Metric Learning for Image Alignment

Image alignment has been a long standing problem in computer vision. Parameterized Appearance Models (PAMs) such as the Lucas-Kanade method, Eigentracking, and Active Appearance Models are commonly used to align images with respect to a template or to a previously learned model. While PAMs have numerous advantages relative to alternate approaches, they have at least two drawbacks. First, they are especially prone to local minima in the registration process. Second, often few, if any, of the local minima of the cost function correspond to acceptable solutions. To overcome these problems, this paper proposes a method to learn a metric for PAMs that explicitly optimizes that local minima occur at and only at the places corresponding to the correct fitting parameters. To the best of our knowledge, this is the first paper to address the problem of learning a metric to explicitly model local properties of the PAMs’ error surface. Synthetic and real examples show improvement in alignment performance in comparison with traditional approaches. In addition, we show how the proposed criteria for a good metric can be used to select good features to track.     

Model selection for primal SVM

This paper introduces two types of nonsmooth optimization methods for selecting model hyperparameters in primal SVM models based on cross-validation. Unlike common grid search approaches for model selection, these approaches are scalable both in the number of hyperparameters and number of data points. Taking inspiration from linear-time primal SVM algorithms, scalability in model selection is achieved by directly working with the primal variables without introducing any dual variables. The proposed implicit primal gradient descent (ImpGrad) method can utilize existing SVM solvers. Unlike prior methods for gradient descent in hyperparameters space, all work is done in the primal space so no inversion of the kernel matrix is required. The proposed explicit penalized bilevel programming (PBP) approach optimizes both the hyperparameters and parameters simultaneously. It solves the original cross-validation problem by solving a series of least squares regression problems with simple constraints in both the hyperparameter and parameter space. Computational results on least squares support vector regression problems with multiple hyperparameters establish that both the implicit and explicit methods perform quite well in terms of generalization and computational time. These methods are directly applicable to other learning tasks with differentiable loss functions and regularization functions. Both the implicit and explicit algorithms investigated represent powerful new approaches to solving large bilevel programs involving nonsmooth loss functions.     

A variational approach to monocular hand-pose estimation

In this paper, we propose a model-based approach to recover 3D hand pose from 2D images. To this end, we describe the hand structure using a compact 3D articulated model and reformulate pose estimation as a binary image segmentation problem aiming to separate the hand from the background. We propose generative models for hand and background pixels leading to a log-likelihood objective function which aims to enclose hand-like pixels within the projected silhouette of the 3D model while excluding background-like pixels. Segmentation and hand-pose estimation are jointly addressed through the minimization of a single likelihood function. Pose is determined through gradient descent in the hand parameter space of such an area-based objective function. Furthermore, we propose a new constrained variable metric gradient descent to speed up convergence and finally the so called smart particle filter to deal with occlusions and local minima through multiple hypotheses. Promising experimental results demonstrate the potentials of our approach.     

Conflating two polygonal lines

A basic technique in comparing and detecting changes in geographical spatial data from satellite images consists of identifying linear features or edges in the image and then matching those features. A chain of connected linear features which form a polygonal line is used as the basic unit for matching two images. We develop a distance measure between two polygonal lines and an efficient algorithm for conflating or optimally matching two polygonal lines based on this distance measure. We show that some of the alternative approaches used in the literature, including Hausdorff's distance, fail to satisfy the basic requirements of a distance measure for image conflation.     

Linear feature extraction using adaptive least‐squares template matching and a scalable slope edge model

This paper presents a linear feature extraction method. Least squares template matching (LSTM) is adopted as the computational tool to fit the linear features with a scalable slope edge (SSE) model, which is based on an explicit function to define the blurred edge profile. In the SSE model, the magnitude of the grey gradient and the edge scale can be described by three parameters; additionally, the edge position can be obtained strictly by the ‘zero crossing’ location of the profile model. In our method the edge templates are locally and adaptively generated by estimating the three parameters via fitting the image patches with the model, accordingly the linear feature can be positioned with high accuracy by using LSTM. We derived the computational models to rectify straight line and spline curve features and tested those algorithms using the synthetic and real remotely sensed images. The experiments using synthetic images show that the method can position the linear features with the mean geometric error of pixel location of less than one pixel in certain noise levels. Examples of semiautomatic extraction of buildings and linear objects from real imagery are also given and demonstrate the potential of the method.     

