(Non-)rigid motion interpretation : a regularized approach

1988 ◽  
Vol 233 (1271) ◽  
pp. 217-234 ◽  
Keyword(s):  
Multiple Scales ◽  
Rigid Motion ◽  
Image Data ◽  
Small Region ◽  
General Assumption ◽  
Naturally Occurring ◽  
Special Cases ◽  
Ill Posed ◽  
Motion Discontinuities ◽  
Variational Condition

Determining 3D motion from a time-varying 2D image is an ill-posed problem; unless we impose additional constraints, an infinite number of solutions is possible. The usual constraint is rigidity, but many naturally occurring motions are not rigid and not even piecewise rigid. A more general assumption is that the parameters (or some of the parameters) characterizing the motion are approximately (but not exactly) constant in any sufficiently small region of the image. If we know the shape of a surface we can uniquely recover the smoothest motion consistent with image data and the known structure of the object, through regularization. This paper develops a general paradigm for the analysis of nonrigid motion. The variational condition we obtain includes many previously studied constraints as ‘special cases’. Among them are isometry, rigidity and planarity. If the variational condition is applied at multiple scales of resolution, it can be applied to turbulent motion. Finally, it is worth noting that our theory does not require the computation of correspondence (optic flow or discrete displacements), and it is effective in the presence of motion discontinuities.

Information and estimation in image processing

1987 ◽  
Vol 45 ◽  
pp. 14-17
Author(s):  
B. Roy Frieden
Keyword(s):  
Image Processing ◽  
Optical System ◽  
Large Amplitude ◽  
Communication Theory ◽  
Image Data ◽  
Direct Approach ◽  
Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

scholarly journals A 3D trabecular bone homogenization technique

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Marco C. Marques ◽  
Jorge Belinha ◽  
António F. Oliveira ◽  
Maria Cristinha M. Cespedes ◽  
Renato M. Natal Jorge
Keyword(s):  
Mechanical Properties ◽  
Mechanical Behavior ◽  
Trabecular Bone ◽  
Multiple Scales ◽  
Bone Adaptation ◽  
Computationally Efficient ◽  
Micro Scale ◽  
Special Cases ◽  
Homogeneous Models ◽  
Time Required

Purpose: Bone is a hierarchical material that can be characterized from the microscale to macroscale. Multiscale models make it possible to study bone remodeling, inducing bone adaptation by using information of bone multiple scales. This work proposes a computationally efficient homogenization methodology useful for multiscale analysis. This technique is capable to define the homogenized microscale mechanical properties of the trabecular bone highly heterogeneous medium. Methods: In this work, a morphology - based fabric tensor and a set of anisotropic phenomenological laws for bone tissue was used, in order to define the bone micro-scale mechanical properties. To validate the developed methodology, several examples were performed in order to analyze its numerical behavior. Thus, trabecular bone and fabricated benchmarks patches (representing special cases of trabecular bone morphologies) were analyzed under compression. Results: The results show that the developed technique is robust and capable to provide a consistent material homogenization, indicating that the homogeneous models were capable to accurately reproduce the micro-scale patch mechanical behavior. Conclusions: The developed method has shown to be robust, computationally less demanding and enabling the authors to obtain close results when comparing the heterogeneous models with equivalent homogenized models. Therefore, it is capable to accurately predict the micro-scale patch mechanical behavior in a fraction of the time required by classic homogenization techniques.

Planar and Spatial Rigid Motion as Special Cases of Spherical and 3-Spherical Motion

1983 ◽  
Vol 105 (3) ◽  
pp. 569-575 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Rigid Motion ◽  
Arc Length ◽  
Spatial Motion ◽  
Special Cases ◽  
Curvature Theory ◽  
Rigid Motions ◽  
Spherical Motion ◽  
Smooth Transformation

This paper examines spherical and 3-spherical rigid motions with instantaneous invariants approaching zero. It is shown that these motions may be identified with planar and spatial motion, respectively. The instantaneous invariants are ratios of arc-length along the surface of the sphere to its radius, thus the process of shrinking their value may be viewed as expanding the sphere while bounding the instantaneous displacements on the sphere. This allows a smooth transformation of the results of the curvature theory of spherical and 3-spherical motion into their planar and spatial counterparts.

scholarly journals Context Aggregation Network for Semantic Labeling in Aerial Images

2019 ◽  
Vol 11 (10) ◽  
pp. 1158 ◽  
Author(s):  
Wensheng Cheng ◽  
Wen Yang ◽  
Min Wang ◽  
Gang Wang ◽  
Jinyong Chen
Keyword(s):  
High Resolution ◽  
Multiple Scales ◽  
Image Data ◽  
Remote Sensing Image ◽  
Object Localization ◽  
Aerial Images ◽  
Localization Accuracy ◽  
Multi Scale ◽  
Semantic Labeling ◽  
Multi Level

