Since the Principal Component Analysis (1D-PCA) extended to the image oriented 2D-PCA by Yang et al, a number of 1D methods have been extended to their corresponding 2D variants. Because of the use of natural spatial information of matrix-form data (e.g., an image), the 2D methods usually yield much better performance than their 1D versions, which is consistent with the theorem of No Free Lunch. However, the 2D methods still suffer from two main drawbacks: (1) they are almost all linear, which might not match the nonlinear structure of actual data; and (2) the spatial information of data is not fully used in existing 2D methods. To address the first drawback, although the kernel trick is theoretically feasible, it is practically difficult since the representation theorem cannot be straightforwardly extended for 2D-form data. To this end, we in this work propose to obtain a simple kernelizing method by changing the measurement without the representation theorem. In view of the second shortcoming, we aim to use the spatial information of data in the nonlinear mapping feature space (or say kernel space). Unfortunately, it usually requires to describe the data in the nonlinear feature space (i.e., kernel space), which is generally implemented through data dimension-increasing as well as implicit kernel mapping. To fulfill this goal, it usually refers to the implicit or explicit kernel mapping, the former, however, might distort the spatial structure of data while the latter leads to dimension risk. As a result, we can preferably preserve the spatial structure of data naturally if we employ the form of explicit kernels in which the dimension is identical and each component is uncoupled. Fortunately, many explicit kernel (e.g., Hellinger and Euler kernels) and approximate explicit mathematical formulations of some implicit additive kernels (e.g., Intersection, JS and χ 2 kernels) meet the requirements. Considering the conciseness and good generalization of the Euler kernel, we in this work attempt to kernelize matrix-form data by Euler kernel and then in the mapped kernel space to compensate the spatial information. Although there exist various ways to compensating the spatial information, e.g., spatial structure information constraints and image distance metric, we in this work take the Image Euclidean Distance as an example to carry out the study and then develop matrix/image-oriented Spatial Euler Kernel. Finally, through experiments, we demonstrate the effectiveness of the proposed strategies.