Shape regression machine

Statistical regression analysis of functional and shape data

We develop a multivariate regression model when responses or predictors are on nonlinear manifolds, rather than on Euclidean spaces. The nonlinear constraint makes the problem challenging and needs to be studied carefully. By performing principal component analysis (PCA) on tangent space of manifold, we use principal directions instead in the model. Then, the ordinary regression tools can be utilized. We apply the framework to both shape data (ozone hole contours) and functional data (spectrums of absorbance of meat in Tecator dataset). Specifically, we adopt the square-root velocity function representation and parametrization-invariant metric. Experimental results have shown that we can not only perform powerful regression analysis on the non-Euclidean data but also achieve high prediction accuracy by the constructed model.

Recurrent Convolutional Shape Regression

The mainstream direction in face alignment is now dominated by cascaded regression methods. These methods start from an image with an initial shape and build a set of shape increments based on features with respect to the current estimated shape. These shape increments move the initial shape to the desired location. Despite the advantages of the cascaded methods, they all share two major limitations: (i) shape increments are learned independently from each other in a cascaded manner, (ii) the use of standard generic computer vision features such SIFT, HOG, does not allow these methods to learn problem-specific features. In this work, we propose a novel Recurrent Convolutional Shape Regression (RCSR) method that overcomes these limitations. We formulate the standard cascaded alignment problem as a recurrent process and learn all shape increments jointly, by using a recurrent neural network with a gated recurrent unit. Importantly, by combining a convolutional neural network with a recurrent one we avoid hand-crafted features, widely adopted in the literature and thus we allow the model to learn task-specific features. Besides, we employ the convolutional gated recurrent unit which takes as input the feature tensors instead of flattened feature vectors. Therefore, the spatial structure of the features can be better preserved in the memory of the recurrent neural network. Moreover, both the convolutional and the recurrent neural networks are learned jointly. Experimental evaluation shows that the proposed method has better performance than the state-of-the-art methods, and further supports the importance of learning a single end-to-end model for face alignment.

Viewpoint-Consistent 3D Face Alignment

Most approaches to face alignment treat the face as a 2D object, which fails to represent depth variation and is vulnerable to loss of shape consistency when the face rotates along a 3D axis. Because faces commonly rotate three dimensionally, 2D approaches are vulnerable to significant error. 3D morphable models, employed as a second step in 2D+3D approaches are robust to face rotation but are computationally too expensive for many applications, yet their ability to maintain viewpoint consistency is unknown. We present an alternative approach that estimates 3D face landmarks in a single face image. The method uses a regression forest-based algorithm that adds a third dimension to the common cascade pipeline. 3D face landmarks are estimated directly, which avoids fitting a 3D morphable model. The proposed method achieves viewpoint consistency in a computationally efficient manner that is robust to 3D face rotation. To train and test our approach, we introduce the Multi-PIE Viewpoint Consistent database. In empirical tests, the proposed method achieved simple yet effective head pose estimation and viewpoint consistency on multiple measures relative to alternative approaches.

Automatic Cystocele Severity Grading in Ultrasound by Spatio-Temporal Regression

Cystocele is a common disease in woman. Accurate assessment of cystocele severity is very important for treatment options. The transperineal ultrasound (US) has recently emerged as an alternative tool for cystocele grading. The cystocele severity is usually evaluated with the manual measurement of the maximal descent of the bladder (MDB) relative to the symphysis pubis (SP) during Valsalva maneuver. However, this process is time-consuming and operator-dependent. In this study, we propose an automatic scheme for csystocele grading from transperineal US video. A two-layer spatio-temporal regression model is proposed to identify the middle axis and lower tip of the SP, and segment the bladder, which are essential tasks for the measurement of the MDB. Both appearance and context features are extracted in the spatio-temporal domain to help the anatomy detection. Experimental results on 85 transperineal US videos show that our method significantly outperforms the state-of-the-art regression method.

Robust and Accurate Shape Model Matching Using Random Forest Regression-Voting

A widely used approach for locating points on deformable objects in images is to generate feature response images for each point, and then to fit a shape model to these response images. We demonstrate that Random Forest regression-voting can be used to generate high quality response images quickly. Rather than using a generative or a discriminative model to evaluate each pixel, a regressor is used to cast votes for the optimal position of each point. We show that this leads to fast and accurate shape model matching when applied in the Constrained Local Model framework. We evaluate the technique in detail, and compare it with a range of commonly used alternatives across application areas: the annotation of the joints of the hands in radiographs and the detection of feature points in facial images. We show that our approach outperforms alternative techniques, achieving what we believe to be the most accurate results yet published for hand joint annotation and state-of-the-art performance for facial feature point detection.

