Shape Registration Research Articles

Shape registration for remote-sensing images with background variation

Image registration is a basic and key processing art for multi-sensor and/or multi-temporal remote-sensing images. Generally speaking, multi-temporal images covering the same region may contain different textures and/or changed backgrounds where the classical autonomous registration methods usually fail, especially those before and after disasters. The main reason is that a single pixel with surrounding region becomes unstable and cannot be applied for descriptor generation. However, the topology (or shape) between points should be viewed as steady description. In this article, we introduce a level line and consequent shape recognition algorithm (level line descriptor (LLD)) from close-range applications and propose an improved LLD for remote sensing. We present our analysis based on multi-temporal images with moderately changed backgrounds. The numerical experiments illustrate the operator's potential to become a relatively robust alternative for shape-based remote-sensing registration.

Bayesian data assimilation in shape registration

In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well-defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterization in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterization vector field ν, informed by regularity results about the forward model. Having done this, we illustrate how maximum likelihood estimators can be used to find regions of high posterior density, but also how we can apply recently developed Markov chain Monte Carlo methods on function spaces to characterize the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem.

Shape Representation and Registration in Vector Implicit Spaces: Adopting a Closed-Form Solution in the Optimization Process

In this paper, a novel method to solve the shape registration problem covering both global and local deformations is proposed. The vector distance function (VDF) is used to represent source and target shapes. The problem is formulated as an energy optimization process by matching the VDFs of the source and target shapes. The minimization process results in estimating the transformation parameters for the global and local deformation cases. Gradient descent optimization handles the computation of scaling, rotation, and translation matrices used to minimize the global differences between source and target shapes. Nonrigid deformations require a large number of parameters which make the use of the gradient descent minimization a very time-consuming process. We propose to compute the local deformation parameters using a closed-form solution as a linear system of equations derived from approximating an objective function. Extensive experimental validations and comparisons performed on generalized 2D shape data demonstrate the robustness and effectiveness of the method.

Functional Currents: A New Mathematical Tool to Model and Analyse Functional Shapes

This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. submanifold-supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a data structure that involves a deformable shape (roughly a finite dimensional submanifold) together with a function defined on this shape taking values in another manifold. Whereas mathematical currents have already proved to be very efficient theoretically and numerically to model and process shapes as curves or surfaces, they are limited to the manipulation of purely geometrical objects. We show that the introduction of the concept of functional currents offers a genuine solution to the simultaneous processing of the geometric and signal information of any functional shape. We explain how functional currents can be equipped with a Hilbertian norm that successfully combines the geometrical and functional content of functional shapes under geometrical and functional perturbations, thus paving the way for various processing algorithms. We illustrate this potential on two problems: the redundancy reduction of functional shape representations through matching pursuit schemes on functional currents and the simultaneous geometric and functional registration of functional shapes under diffeomorphic transport.

A Shape Registration Method Considering the Regional Difference in Precision

The shape of a mechanical part is composed of a number of specific feature regions,each with their own precision level.If the shape registration between the scanned data and the CAD model is performed when ignoring the precision difference,an inaccurate alignment result will be produced due to the deviation of low fidelity regions.A new registration method taking into consideration of the region precision is proposed.The procedure is divided into several region-to-region matching steps.The regions with high precision are matched.This matching transformation brings a set of standard orthogonal bases for the transformation space,and at the same time it gives registration constraints on some principal directions.The low precision regions are used to do a new matching.By projecting the new transformation on the previous standard orthogonal bases and setting some terms to zero,the model transformation is restricted and has no movement on the principal directions determined by the high precision regions.Our method produces high matching accuracy on high precision regions and low matching accuracy on low precision regions,which is suitable for practical utility in engineering.The experiments on a simulated cube and a real impeller are presented.

Erratum to "Automatic Renal Cortex Segmentation Using Implicit Shape Registration and Novel Multiple Surfaces Graph Search" [Oct 12 1849-1860

In the above-named article (ibid., vol. 31, no. 10, pp. 1849-1860, Oct. 2012), the author name Jian Tian should have been Jie Tian.

Field-guided registration for feature-conforming shape composition

We present an automatic shape composition method to fuse two shape parts which may not overlap and possibly contain sharp features, a scenario often encountered when modeling man-made objects. At the core of our method is a novel field-guided approach to automatically align two input parts in a feature-conforming manner. The key to our field-guided shape registration is a natural continuation of one part into the ambient field as a means to introduce an overlap with the distant part, which then allows a surface-to-field registration. The ambient vector field we compute is feature-conforming; it characterizes a piecewise smooth field which respects and naturally extrapolates the surface features. Once the two parts are aligned, gap filling is carried out by spline interpolation between matching feature curves followed by piecewise smooth least-squares surface reconstruction. We apply our algorithm to obtain feature-conforming shape composition on a variety of models and demonstrate generality of the method with results on parts with or without overlap and with or without salient features.