Simulated annealing and weight decay in adaptive learning: theSARPROP algorithm

A problem with gradient descent algorithms is that they can converge to poorly performing local minima. Global optimization algorithms address this problem, but at the cost of greatly increased training times. This work examines combining gradient descent with the global optimization technique of simulated annealing (SA). Simulated annealing in the form of noise and weight decay is added to resiliant backpropagation (RPROP), a powerful gradient descent algorithm for training feedforward neural networks. The resulting algorithm, SARPROP, is shown through various simulations not only to be able to escape local minima, but is also able to maintain, and often improve the training times of the RPROP algorithm. In addition, SARPROP may be used with a restart training phase which allows a more thorough search of the error surface and provides an automatic annealing schedule.     

一种计算图象形态梯度的多尺度算法

分水岭变换是一种非常适用于图象分割的形态算子,然而,基于分水岭变换的图象分割方法,其性能在很大程度上依赖于用来计算待分割图象梯度的算法。为了高效地进行分水岭变换,提出了一种计算图象形态梯度的多尺度算法,从而对阶跃边缘和“模糊”边缘进行了有效的处理,此外,还提出了一种去除因噪声或量化误差造成的局部“谷底”的算法,实验结果表明,图象采用本文算法处理后,再进行分水岭变换,即使不进行区域合并,也能产生有意义的分割,因而极大地减轻了计算负担。     

On the problem of local minima in recurrent neural networks

Many researchers have recently focused their efforts on devising efficient algorithms, mainly based on optimization schemes, for learning the weights of recurrent neural networks. As in the case of feedforward networks, however, these learning algorithms may get stuck in local minima during gradient descent, thus discovering sub-optimal solutions. This paper analyses the problem of optimal learning in recurrent networks by proposing conditions that guarantee local minima free error surfaces. An example is given that also shows the constructive role of the proposed theory in designing networks suitable for solving a given task. Moreover, a formal relationship between recurrent and static feedforward networks is established such that the examples of local minima for feedforward networks already known in the literature can be associated with analogous ones in recurrent networks.     

Relative loss bounds for single neurons

We analyze and compare the well-known gradient descent algorithm and the more recent exponentiated gradient algorithm for training a single neuron with an arbitrary transfer function. Both algorithms are easily generalized to larger neural networks, and the generalization of gradient descent is the standard backpropagation algorithm. We prove worst-case loss bounds for both algorithms in the single neuron case. Since local minima make it difficult to prove worst case bounds for gradient-based algorithms, we must use a loss function that prevents the formation of spurious local minima. We define such a matching loss function for any strictly increasing differentiable transfer function and prove worst-case loss bounds for any such transfer function and its corresponding matching loss. The different forms of the two algorithms' bounds indicates that exponentiated gradient outperforms gradient descent when the inputs contain a large number of irrelevant components. Simulations on synthetic data confirm these analytical results.     

Partial retrieval of CAD models based on the gradient flows in Lie group

Based on the gradient flows in Lie group, a partial retrieval approach for CAD models is presented in this paper. First, a representation of the face Attributed Relational Graph (ARG) for a CAD model is created from its B-rep model and thus partial retrieval is converted to a subgraph matching problem. Then, an optimization method is adopted to solve the matching problem, where the optimization variable is the vertex mapping and the objective function is the measurement of compatibility between the mapped vertices and between the mapped edges. Different from most previously proposed methods, a homogeneous transformation matrix is introduced to represent the vertex mapping in subgraph matching, whose translational sub-matrix gives the vertex selection in the larger graph and whose orthogonal sub-matrix presents the vertex permutation for the same-sized mapping from the selected vertices to the smaller graph's vertices. Finally, a gradient flow method is developed to search for optimal matching matrix in Special Euclidean group SE(n). Here, a penalty approach is used to handle the constraints on the elements of the matching matrix, which leads its orthogonal part to be a permutation matrix and its translational part to have different integer elements. Experimental results show that it is a promising method to support the partial retrieval of CAD models.     

基于连接点的二维多角弧匹配

多角弧匹配问题的关键是，其既能反映多角弧的几何性质，又能反映多角弧拓扑结构的特征选取．在分析了多角弧几何形状的基础上，引入了连接点的概念，并用连接点集表示多角弧，这一表示在旋转和平移变换下是不变的。进一步取该连接点集作为匹配的特征集，给出了特征集之间匹配的算法．该算法是将连接点间的距离积分作为测量函数，使二维多角弧的匹配由连接点的匹配来决定．给出的模拟试验结果表明，该算法效果良好，并且对于数值污染具有健壮性。     

Constructive granular systems with universal approximation and fast knowledge discovery

Conventional gradient descent learning algorithms for soft computing systems have the learning speed bottleneck problem and the local minima problem. To effectively solve the two problems, the n-variable constructive granular system with high-speed granular constructive learning is proposed based on granular computing and soft computing, and proved to be a universal approximator. The fast granular constructive learning algorithm can highly speed up granular knowledge discovery by directly calculating all parameters of the n-variable constructive granular system using training data, and then construct the n-variable constructive granular system with any required accuracy using a small number of granular rules. Predictive granular knowledge discovery simulation results indicate that the direct-calculation-based granular constructive algorithm is better than the conventional gradient descent learning algorithm in terms of learning speed, learning error, and prediction error.     

