FEBRUARY 2001 | Tony F. Chan, Member, IEEE, and Luminita A. Vese
This paper proposes a new active contour model for object detection in images, which does not rely on gradient-based edge detection. The model is based on the Mumford–Shah functional for segmentation and level set methods. Unlike classical active contours that use gradient information to stop the evolution of the curve on object boundaries, this model uses a segmentation-based stopping term. The energy functional to be minimized includes a term that depends on the segmentation of the image, allowing the detection of objects with boundaries not necessarily defined by gradient. The model is formulated in terms of level sets, enabling the automatic detection of interior contours and the use of any initial curve in the image. The paper presents a numerical algorithm using finite differences and provides experimental results demonstrating the model's effectiveness in detecting objects with smooth or discontinuous boundaries, as well as in handling noisy images. The model is also shown to detect objects that classical gradient-based active contours cannot. The paper concludes with a discussion of the model's advantages and potential extensions.This paper proposes a new active contour model for object detection in images, which does not rely on gradient-based edge detection. The model is based on the Mumford–Shah functional for segmentation and level set methods. Unlike classical active contours that use gradient information to stop the evolution of the curve on object boundaries, this model uses a segmentation-based stopping term. The energy functional to be minimized includes a term that depends on the segmentation of the image, allowing the detection of objects with boundaries not necessarily defined by gradient. The model is formulated in terms of level sets, enabling the automatic detection of interior contours and the use of any initial curve in the image. The paper presents a numerical algorithm using finite differences and provides experimental results demonstrating the model's effectiveness in detecting objects with smooth or discontinuous boundaries, as well as in handling noisy images. The model is also shown to detect objects that classical gradient-based active contours cannot. The paper concludes with a discussion of the model's advantages and potential extensions.