Sparse representations using overcomplete dictionaries have proved to be a powerful tool in many signal processing applications such as denoising, super-resolution, inpainting, compression or classification. The sparsity of the representation very much depends on how well the dictionary is adapted to the data at hand. In this paper, we propose a method for learning structured multilevel dictionaries with discriminative constraints to make them well suited for the supervised pixelwise classification of images. A multilevel tree-structured discriminative dictionary is learnt for each class, with a learning objective concerning the reconstruction errors of the image patches around the pixels over each class-representative dictionary. After the initial assignment of the class labels to image pixels based on their sparse representations over the learnt dictionaries, the final classification is achieved by smoothing the label image with a graph cut method and an erosion method. Applied to a common set of texture images, our supervised classification method shows competitive results with the state of the art.
Many dictionary learning algorithms such as the Method of Optimal Directions (MOD) @cite_3 @cite_28 and K-SVD @cite_30 apply an iterative optimization procedure with two major steps. The first step consists of the sparse coding of the training vectors over the fixed dictionary @math to compute @math , which can be solved with pursuit algorithms; and the second step is the update of the dictionary @math based on the decompositions computed in the previous step. Some dictionary learning algorithms impose constraints on the dictionary, such as the Sparse K-SVD method @cite_26 , which aims to learn a sparse dictionary, or the Non-Negative K-SVD method @cite_36 , which learns a non-negative dictionary. An online dictionary learning method based on stochastic approximations is proposed in @cite_46 . Finally, structured multilevel dictionaries are learnt in @cite_38 @cite_29 based on the idea of adapting each dictionary to one iteration of the pursuit algorithm, so that atoms are sequentially selected from dictionaries at different levels by going down the branches in sparse coding. While the multilevel dictionary structure used in our method is based on the principle developed in these previous works, we focus here on the supervised learning problem for classification applications unlike these works.
@cite_30 @cite_38 @cite_26 @cite_28 @cite_36 @cite_29 @cite_3 @cite_46
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A label consistent K-SVD (LC-KSVD) algorithm to learn a discriminative dictionary for sparse coding is presented. In addition to using class labels of training data, we also associate label information with each dictionary item (columns of the dictionary matrix) to enforce discriminability in sparse codes during the dictionary learning process. More specifically, we introduce a new label consistency constraint called "discriminative sparse-code error" and combine it with the reconstruction error and the classification error to form a unified objective function. The optimal solution is efficiently obtained using the K-SVD algorithm. Our algorithm learns a single overcomplete dictionary and an optimal linear classifier jointly. The incremental dictionary learning algorithm is presented for the situation of limited memory resources. It yields dictionaries so that feature points with the same class labels have similar sparse codes. Experimental results demonstrate that our algorithm outperforms many recently proposed sparse-coding techniques for face, action, scene, and object category recognition under the same learning conditions. We introduce a new dictionary structure for sparse representations better adapted to pursuit algorithms used in practical scenarios. The new structure, which we call an Iteration-Tuned Dictionary (ITD), consists of a set of dictionaries each associated to a single iteration index of a pursuit algorithm. In this work we first adapt pursuit decompositions to the case of ITD structures and then introduce a training algorithm used to construct ITDs. The training algorithm consists of applying a K-means to the (i −1)-th residuals of the training set to thus produce the i-th dictionary of the ITD structure. In the results section we compare our algorithm against the state-of-the-art dictionary training scheme and show that our method produces sparse representations yielding better signal approximations for the same sparsity level. A label consistent K-SVD (LC-KSVD) algorithm to learn a discriminative dictionary for sparse coding is presented. In addition to using class labels of training data, we also associate label information with each dictionary item (columns of the dictionary matrix) to enforce discriminability in sparse codes during the dictionary learning process. More specifically, we introduce a new label consistent constraint called ‘discriminative sparse-code error’ and combine it with the reconstruction error and the classification error to form a unified objective function. The optimal solution is efficiently obtained using the K-SVD algorithm. Our algorithm learns a single over-complete dictionary and an optimal linear classifier jointly. It yields dictionaries so that feature points with the same class labels have similar sparse codes. Experimental results demonstrate that our algorithm outperforms many recently proposed sparse coding techniques for face and object category recognition under the same learning conditions. In a sparse-representation-based face recognition scheme, the desired dictionary should have good representational power (i.e., being able to span the subspace of all faces) while supporting optimal discrimination of the classes (i.e., different human subjects). We propose a method to learn an over-complete dictionary that attempts to simultaneously achieve the above two goals. The proposed method, discriminative K-SVD (D-KSVD), is based on extending the K-SVD algorithm by incorporating the classification error into the objective function, thus allowing the performance of a linear classifier and the representational power of the dictionary being considered at the same time by the same optimization procedure. The D-KSVD algorithm finds the dictionary and solves for the classifier using a procedure derived from the K-SVD algorithm, which has proven efficiency and performance. This is in contrast to most existing work that relies on iteratively solving sub-problems with the hope of achieving the global optimal through iterative approximation. We evaluate the proposed method using two commonly-used face databases, the Extended YaleB database and the AR database, with detailed comparison to 3 alternative approaches, including the leading state-of-the-art in the literature. The experiments show that the proposed method outperforms these competing methods in most of the cases. Further, using Fisher criterion and dictionary incoherence, we also show that the learned dictionary and the corresponding classifier are indeed better-posed to support sparse-representation-based recognition.