"Handbook of Biomedical Image Analysis: Segmentation Models (Volume I)" is dedicated to the segmentation of complex shapes from the field of imaging sciences using different mathematical techniques. This volume is aimed at researchers and educators in imaging sciences, radiological imaging, clinical and diagnostic imaging, physicists covering different medical imaging modalities, as well as researchers in biomedical engineering, applied mathematics, algorithmic development, computer vision, signal processing, computer graphics and multimedia in general, both in academia and industry. The key features are: principles of intra-vascular ultrasound (IVUS); principles of positron emission tomography (PET); physical principles of magnetic resonance angiography (MRA); basic and advanced level set methods; shape for shading method for medical image analysis; wavelet transforms and other multi-scale analysis functions; three dimensional deformable surfaces; level Set application for CT lungs, brain MRI and MRA volume segmentation; segmentation of incomplete tomographic medical data sets; and, subjective level sets for missing boundaries for segmentation.