Heart angiography is a test that allows the treating physician to identify heart vessel abnormalities. The concerned doctor must spend a lot of time on this diagnosis. The heart vessels' targeted areas are segmented, and the blood vessel types are classified in the proposed approach. The heart angiography segmentation and classification provide essential information for the patient and the doctor. In contrast, the charge for cardiac angiography is a risky, mentally challenging task for the doctor (a heart specialist). Improved transparency and faster detection of heart diseases can result from automated segmentation and categorization of representations of heart blood vessels. Since accuracy is critical in classification, computer vision researchers are introducing several techniques; however, achieving high accuracy remains challenging when classifying heart diseases. This research proposes a multi-class ensemble classification mechanism-based computer-aided hybrid deep learning (DL) network model for localizing human blood vessels inside heart coronary computed tomography (CT) angiography images. First, the modified U-Net model is used to segment the heart blood vessels, and the self-attention network (SAT-Net) model is used to extract various features from the segmented blood vessel images. In segmented human heart blood vessels, low-level features are retrieved, including geometrical, statistical, and texture features. The enhanced elman spike neural network (EESNN) model has been used to finally classify cardiac blood vessels into four distinct groups: blood flow-reduced, narrow, block, and regular vessels. The suggested strategy has produced the best results, creating a conducive environment for cardiologists to diagnose heart-related disorders that is quick, simple, accurate, and time-saving.