Adaptive Regularization of Ill-Posed Problems: Application to Non-rigid Image Registration

We introduce an adaptive regularization approach. In contrast to conventional Tikhonov regularization, which specifies a fixed regularization operator, we estimate it simultaneously with parameters. From a Bayesian perspective we estimate the prior distribution on parameters assuming that it is close to some given model distribution. We constrain the prior distribution to be a Gauss-Markov random field (GMRF), which allows us to solve for the prior distribution analytically and provides a fast optimization algorithm. We apply our approach to non-rigid image registration to estimate the spatial transformation between two images. Our evaluation shows that the adaptive regularization approach significantly outperforms standard variational methods

Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces

Classical deformable registration techniques achieve impressive results and offer a rigorous theoretical treatment, but are computationally intensive since they solve an optimization problem for each image pair. Recently, learning-based methods have facilitated fast registration by learning spatial deformation functions. However, these approaches use restricted deformation models, require supervised labels, or do not guarantee a diffeomorphic (topology-preserving) registration. Furthermore, learning-based registration tools have not been derived from a probabilistic framework that can offer uncertainty estimates. In this paper, we build a connection between classical and learning-based methods. We present a probabilistic generative model and derive an unsupervised learning-based inference algorithm that uses insights from classical registration methods and makes use of recent developments in convolutional neural networks (CNNs). We demonstrate our method on a 3D brain registration task for both images and anatomical surfaces, and provide extensive empirical analyses. Our principled approach results in state of the art accuracy and very fast runtimes, while providing diffeomorphic guarantees. Our implementation is available at http://voxelmorph.csail.mit.edu.Comment: MedIA: Medical Image Analysis (MICCAI2018 Special Issue). Expands on MICCAI 2018 paper (arXiv:1805.04605) by introducing an extension to anatomical surface registration, new experiments, and analysis of diffeomorphic implementations. Keywords: medical image registration; diffeomorphic; invertible; probabilistic modeling; variational inference. Code available at http://voxelmorph.csail.mit.edu. arXiv admin note: text overlap with arXiv:1805.0460

Inverse-Consistent Deep Networks for Unsupervised Deformable Image Registration

Deformable image registration is a fundamental task in medical image analysis, aiming to establish a dense and non-linear correspondence between a pair of images. Previous deep-learning studies usually employ supervised neural networks to directly learn the spatial transformation from one image to another, requiring task-specific ground-truth registration for model training. Due to the difficulty in collecting precise ground-truth registration, implementation of these supervised methods is practically challenging. Although several unsupervised networks have been recently developed, these methods usually ignore the inherent inverse-consistent property (essential for diffeomorphic mapping) of transformations between a pair of images. Also, existing approaches usually encourage the to-be-estimated transformation to be locally smooth via a smoothness constraint only, which could not completely avoid folding in the resulting transformation. To this end, we propose an Inverse-Consistent deep Network (ICNet) for unsupervised deformable image registration. Specifically, we develop an inverse-consistent constraint to encourage that a pair of images are symmetrically deformed toward one another, until both warped images are matched. Besides using the conventional smoothness constraint, we also propose an anti-folding constraint to further avoid folding in the transformation. The proposed method does not require any supervision information, while encouraging the diffeomoprhic property of the transformation via the proposed inverse-consistent and anti-folding constraints. We evaluate our method on T1-weighted brain magnetic resonance imaging (MRI) scans for tissue segmentation and anatomical landmark detection, with results demonstrating the superior performance of our ICNet over several state-of-the-art approaches for deformable image registration. Our code will be made publicly available.Comment: 13 pages, 11 figure

A Learning Framework for Robust Bin Picking by Customized Grippers

Customized grippers have specifically designed fingers to increase the contact area with the workpieces and improve the grasp robustness. However, grasp planning for customized grippers is challenging due to the object variations, surface contacts and structural constraints of the grippers. In this paper, we propose a learning framework to plan robust grasps for customized grippers in real-time. The learning framework contains a low-level optimization-based planner to search for optimal grasps locally under object shape variations, and a high-level learning-based explorer to learn the grasp exploration based on previous grasp experience. The optimization-based planner uses an iterative surface fitting (ISF) to simultaneously search for optimal gripper transformation and finger displacement by minimizing the surface fitting error. The high-level learning-based explorer trains a region-based convolutional neural network (R-CNN) to propose good optimization regions, which avoids ISF getting stuck in bad local optima and improves the collision avoidance performance. The proposed learning framework with RCNN-ISF is able to consider the structural constraints of the gripper, learn grasp exploration strategy from previous experience, and plan optimal grasps in clutter environment in real-time. The effectiveness of the algorithm is verified by experiments.Comment: Submitted to 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2019). arXiv admin note: text overlap with arXiv:1803.1129

