User-interactive level set image segmentation

We consider the problem of image segmentation with the additional property that the user can give input to the segmentation procedure. We demonstrate two complementary methods for user input. We refer to the first method presented as the region method because the user input affects all pixels in a region where they have clicked. We refer to the second method presented as the boundary method because the user supplies a piece of the boundary of an object in the image. These two methods are complementary in the sense that interiors and boundaries are complementary.;Both of these user input methods require a computation which is similar to a Gaussian convolution. The purpose of this convolution-like operation is to propagate the user input to neighboring areas. The computation of this convolution-like operation is more involved than a Gaussian convolution because the pairwise distance between points is generally non- Euclidean. This is because we formulate the distance to depend on image data. In this sense, Gaussian convolution is a special case in our model when the distance does not depend on the image being segmented. When computing this convolution-like operation, the computation of all pairwise distances would not be feasible. In order to make these methods feasible, we demonstrate a fast approximation to this convolution-like operation. This approximation allows us to update the segmentation with the user input at interactive rates. Therefore the word interactive in the title of this report should be understood in two senses: we interact with the user and this interaction occurs rapidly enough to be labeled interactive.;The results from the convolutions just mentioned are then used in addition to existing level set method image segmentation procedures. We stress that the user input methods in this report can be added to any segmentation procedure which uses level set methods. The qualitative properties of these user input methods are explored and demonstrated with numerical experiments throughout this report. The result is that many segmentation tasks which are impossible with generic segmentation procedures can be accomplished with this user input method with just a few clicks.