Multi-organ localization combining global-to-local regression and confidence maps

We propose a method for fast, accurate and robust localization of several organs in medical images. We generalize global-to-local cascades of regression forests [1] to multiple organs. A first regressor encodes global relationships between organs. Subsequent regressors refine the localization of each organ locally and independently for improved accuracy. We introduce confidence maps, which incorporate information about both the regression vote distribution and the organ shape through probabilistic atlases. They are used within the cascade itself, to better select the test voxels for the second set of regressors, and to provide richer information than the classical bounding boxes thanks to the shape prior. We demonstrate the robustness and accuracy of our approach through a quantitative evaluation on a large database of 130 CT volumes.

Improved image registration by sparse patch-based deformation estimation

Despite intensive efforts for decades, deformable image registration is still a challenging problem due to the potential large anatomical differences across individual images, which limits the registration performance. Fortunately, this issue could be alleviated if a good initial deformation can be provided for the two images under registration, which are often termed as the moving subject and the fixed template, respectively. In this work, we present a novel patch-based initial deformation prediction framework for improving the performance of existing registration algorithms. Our main idea is to estimate the initial deformation between subject and template in a patch-wise fashion by using the sparse representation technique. We argue that two image patches should follow the same deformation toward the template image if their patch-wise appearance patterns are similar. To this end, our framework consists of two stages, i.e., the training stage and the application stage. In the training stage, we register all training images to the pre-selected template, such that the deformation of each training image with respect to the template is known. In the application stage, we apply the following four steps to efficiently calculate the initial deformation field for the new test subject: (1) We pick a small number of key points in the distinctive regions of the test subject; (2) for each key point, we extract a local patch and form a coupled appearance-deformation dictionary from training images where each dictionary atom consists of the image intensity patch as well as their respective local deformations; (3) a small set of training image patches in the coupled dictionary are selected to represent the image patch of each subject key point by sparse representation. Then, we can predict the initial deformation for each subject key point by propagating the pre-estimated deformations on the selected training patches with the same sparse representation coefficients; and (4) we employ thin-plate splines (TPS) to interpolate a dense initial deformation field by considering all key points as the control points. Thus, the conventional image registration problem becomes much easier in the sense that we only need to compute the remaining small deformation for completing the registration of the subject to the template. Experimental results on both simulated and real data show that the registration performance can be significantly improved after integrating our patch-based deformation prediction framework into the existing registration algorithms.

Robust anatomical landmark detection for MR brain image registration

Correspondence matching between MR brain images is often challenging due to large inter-subject structural variability. In this paper, we propose a novel landmark detection method for robust establishment of correspondences between subjects. Specifically, we first annotate distinctive landmarks in the training images. Then, we use regression forest to simultaneously learn (1) the optimal set of features to best characterize each landmark and (2) the non-linear mappings from local patch appearances of image points to their displacements towards each landmark. The learned regression forests are used as landmark detectors to predict the locations of these landmarks in new images. Since landmark detection is performed in the entire image domain, our method can cope with large anatomical variations among subjects. We evaluated our method by applying it to MR brain image registration. Experimental results indicate that by combining our method with existing registration method, obvious improvement in registration accuracy can be achieved.

Local evidence aggregation for regression-based facial point detection

We propose a new algorithm to detect facial points in frontal and near-frontal face images. It combines a regression-based approach with a probabilistic graphical model-based face shape model that restricts the search to anthropomorphically consistent regions. While most regression-based approaches perform a sequential approximation of the target location, our algorithm detects the target location by aggregating the estimates obtained from stochastically selected local appearance information into a single robust prediction. The underlying assumption is that by aggregating the different estimates, their errors will cancel out as long as the regressor inputs are uncorrelated. Once this new perspective is adopted, the problem is reformulated as how to optimally select the test locations over which the regressors are evaluated. We propose to extend the regression-based model to provide a quality measure of each prediction, and use the shape model to restrict and correct the sampling region. Our approach combines the low computational cost typical of regression-based approaches with the robustness of exhaustive-search approaches. The proposed algorithm was tested on over 7,500 images from five databases. Results showed significant improvement over the current state of the art.

