With the rapid development of neuroimaging techniques, scientists are interested in identifying imaging biomarkers that are related to different subtypes or transitional stages of various cancers, neuropsychiatric diseases, and neurodegenerative diseases. Scalar-on-image models have been proven to demonstrate good performance in such tasks. However, due to their high dimensionality, traditional methods may not work well in the estimation of such models. Some existing penalization methods may improve the performance but fail to take the complex spatial structure of the neuroimaging data into account. In the past decade, the spatially regularized methods have been popular due to their good performance in terms of both estimation and prediction. Despite the progress, many challenges still remain. In particular, most existing image classification methods focus on binary classification and consequently may underperform for the tasks of classifying diseases with multiple subtypes or transitional stages. Moreover, neuroimaging data usually present significant heterogeneity across subjects. As a result, existing methods for homogeneous data may fail. In this dissertation, we investigate several new statistical learning techniques and propose a Spatial Multi-category Angle based Classifier (SMAC), a Subject Variant Scalar-on-Image Regression (SVSIR) model and a Masking Convolutional Neural Network (MCNN) model to address the above issues. Extensive simulation studies and practical applications in neuroscience are presented to demonstrate the effectiveness of our proposed methods.