This chapter introduces a method for boundary finding in two and three-dimensional images using deformable shape models. The approach leverages both local and global shape information to enhance boundary detection, particularly in challenging conditions such as poor contrast, occlusions, and noise. The method formulates boundary finding as an optimization problem using parametric Fourier models, which are matched to the image by optimizing the match between the model and a boundary measure applied to the image. Probability distributions on the parameters of the representation can be incorporated to bias the model towards specific shapes while allowing for deformations, leading to a maximum a posteriori objective function. The chapter reviews related work in boundary finding, including methods based on contextual information, pixel search, the Hough transform, and whole-boundary methods. It also discusses various parametric representations for curves and surfaces, such as polynomials, superquadrics, generalized cylinders, and spherical harmonics. The Fourier models are detailed, including their application to curves and surfaces, and the optimization of these models is described. Experiments demonstrate the effectiveness of the method in real and synthetic images, particularly in delineating structures in magnetic resonance images of the brain and heart. The system is shown to perform well, even in the presence of broken boundaries and spurious edges. The chapter concludes by discussing potential improvements and extensions, including the need for view invariance and the potential use of the framework for object recognition.This chapter introduces a method for boundary finding in two and three-dimensional images using deformable shape models. The approach leverages both local and global shape information to enhance boundary detection, particularly in challenging conditions such as poor contrast, occlusions, and noise. The method formulates boundary finding as an optimization problem using parametric Fourier models, which are matched to the image by optimizing the match between the model and a boundary measure applied to the image. Probability distributions on the parameters of the representation can be incorporated to bias the model towards specific shapes while allowing for deformations, leading to a maximum a posteriori objective function. The chapter reviews related work in boundary finding, including methods based on contextual information, pixel search, the Hough transform, and whole-boundary methods. It also discusses various parametric representations for curves and surfaces, such as polynomials, superquadrics, generalized cylinders, and spherical harmonics. The Fourier models are detailed, including their application to curves and surfaces, and the optimization of these models is described. Experiments demonstrate the effectiveness of the method in real and synthetic images, particularly in delineating structures in magnetic resonance images of the brain and heart. The system is shown to perform well, even in the presence of broken boundaries and spurious edges. The chapter concludes by discussing potential improvements and extensions, including the need for view invariance and the potential use of the framework for object recognition.