Dependent landmark drift: robust point set registration with a Gaussian mixture model and a statistical shape model

The goal of point set registration is to find point-by-point correspondences between point sets, each of which characterizes the shape of an object. Because local preservation of object geometry is assumed, prevalent algorithms in the area can often elegantly solve the problems without using geometric information specific to the objects. This means that registration performance can be further improved by using prior knowledge of object geometry. In this paper, we propose a novel point set registration method using the Gaussian mixture model with prior shape information encoded as a statistical shape model. Our transformation model is defined as a combination of the similar transformation, motion coherence, and the statistical shape model. Therefore, the proposed method works effectively if the target point set includes outliers and missing regions, or if it is rotated. The computational cost can be reduced to linear, and therefore the method is scalable to large point sets. The effectiveness of the method will be verified through comparisons with existing algorithms using datasets concerning human body shapes, hands, and faces

The Coherent Point Drift for Clustered Point Sets

The problem of non-rigid point set registration is a key problem for many computer vision tasks. In many cases the nature of the data or capabilities of the point detection algorithms can give us some prior information on point sets distribution. In non-rigid case this information is able to drastically improve registration results by limiting number of possible solutions. In this paper we explore use of prior information about point sets clustering, such information can be obtained with preliminary segmentation. We extend existing probabilistic framework for fitting two level Gaussian mixture model and derive closed form solution for maximization step of the EM algorithm. This enables us to improve method accuracy with almost no performance loss. We evaluate our approach and compare the Cluster Coherent Point Drift with other existing non-rigid point set registration methods and show it's advantages for digital medicine tasks, especially for heart template model personalization using patient's medical data

Point-Set Registration: Coherent Point Drift

Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown non-rigid spatial transformation, large dimensionality of point set, noise and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and non-rigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the GMM centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by re-parametrization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the non-rigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and non-rigid transformations in the presence of noise, outliers and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods

Regression-Based Image Alignment for General Object Categories

Gradient-descent methods have exhibited fast and reliable performance for image alignment in the facial domain, but have largely been ignored by the broader vision community. They require the image function be smooth and (numerically) differentiable -- properties that hold for pixel-based representations obeying natural image statistics, but not for more general classes of non-linear feature transforms. We show that transforms such as Dense SIFT can be incorporated into a Lucas Kanade alignment framework by predicting descent directions via regression. This enables robust matching of instances from general object categories whilst maintaining desirable properties of Lucas Kanade such as the capacity to handle high-dimensional warp parametrizations and a fast rate of convergence. We present alignment results on a number of objects from ImageNet, and an extension of the method to unsupervised joint alignment of objects from a corpus of images

DeepWrinkles: Accurate and Realistic Clothing Modeling

We present a novel method to generate accurate and realistic clothing deformation from real data capture. Previous methods for realistic cloth modeling mainly rely on intensive computation of physics-based simulation (with numerous heuristic parameters), while models reconstructed from visual observations typically suffer from lack of geometric details. Here, we propose an original framework consisting of two modules that work jointly to represent global shape deformation as well as surface details with high fidelity. Global shape deformations are recovered from a subspace model learned from 3D data of clothed people in motion, while high frequency details are added to normal maps created using a conditional Generative Adversarial Network whose architecture is designed to enforce realism and temporal consistency. This leads to unprecedented high-quality rendering of clothing deformation sequences, where fine wrinkles from (real) high resolution observations can be recovered. In addition, as the model is learned independently from body shape and pose, the framework is suitable for applications that require retargeting (e.g., body animation). Our experiments show original high quality results with a flexible model. We claim an entirely data-driven approach to realistic cloth wrinkle generation is possible.Comment: 18 pages, 12 figures, 15th European Conference on Computer Vision (ECCV) 2018, Oral Presentatio

Feature-based groupwise registration of historical aerial images to present-day ortho-photo maps

In this paper, we address the registration of historical WWII images to present-day ortho-photo maps for the purpose of geolocalization. Due to the challenging nature of this problem, we propose to register the images jointly as a group rather than in a step-by-step manner. To this end, we exploit Hough Voting spaces as pairwise registration estimators and show how they can be integrated into a probabilistic groupwise registration framework that can be efficiently optimized. The feature-based nature of our registration framework allows to register images with a-priori unknown translational and rotational relations, and is also able to handle scale changes of up to 30% in our test data due to a final geometrically guided matching step. The superiority of the proposed method over existing pairwise and groupwise registration methods is demonstrated on eight highly challenging sets of historical images with corresponding ortho-photo maps.Comment: Under review at Elsevier Pattern Recognitio