhabditis elegans embryo and a segment of the Drosophila melanogaster larval ventral nerve cord. DOI: https://doi.org/10. 1038/nmeth.2072 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-127852 Accepted Version Originally published at: Saalfeld, Stephan; Fetter, Richard; Cardona, Albert; Tomancak, Pavel (2012). Elastic volume reconstruction from series of ultra-thin microscopy sections. Nature Methods, 9(7):717-720. DOI: https://doi.org/10.1038/nmeth.2072 Elastic Volume Reconstruction from Series of Ultra-thin Microscopy SectionsStephan The downside of the method is that by physically cutting a block into sections the continuity between sections is lost and individual sections are deformed. To recover the imaged volume and extract biologically interesting information such as the reconstruction of neuronal circuits 2,3,5 , sections need to be aligned and distortion must be removed.Alignment can be achieved by maximizing the overlap of similar image content between adjacent sections. However, there are two unknowns that change image content across the section series: specimen's shape and independent section distortion introduced during preparation. Naively warping one section into another would compensate for the shape of the specimen and by that introduce artificial deformation. Our method exploits the fact that the biological specimen's shape typically changes smoothly across sections whereas the independent distortion in each section is random and uncorrelated with neighboring sections. We align all sections not only to their direct neighbors in the series but to all sections in a local neighborhood by modelling sections as two-dimensional elastic sheets that penalize non-rigid deformation ( Fig. 1a and Supplementary Fig. 1).All sections are treated as moving targets in a template-free global alignment. The elastic constraint is implemented as a spring-connected particle system where each section is represented as a triangular spring-mesh ( Fig. 1b and Supplementary Video 1 and Online methods).For each vertex of the spring-mesh, we search for the corresponding location in other sections by pairwise block-matching using normalized cross-correlation (NCC). To that end, we explore all translation vectors in an immediate neighborhood which requires sections to be in approximate alignment (Fig. 1c,d). We estimate this approximate alignment using automatically extracted landmark correspondences from invariant local image features as described previously 7,8 . Originally proposed for robust object recognition under partial occlus...

show abstract

Section: Artificially Generated Ground Truthmentioning

confidence: 99%

Elastic volume reconstruction from series of ultra-thin microscopy sections

et al. 2012

View full text Add to dashboard Cite

show abstract

“…However, deformations have been more principally investigated in the domain of images. Moving Least Squares is a state-of-art technique to produce realistic deformations [7]. In this work we use the Moving Least Squares method for applying the transformations over series.…”

Section: Instance Transformationsmentioning

confidence: 99%

“…This algorithm is used to transform one signal that passes through a set of points P , called control points. The transformation is defined by a new set of control points Q, which are the transformed positions of the control points P [7]. The control points Q are obtained, in our implementation, by applying transformation fields F translations to the original control points P .…”

Section: Transformation Fields and Moving Least Squaresmentioning

confidence: 99%

“…The time series is divided into a number of local regions and transformation fields/vectors are created to represent the direction and magnitude of the translational variance at every region center, based on the constructed variance distributions. Finally, the application of the transformation fields to time series is conducted using the Moving Least Squares algorithm [7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Invariant Time-Series Classification

Grabocka

Νανόπουλος

Schmidt-Thieme

2012

Machine Learning and Knowledge Discovery in Databases

View full text Add to dashboard Cite

Abstract. Time-series classification is a field of machine learning that has attracted considerable focus during the recent decades. The large number of time-series application areas ranges from medical diagnosis up to financial econometrics. Support Vector Machines (SVMs) are reported to perform non-optimally in the domain of time series, because they suffer detecting similarities in the lack of abundant training instances. In this study we present a novel time-series transformation method which significantly improves the performance of SVMs. Our novel transformation method is used to enlarge the training set through creating new transformed instances from the support vector instances. The new transformed instances encapsulate the necessary intra-class variations required to redefine the maximum margin decision boundary. The proposed transformation method utilizes the variance distributions from the intra-class warping maps to build transformation fields, which are applied to series instances using the Moving Least Squares algorithm. Extensive experimentations on 35 time series datasets demonstrate the superiority of the proposed method compared to both the Dynamic Time Warping version of the Nearest Neighbor and the SVMs classifiers, outperforming them in the majority of the experiments.

show abstract

“…For both methods, the user needed to define many control points on the object if the deformation is complex or for complex characters, which represents a disadvantage for cartoon production. Schaefer et al [2006] proposed a 2D shape deformation algorithm based on linear moving least squares.…”

Section: D Shape Deformationmentioning

confidence: 99%