# A Geometric Dictionary Learning Based Approach for Fluorescence Spectroscopy Image Fusion
## 1 Introduction
They proposed a multi-focus image fusion method with a fixed-dictionary. [PERSON] and [PERSON] [36] applied morphologically filtering sparse feature to matrix decomposition method for improving the accuracy of sparse representation in image fusion. [PERSON] and [PERSON] [37] proposed an approximate K-SVD based sparse representation method for image fusion and exposure fusion to reduce computation costs. [PERSON] and [PERSON] [38] proposed a joint clustering dictionary learning method for image fusion. They used the steering kernel regression to strength the local geometric features of source images first. Then K-means clustering method was applied to image pixels clustering based on the local image features. The proposed method by [PERSON] and [PERSON] can significantly group the pixels of input source images into a few classes. The principle components of local features are extracted from each group to construct a dictionary, which can make a compact and informative dictionary. This method reduces the sparse coding time by using the constructed compact dictionary. However, the performance of [PERSON] and [PERSON]'s method depends on the presetting cluster number, that is difficult to confirm before clustering. The number of local geometric-feature types is usually used as the presetting cluster number, but the actual clustering results do not exactly follow the geometric features every time. So the clustering results cannot reach the expectations all the time. To optimize the weakness of existing clustering methods, a geometric information based image block classification method is proposed in this paper. Geometric information, as one type of the most important image information, including edges, contours, and textures of image, and so on, can remarkably influence the quality of image perception [39]. The information can be used in patch classification as a supervised dictionary prior to improve the performance of trained dictionary [40; 41]. In this paper, a geometric classification based dictionary learning method is proposed for sparse-representation based image fusion. Instead of grouping the pixels of images, the proposed geometric classification method groups image blocks directly by the geometric similarity of each image block. Since sparse-representation based fusion method uses image blocks for sparse coding and coefficients fusion, extracting underlying geometric information from image-block groups is an efficient way to construct a dictionary. Moreover, the geometric classification can group image blocks based on edge, sharp line information for dictionary learning, which can improve the accuracy of sparse representation. The proposed dictionary learning approach consists of three steps:  
* In the first step, input source images are split into small blocks. According to the similarity of geometric patterns, these blocks are classified into smooth patches, stochastic patches, and dominant orientation patches. * In the second step, it does principal component analysis (PCA) on each type of patches to extract crucial bases. The extracted PCA bases are used to construct the sub-dictionary of each image patch group. * In the last step, the obtained sub-dictionaries are merged into a complete dictionary for sparse-representation-based fusion approach and the integrated sparse coefficients are inverted to fused image. This paper has two main contributions. * A geometric image patches classification method is proposed for dictionary learning. The proposed geometry classification method can accurately split source image patches into different image patch groups for dictionary learning. Dictionary bases extracted from each image patch group have good performance, when they are used to describe the geometric features of source images. * A PCA-based geometry dictionary construction method is proposed. The trained dictionary with PCA bases is informative and compact for sparse representation.