A new set distance and its application to shape registration

We propose a new distance measure, called Complement weighted sum of minimal distances, between finite sets in $${\mathbb Z }^n$$ and evaluate its usefulness for shape registration and matching. In this set distance the contribution of each point of each set is weighted according to its distance to the complement of the set. In this way, outliers and noise contribute less to the new similarity measure. We evaluate the performance of the new set distance for registration of shapes in binary images and compare it to a number of often used set distances found in the literature. The most extensive evaluation uses a set of synthetic 2D images. We also show three examples of real problems: registering a set of 2D images extracted from synchrotron radiation micro-computed tomography (SR $$\upmu $$ CT) volumes depicting bone implants; the difficult multi-modal registration task of finding the exact location of a 2D slice of a bone implant, as imaged by a light microscope, within a 3D SR $$\upmu $$ CT volume of the same implant; and finally recognition of handwritten characters. The evaluation shows that our new set distance performs well for all tasks and outperforms the other observed distance measures in most cases. It is therefore useful in many image registration and shape comparison tasks.

Robust Dense Registration of Partial Nonrigid Shapes

This paper presents a complete and robust solution for dense registration of partial nonrigid shapes. Its novel contributions are founded upon the newly proposed heat kernel coordinates (HKCs) that can accurately position points on the shape, and the priority-vicinity search that ensures geometric compatibility during the registration. HKCs index points by computing heat kernels from multiple sources, and their magnitudes serve as priorities of queuing points in registration. We start with shape features as the sources of heat kernels via feature detection and matching. Following the priority order of HKCs, the dense registration is progressively propagated from feature sources to all points. Our method has a superior indexing ability that can produce dense correspondences with fewer flips. The diffusion nature of HKCs, which can be interpreted as a random walk on a manifold, makes our method robust to noise and small holes avoiding surface surgery and repair. Our method searches correspondence only in a small vicinity of registered points, which significantly improves the time performance. Through comprehensive experiments, our new method has demonstrated its technical soundness and robustness by generating highly compatible dense correspondences.

D-Snake: Image Registration by As-Similar-As-Possible Template Deformation

We describe a snake-type method for shape registration in 2D and 3D, by fitting a given polygonal template to an acquired image or volume data. The snake aspires to fit itself to the data in a shape which is locally As-Similar-As-Possible (ASAP) to the template. Our ASAP regulating force is based on the Moving Least Squares (MLS) similarity deformation. Combining this force with the traditional internal and external forces associated with a snake leads to a powerful and robust registration algorithm, capable of extracting precise shape information from image data.

Automatic Renal Cortex Segmentation Using Implicit Shape Registration and Novel Multiple Surfaces Graph Search

In this paper, we present an automatic renal cortex segmentation approach using the implicit shape registration and novel multiple surfaces graph search. The proposed approach is based on a hierarchy system. First, the whole kidney is roughly initialized using an implicit shape registration method, with the shapes embedded in the space of Euclidean distance functions. Second, the outer and inner surfaces of renal cortex are extracted utilizing multiple surfaces graph searching, which is extended to allow for varying sampling distances and physical constraints to better separate the renal cortex and renal column. Third, a renal cortex refining procedure is applied to detect and reduce incorrect segmentation pixels around the renal pelvis, further improving the segmentation accuracy. The method was evaluated on 17 clinical computed tomography scans using the leave-one-out strategy with five metrics: Dice similarity coefficient (DSC), volumetric overlap error (OE), signed relative volume difference (SVD), average symmetric surface distance (D(avg)), and average symmetric rms surface distance (D(rms)). The experimental results of DSC, OE, SVD, D(avg) , and D(rms) were 90.50% ± 1.19%, 4.38% ± 3.93%, 2.37% ± 1.72%, 0.14 mm ± 0.09 mm , and 0.80 mm ± 0.64 mm, respectively. The results showed the feasibility, efficiency, and robustness of the proposed method.

Robust Facial Expression Recognition Using Near Infrared Cameras

In human-human communication we use verbal, vocal and non-verbal signals to communicate with others. Facial expressions are a form of non-verbal communication, recognizing them helps to improve the human-machine interaction. This paper proposes a system for pose- and illumination-invariant recognition of facial expressions using near-infrared camera images and precise 3D shape registration. Precise 3D shape information of the human face can be computed by means of Constrained Local Models (CLM), which fits a dense model to an unseen image in an iterative manner. We used a multi-class SVM to classify the acquired 3D shape into different emotion categories. Results surpassed human performance and show poseinvariant performance. Varying lighting conditions can influence the fitting process and reduce the recognition precision. We built a near-infrared and visible light camera array to test the method with different illuminations. Results shows that the near-infrared camera configuration is suitable for robust and reliable facial expression recognition with changing lighting conditions.