Learning Deformable Shape Manifolds

We propose an approach to shape detection of highly deformable shapes in images via manifold learning with regression. Our method does not require shape key points be defined at high contrast image regions, nor do we need an initial estimate of the shape. We only require sufficient representative training data and a rough initial estimate of the object position and scale. We demonstrate the method for face shape learning, and provide a comparison to nonlinear Active Appearance Model. Our method is extremely accurate, to nearly pixel precision and is capable of accurately detecting the shape of faces undergoing extreme expression changes. The technique is robust to occlusions such as glasses and gives reasonable results for extremely degraded image resolutions.

Learning task-optimal registration cost functions for localizing cytoarchitecture and function in the cerebral cortex

Image registration is typically formulated as an optimization problem with multiple tunable, manually set parameters. We present a principled framework for learning thousands of parameters of registration cost functions, such as a spatially-varying tradeoff between the image dissimilarity and regularization terms. Our approach belongs to the classic machine learning framework of model selection by optimization of cross-validation error. This second layer of optimization of cross-validation error over and above registration selects parameters in the registration cost function that result in good registration as measured by the performance of the specific application in a training data set. Much research effort has been devoted to developing generic registration algorithms, which are then specialized to particular imaging modalities, particular imaging targets and particular postregistration analyses. Our framework allows for a systematic adaptation of generic registration cost functions to specific applications by learning the "free" parameters in the cost functions. Here, we consider the application of localizing underlying cytoarchitecture and functional regions in the cerebral cortex by alignment of cortical folding. Most previous work assumes that perfectly registering the macro-anatomy also perfectly aligns the underlying cortical function even though macro-anatomy does not completely predict brain function. In contrast, we learn 1) optimal weights on different cortical folds or 2) optimal cortical folding template in the generic weighted sum of squared differences dissimilarity measure for the localization task. We demonstrate state-of-the-art localization results in both histological and functional magnetic resonance imaging data sets.

Training an active random field for real-time image denoising

Many computer vision problems can be formulated in a Bayesian framework based on Markov random fields (MRF) or conditional random fields (CRF). Generally, the MRF/CRF model is learned independently of the inference algorithm that is used to obtain the final result. In this paper, we observe considerable gains in speed and accuracy by training the MRF/CRF model together with a fast and suboptimal inference algorithm. An active random field (ARF) is defined as a combination of a MRF/CRF based model and a fast inference algorithm for the MRF/CRF model. This combination is trained through an optimization of a loss function and a training set consisting of pairs of input images and desired outputs. We apply the ARF concept to image denoising, using the Fields of Experts MRF together with a 1-4 iteration gradient descent algorithm for inference. Experimental validation on unseen data shows that the ARF approach obtains an improved benchmark performance as well as a 1000-3000 times speedup compared to the Fields of Experts MRF. Using the ARF approach, image denoising can be performed in real-time, at 8fps on a single CPU for a 256 x 256 image sequence, with close to state-of-the-art accuracy.

Learning-based Deformation Estimation for Fast Non-rigid Registration

This paper presents a learning-based deformation estimation method for fast non-rigid registration. First, a PCA-based statistical deformation model is constructed using the deformation fields obtained by conventional registration algorithms between a template image and training subject images. Then, the constructed statistical model is used to generate a large number of sample deformation fields by resampling in the PCA space. In the meanwhile, by warping the template using these sample deformation fields, the respective sample images in the PCA space can be also generated. Finally, after learning the correlation between the features of the sample images and their deformation coefficients, given a new test image, we can immediately estimate its relative deformations to the template based on its image information. Using this estimated deformation, we can warp the template to generate an intermediate template close to the test image. Since the intermediate template is more similar to the test image compared to the original template, the deformable registration via the intermediate template becomes much easier and faster. Experimental results show that the proposed learning-based registration method can fast register MR brain image with robust performance.

Customized design of hearing aids using statistical shape learning

3D shape modeling is a crucial component of rapid prototyping systems that customize shapes of implants and prosthetic devices to a patient's anatomy. In this paper, we present a solution to the problem of customized 3D shape modeling using a statistical shape analysis framework. We design a novel method to learn the relationship between two classes of shapes, which are related by certain operations or transformation. The two associated shape classes are represented in a lower dimensional manifold, and the reduced set of parameters obtained in this subspace is utilized in an estimation, which is exemplified by a multivariate regression in this paper. We demonstrate our method with a felicitous application to estimation of customized hearing aid devices.