Multidimensional Morphable Models: A Framework for Representing and Matching Object Classes

We describe a flexible model for representing images of objects of a certain class, known a priori, such as faces, and introduce a new algorithm for matching it to a novel image and thereby perform image analysis. The flexible model, known as a multidimensional morphable model, is learned from example images of objects of a class. In this paper we introduce an effective stochastic gradient descent algorithm that automatically matches a model to a novel image. Several experiments demonstrate the robustness and the broad range of applicability of morphable models. Our approach can provide novel solutions to several vision tasks, including the computation of image correspondence, object verification and image compression.     

Person re-identification by discriminant analytical least squares metric learning

Person re-identification means retrieving a same person in large amounts of images among disjoint camera views. An effective and robust similarity measure between a person image pair plays an important role in the re-identification tasks. In this work, we propose a new metric learning method based on least squares for person re-identification. Specifically, the similar training images pairs are used to learn a linear transformation matrix by being projected to finite discrete discriminant points using regression model; then, the metric matrix can be deduced by solving least squares problem with a closed form solution. We call it discriminant analytical least squares (DALS) metric. In addition, we develop the incremental learning scheme of DALS, which is particularly valuable in model retraining when given additional samples. Furthermore, DALS could be effectively kernelized to further improve the matching performance. Extensive experiments on the VIPeR, GRID, PRID450S and CUHK01 datasets demonstrate the effectiveness and efficiency of our approaches.     

Uncertainty Propagation in Model-Based Recognition

Robust recognition systems require a careful understanding of the effects of error in sensed features. In model-based recognition, matches between model features and sensed image features typically are used to compute a model pose and then project the unmatched model features into the image. The error in the image features results in uncertainty in the projected model features. We first show how error propagates when poses are based on three pairs of 3D model and 2D image points. In particular, we show how to simply and efficiently compute the distributed region in the image where an unmatched model point might appear, for both Gaussian and bounded error in the detection of image points, and for both scaled-orthographic and perspective projection models. Next, we provide geometric and experimental analyses to indicate when this linear approximation will succeed and when it will fail. Then, based on the linear approximation, we show how we can utilize Linear Programming to compute bounded propagated error regions for any number of initial matches. Finally, we use these results to extend, from two-dimensional to three-dimensional objects, robust implementations of alignment, interpretation-tree search, and transformation clustering.     

An Evolutionary-Based Stereo Matching Method with a Multilevel Searching Strategy

Stereo matching is one of the fundamental problems in computer vision. It consists in identifying features in two or more stereo images that are generated by the same physical feature in the three-dimensional space. This paper presents an evolutionary approach with a multilevel searching strategy for matching edges extracted from two stereo images. The matching problem is turned into an optimization task, which is performed by means of a genetic algorithm with a new encoding scheme. For an effective exploitation of the genetic stereo matching algorithm for real-time obstacle detection, a multilevel searching strategy is proposed to match the edges at different levels by considering their gradient magnitudes. Experimental results and comparative analysis are presented to demonstrate the effectiveness of the proposed method for real-time obstacle detection in front of a moving vehicle using linear stereo vision.     

A similarity metric for edge images

The performance of several discrepancy measures for the comparison of edge images is analyzed and a novel similarity metric aimed at overcoming their problems is proposed. The algorithm finds an optimal matching of the pixels between the images and estimates the error produced by this matching. The resulting Pixel Correspondence Metric (PCM) can take into account edge strength as well as the displacement of edge pixel positions in the estimation of similarity. A series of experimental tests shows the new metric to be a robust and effective tool in the comparison of edge images when a small localization error of the detected edges is allowed.     

Sobolev Active Contours

All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L ²-type inner product to define the notion of gradient. Recent work has shown that this inner product induces a pathological Riemannian metric on the space of smooth curves. However, there are also undesirable features associated with the gradient flows that this inner product induces. In this paper, we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with Sobolev-type inner products. We call the resulting flows Sobolev active contours. Sobolev metrics induce favorable regularity properties in their gradient flows. In addition, Sobolev active contours favor global translations, but are not restricted to such motions; they are also less susceptible to certain types of local minima in contrast to traditional active contours. These properties are particularly useful in tracking applications. We demonstrate the general methodology by reformulating some standard edge-based and region-based active contour models as Sobolev active contours and show the substantial improvements gained in segmentation.