A methodology to accurately quantify patellofemoral cartilage contact kinematics by combining 3D image shape registration and cine-PC MRI velocity data

Patellofemoral osteoarthritis and its potential precursor patellofemoral pain syndrome (PFPS) are common, costly, and debilitating diseases. PFPS has been shown to be associated with altered patellofemoral joint mechanics; however, an actual variation in joint contact stresses has not been established due to challenges in accurately quantifying in vivo contact kinematics (area and location). This study developed and validated a method for tracking dynamic, in vivo cartilage contact kinematics by combining three magnetic resonance imaging (MRI) techniques, cine-phase contrast (CPC), multi-plane cine (MPC), and 3D high-resolution static imaging. CPC and MPC data were acquired from 12 healthy volunteers while they actively extended/flexed their knee within the MRI scanner. Since no gold standard exists for the quantification of in vivo dynamic cartilage contact kinematics, the accuracy of tracking a single point (patellar origin relative to the femur) represented the accuracy of tracking the kinematics of an entire surface. The accuracy was determined by the average absolute error between the PF kinematics derived through registration of MPC images to a static model and those derived through integration of the CPC velocity data. The accuracy ranged from 0.47mm to 0.77mm for the patella and femur and from 0.68mm to 0.86mm for the patellofemoral joint. For purely quantifying joint kinematics, CPC remains an analytically simpler and more accurate (accuracy <0.33mm) technique. However, for application requiring the tracking of an entire surface, such as quantifying cartilage contact kinematics, this combined imaging approach produces accurate results with minimal operator intervention.

Discriminative Sketch‐based 3D Model Retrieval via Robust Shape Matching

AbstractWe propose a sketch‐based 3D shape retrieval system that is substantially more discriminative and robust than existing systems, especially for complex models. The power of our system comes from a combination of a contour‐based 2D shape representation and a robust sampling‐based shape matching scheme. They are defined over discriminative local features and applicable for partial sketches; robust to noise and distortions in hand drawings; and consistent when strokes are added progressively. Our robust shape matching, however, requires dense sampling and registration and incurs a high computational cost. We thus devise critical acceleration methods to achieve interactive performance: precomputing kNN graphs that record transformations between neighboring contour images and enable fast online shape alignment; pruning sampling and shape registration strategically and hierarchically; and parallelizing shape matching on multi‐core platforms or GPUs. We demonstrate the effectiveness of our system through various experiments, comparisons, and user studies.

Deformable 3D Shape Registration Based on Local Similarity Transforms

AbstractIn this paper, a new method for deformable 3D shape registration is proposed. The algorithm computes shape transitions based on local similarity transforms which allows to model not only as‐rigid‐as‐possible deformations but also local and global scale. We formulate an ordinary differential equation (ODE) which describes the transition of a source shape towards a target shape. We assume that both shapes are roughly pre‐aligned (e.g., frames of a motion sequence). The ODE consists of two terms. The first one causes the deformation by pulling the source shape points towards corresponding points on the target shape. Initial correspondences are estimated by closest‐point search and then refined by an efficient smoothing scheme. The second term regularizes the deformation by drawing the points towards locally defined rest positions. These are given by the optimal similarity transform which matches the initial (undeformed) neighborhood of a source point to its current (deformed) neighborhood. The proposed ODE allows for a very efficient explicit numerical integration. This avoids the repeated solution of large linear systems usually done when solving the registration problem within general‐purpose non‐linear optimization frameworks. We experimentally validate the proposed method on a variety of real data and perform a comparison with several state‐of‐the‐art approaches.

TH-A-220-09: A Study of Prostate Edema Resolution Pattern by Principle Component Analysis