Semantic labeling for high resolution aerial images is a fundamental and necessary task in remote sensing image analysis. It is widely used in land-use surveys, change detection, and environmental protection. Recent researches reveal the superiority of Convolutional Neural Networks (CNNs) in this task. However, multi-scale object recognition and accurate object localization are two major problems for semantic labeling methods based on CNNs in high resolution aerial images. To handle these problems, we design a Context Fuse Module, which is composed of parallel convolutional layers with kernels of different sizes and a global pooling branch, to aggregate context information at multiple scales. We propose an Attention Mix Module, which utilizes a channel-wise attention mechanism to combine multi-level features for higher localization accuracy. We further employ a Residual Convolutional Module to refine features in all feature levels. Based on these modules, we construct a new end-to-end network for semantic labeling in aerial images. We evaluate the proposed network on the ISPRS Vaihingen and Potsdam datasets. Experimental results demonstrate that our network outperforms other competitors on both datasets with only raw image data.

Statistical Support for Uncertainty in Radiological Diagnosis

2000 ◽  
Vol 39 (01) ◽  
pp. 1-6 ◽  
Author(s):  
B. A. Teather ◽  
N. P. Jeffery ◽  
G. H. du Boulay ◽  
B. du Boulay ◽  
M. Sharples ◽  
...  
Keyword(s):  
Magnetic Resonance Imaging ◽  
Observational Studies ◽  
Image Data ◽  
Statistical Modelling ◽  
Probabilistic Interpretation ◽  
Resonance Imaging ◽  
Naturally Occurring ◽  
Statistical Support ◽  
The Subject

Abstract:Radiological interpretation and diagnosis involves the comparison and classification of complex medical images and is typical of the categorisation tasks that have been the subject of observational studies in Cognitive Science. This paper considers the affinity between statistical modelling and theories of categorisation for naturally occurring categories. Statistical based measures of similarity and typicality with a probabilistic interpretation are derived. The utilisation of these measures in the support of diagnosis under uncertainty via interactive overview plots is described. The application of the methodology to magnetic resonance imaging of the head is considered. The methods detailed have application to other fields involving archiving and retrieving of image data.

scholarly journals Sparse signal recovery from modulo observations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Viraj Shah ◽  
Chinmay Hegde
Keyword(s):  
Dynamic Range ◽  
Signal Reconstruction ◽  
Image Data ◽  
Signal Recovery ◽  
Reconstruction Methods ◽  
Novel Approach ◽  
Sparsity Constraints ◽  
Ill Posed ◽  
Special Case ◽  
Recovery Problem

AbstractWe consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a relatively new imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the under-determined regime with modulo observations is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the signal recovery problem under sparsity constraints for the special case to modulo folding limited to two periods. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal. We also provide experiments validating our approach on toy signal and image data and demonstrate its promising performance.

scholarly journals 3D Flexible Refinement: Structure and Motion of Flexible Proteins from Cryo-EM

2021 ◽  
Author(s):  
Ali Punjani ◽  
David J. Fleet
Keyword(s):  
3D Structure ◽  
Rigid Motion ◽  
Image Data ◽  
Deformation Field ◽  
Local Geometry ◽  
Biological Macromolecules ◽  
Conformational Variability ◽  
Structure And Motion ◽  
Flow Generator ◽  
And Function

Single particle cryo-EM excels in determining static structures of biological macromolecules such as proteins. However, many proteins are dynamic, with their motion inherently linked to their function. Recovering the continuous motion and detailed 3D structure of flexible proteins from cryo-EM data has remained an open challenge. We introduce 3D Flexible Refinement (3DFlex), a motion-based deep neural network model of continuous heterogeneity. 3DFlex directly exploits the knowledge that conformational variability of a protein is often the result of physical processes that transport density over space and tend to conserve mass and preserve local geometry. From 2D image data, the 3DFlex model jointly learns a single canonical 3D map, latent coordinate vectors that specify positions on the protein's conformational landscape, and a flow generator that, given a latent position as input, outputs a 3D deformation field. This deformation field convects the canonical map into appropriate conformations to explain experimental images. Applied to experimental data, 3DFlex learns non-rigid motion spanning several orders of magnitude while preserving high-resolution details of secondary structure elements. Further, 3DFlex resolves canonical maps that are improved relative to conventional refinement methods because particle images contribute to the maps coherently regardless of the conformation of the protein in the image. Together, the ability to obtain insight into motion in macromolecules, as well as the ability to resolve features that are usually lost in cryo-EM of flexible specimens, will provide new insight and allow new avenues of investigation into biomolecular structure and function.

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