Identification and detection of dendritic spines in neuron images are of high interest in diagnosis and treatment of neurological and psychiatric disorders (e.g., Alzheimer's disease, Parkinson's diseases, and autism). In this paper, we have proposed a novel automatic approach using wavelet-based conditional symmetric analysis and regularized morphological shared-weight neural networks (RMSNN) for dendritic spine identification involving the following steps: backbone extraction, localization of dendritic spines, and classification. First, a new algorithm based on wavelet transform and conditional symmetric analysis has been developed to extract backbone and locate the dendrite boundary. Then, the RMSNN has been proposed to classify the spines into three predefined categories (mushroom, thin, and stubby). We have compared our proposed approach against the existing methods. The experimental result demonstrates that the proposed approach can accurately locate the dendrite and accurately classify the spines into three categories with the accuracy of 99.1% for "mushroom" spines, 97.6% for "stubby" spines, and 98.6% for "thin" spines.