Purpose: To investigate and characterize the spatial resolutionpatterns of prostate edema in permanent prostate brachytherapy for accurate post‐implant dosimetry. Methods: Three patients with prostate cancer received 103Pd seed implant (day‐0) and consented to participate in an IRB approved post‐implant serial CTimaging study. Patient 1 was scanned on days: −1,1, 7, 10, 17, 30, 42; Patient 2: −1, 0, 1, 7, 16, 40; and patient 3: −1, 0, 1, 6, 11, 15, 30, 42. The image of patient 1 on day‐0 was contoured by a radiation oncologist and set as the template image for registration using a validated deformable image registration algorithm. For all voxel points inside the prostate in the template image, their corresponding coordinates in the subsequent images were obtained by the resulting deformation fields. These point sets were further aligned by rigid shape registration so as to reflect the intrinsic edema resolution. Principle component analysis (PCA) was used to compute the variation pattern among the point sets of each patient, and also among the point sets averaged from all patients on days −1, 1, 6/7, 15/16/17, and 40/42. Results: The percentages of the greatest four components of variation over the total variation are 92.0%, 2.9%, 2.1%, 1.2% for patient 1, 43.8%, 32.0%, 10.4%, 8.2% for patient 2, 45.6%, 15.1%, 12.3%, 10.5% for patient 3, and 63.0%, 18.4%, 11.3%, 7.2% for the averaged one. The greatest four components of variation plotted on the surfaces of prostate and of a sphere of similar size provided an easy visualization of major edema resolution patterns. Conclusions: Strong anisotropic edema resolution patterns were observed in patients receiving permanent prostate brachytherapy. PCA analysis and visual inspections indicated that different patients have significantly different edema resolution patterns. It suggests that spatialanisotropy of edema resolution should be considered for accurate dosimetry. This research project is currently funded by the NIH grant R01CA134627‐01

Penalizing Closest Point Sharing for Automatic Free Form Shape Registration

For accurate registration of overlapping free form shapes, different points in one shape must select different points in another as their most sensible correspondents. To reach this ideal state, in this paper we develop a novel algorithm to penalize those points in one shape that select the same closest point in another as their tentative correspondents. The novel algorithm then models the relative weight change over time of a tentative correspondence as the difference between the negative functions of the numbers of points in one shape that actually and ideally select the same closest point in another. Such modeling results in an optimal estimation of the weights of different tentative correspondences, in the sense of deterministic annealing, that lead the camera motion parameters to be estimated in the weighted least squares sense. The proposed algorithm is initialized using the pure translational motion derived from the centroids difference of the overlapping free form shapes being registered. Experimental results show that it outperforms three selected state-of-the-art algorithms on the whole for the accurate and robust registration of real overlapping free form shapes captured using two different laser scanners under typical imaging conditions.

Reconstruction of non-rigid 3D shapes from stereo-motion

Several non-rigid structure from motion methods have been proposed so far in order to recover both the motion and the non-rigid structure of an object. However, these monocular algorithms fail to give reliable 3D shape estimates when the overall rigid motion of the sequence is small. Aiming to overcome this limitation, in this paper we propose a novel approach for the 3D Euclidean reconstruction of deformable objects observed by an uncalibrated stereo rig. Using a stereo setup drastically improves the 3D model estimation when the observed 3D shape is mostly deforming without undergoing strong rigid motion. Our approach is based on the following steps. Firstly, the stereo system is automatically calibrated and used to compute metric rigid structures from pairs of views. Afterwards, these 3D shapes are aligned to a reference view using a RANSAC method in order to compute the mean shape of the object and to select the subset of points which have remained rigid throughout the sequence. The selected rigid points are then used to compute frame-wise shape registration and to robustly extract the motion parameters from frame to frame. Finally, all this information is used as initial estimates of a non-linear optimization which allows us to refine the initial solution and also to recover the non-rigid 3D model. Exhaustive results on synthetic and real data prove the performance of our proposal estimating motion, non-rigid models and stereo camera parameters even when there is no rigid motion in the original sequence.

Three-dimensional point-based shape registration algorithm based on adaptive distance function

In this study, the authors propose an iterative registration algorithm with point-based representation. The task is to geometrically transform a mobile object to a stationary object. Without a good initial position for two shapes with high-curvature features, traditional point-based algorithms have many challenges, such as suffering from slow convergence or divergence. For these problems, the authors define a new distance function to describe the point-surface distance, where the point-surface shortest distance is considered. Then, a non-linear optimisation model is established to calculate the optimal transformation. Moreover, the convergence of the proposed algorithm is derived and analysed from the viewpoint of geometrical optimisation. The proposed method does not require surface representation, feature extraction, curvature computation and is more applicable when initial position is rough. Its efficiency and robustness are verified by a series of experiments.

A robust hybrid method for nonrigid image registration

A nonrigid registration method is proposed to automatically align two images by registering two sets of sparse features extracted from the images. Motivated by the paradigm of Robust Point Matching (RPM) algorithms 1,2], which were originally proposed for shape registration, we develop Robust Hybrid Image Matching (RHIM) algorithm by alternatively optimizing feature correspondence and spatial transformation for image registration. Our RHIM algorithm is built to be robust to feature extraction errors. A novel dynamic outlier rejection approach is described for removing outliers and a local refinement technique is applied to correct non-exactly matched correspondences arising from image noise and deformations. Experimental results demonstrate the robustness and accuracy of our method.