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Register a new userImage registration with sparse approximations in parametric dictionaries
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Added by
Alhussein Fawzi
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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We examine in this paper the problem of image registration from the new perspective where images are given by sparse approximations in parametric dictionaries of geometric functions. We propose a registration algorithm that looks for an estimate of the global transformation between sparse images by examining the set of relative geometrical transformations between the respective features. We propose a theoretical analysis of our registration algorithm and we derive performance guarantees based on two novel important properties of redundant dictionaries, namely the robust linear independence and the transformation inconsistency. We propose several illustrations and insights about the importance of these dictionary properties and show that common properties such as coherence or restricted isometry property fail to provide sufficient information in registration problems. We finally show with illustrative experiments on simple visual objects and handwritten digits images that our algorithm outperforms baseline competitor methods in terms of transformation-invariant distance computation and classification.
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We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse polynomial expansions, general low-rank approximations separating spatial and parametric variables, and hierarchical tensor decompositions separating all variables. We describe corresponding adaptive algorithms based on a common generic template and show their near-optimality with respect to natural approximability assumptions for each type of approximation. A central ingredient in the resulting bounds for the total computational complexity are new operator compression results for the case of infinitely many parameters. We conclude with a comparison of the complexity estimates based on the actual approximability properties of classes of parametric model problems, which shows that the computational costs of optimized low-rank expansions can be significantly lower or higher than those of sparse polynomial expansions, depending on the particular type of parametric problem.
Multimodal image registration (MIR) is a fundamental procedure in many image-guided therapies. Recently, unsupervised learning-based methods have demonstrated promising performance over accuracy and efficiency in deformable image registration. However, the estimated deformation fields of the existing methods fully rely on the to-be-registered image pair. It is difficult for the networks to be aware of the mismatched boundaries, resulting in unsatisfactory organ boundary alignment. In this paper, we propose a novel multimodal registration framework, which leverages the deformation fields estimated from both: (i) the original to-be-registered image pair, (ii) their corresponding gradient intensity maps, and adaptively fuses them with the proposed gated fusion module. With the help of auxiliary gradient-space guidance, the network can concentrate more on the spatial relationship of the organ boundary. Experimental results on two clinically acquired CT-MRI datasets demonstrate the effectiveness of our proposed approach.
We introduce a learning strategy for contrast-invariant image registration without requiring imaging data. While classical registration methods accurately estimate the spatial correspondence between images, they solve a costly optimization problem for every image pair. Learning-based techniques are fast at test time, but can only register images with image contrast and geometric content that are similar to those available during training. We focus on removing this image-data dependency of learning methods. Our approach leverages a generative model for diverse label maps and images that exposes networks to a wide range of variability during training, forcing them to learn features invariant to image type (contrast). This strategy results in powerful networks trained to generalize to a broad array of real input images. We present extensive experiments, with a focus on 3D neuroimaging, showing that this strategy enables robust registration of arbitrary image contrasts without the need to retrain for new modalities. We demonstrate registration accuracy that most often surpasses the state of the art both within and across modalities, using a single model. Critically, we show that input labels from which we synthesize images need not be of actual anatomy: training on randomly generated geometric shapes also results in competitive registration performance, albeit slightly less accurate, while alleviating the dependency on real data of any kind. Our code is available at: http://voxelmorph.csail.mit.edu
This paper presents a novel algorithm that registers a collection of mono-modal 3D images in a simultaneous fashion, named as Direct Simultaneous Registration (DSR). The algorithm optimizes global poses of local frames directly based on the intensities of images (without extracting features from the images). To obtain the optimal result, we start with formulating a Direct Bundle Adjustment (DBA) problem which jointly optimizes pose parameters of local frames and intensities of panoramic image. By proving the independence of the pose from panoramic image in the iterative process, DSR is proposed and proved to be able to generate the same optimal poses as DBA, but without optimizing the intensities of the panoramic image. The proposed DSR method is particularly suitable in mono-modal registration and in the scenarios where distinct features are not available, such as Transesophageal Echocardiography (TEE) images. The proposed method is validated via simulated and in-vivo 3D TEE images. It is shown that the proposed method outperforms conventional sequential registration method in terms of accuracy and the obtained results can produce good alignment in in-vivo images.
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. The learning algorithm adapts the patterns to a training set of graph signals. Experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state-of-the-art numerical learning algorithms in terms of sparse approximation of graph signals. In contrast to the unstructured dictionaries, however, the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression, denoising, and classification.
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