This chapter presents a method for boundary finding in two and three-dimensional images using parametrically deformable models. The approach incorporates model-based shape information to enhance boundary detection, particularly in cases where local image information is insufficient due to noise, occlusion, or poor contrast. The method formulates boundary finding as an optimization problem, using parametric Fourier models for both curves and surfaces. These models allow for the representation of complex shapes in a compact form, enabling efficient optimization in a lower-dimensional space. The method also incorporates probabilistic information to bias the model towards a particular shape while allowing for deformations. The chapter discusses various parametric representations for curves and surfaces, including polynomials, superquadrics, generalized cylinders, and spherical harmonics. Each representation has its own advantages and limitations in terms of expressiveness and computational complexity. Fourier models are particularly effective for representing deformable shapes, as they allow for the decomposition of a shape into a series of harmonic components, each contributing to the overall shape. For curves, Fourier representations are used to decompose the boundary into a series of ellipses, allowing for the extraction of geometric properties such as semi-major and semi-minor axes, rotation, and phase shift. For surfaces, Fourier models are extended to two dimensions, allowing for the representation of complex shapes using a combination of cosine and sine terms. These models are used to represent a wide range of surfaces, including closed and open surfaces, tubes, and tori. The boundary finding objective function is formulated as a maximum a posteriori (MAP) objective, incorporating both prior probability and likelihood terms. This allows for the incorporation of probabilistic information to guide the optimization process. The method is tested on a variety of real and synthetic images, demonstrating its effectiveness in delineating structures and being relatively insensitive to issues such as broken boundaries and spurious edges. The chapter concludes with a summary of the method's performance and potential improvements, highlighting its flexibility and effectiveness in boundary finding for both two- and three-dimensional images. The method is particularly useful for modeling natural objects and has applications in medical imaging, where it can be used to delineate structures such as the corpus callosum, heart, and brain.This chapter presents a method for boundary finding in two and three-dimensional images using parametrically deformable models. The approach incorporates model-based shape information to enhance boundary detection, particularly in cases where local image information is insufficient due to noise, occlusion, or poor contrast. The method formulates boundary finding as an optimization problem, using parametric Fourier models for both curves and surfaces. These models allow for the representation of complex shapes in a compact form, enabling efficient optimization in a lower-dimensional space. The method also incorporates probabilistic information to bias the model towards a particular shape while allowing for deformations. The chapter discusses various parametric representations for curves and surfaces, including polynomials, superquadrics, generalized cylinders, and spherical harmonics. Each representation has its own advantages and limitations in terms of expressiveness and computational complexity. Fourier models are particularly effective for representing deformable shapes, as they allow for the decomposition of a shape into a series of harmonic components, each contributing to the overall shape. For curves, Fourier representations are used to decompose the boundary into a series of ellipses, allowing for the extraction of geometric properties such as semi-major and semi-minor axes, rotation, and phase shift. For surfaces, Fourier models are extended to two dimensions, allowing for the representation of complex shapes using a combination of cosine and sine terms. These models are used to represent a wide range of surfaces, including closed and open surfaces, tubes, and tori. The boundary finding objective function is formulated as a maximum a posteriori (MAP) objective, incorporating both prior probability and likelihood terms. This allows for the incorporation of probabilistic information to guide the optimization process. The method is tested on a variety of real and synthetic images, demonstrating its effectiveness in delineating structures and being relatively insensitive to issues such as broken boundaries and spurious edges. The chapter concludes with a summary of the method's performance and potential improvements, highlighting its flexibility and effectiveness in boundary finding for both two- and three-dimensional images. The method is particularly useful for modeling natural objects and has applications in medical imaging, where it can be used to delineate structures such as the corpus callosum, heart, and brain.