| This thesis presents a machine learning framework for the automatic classification and refinement of curves. The proposed framework is composed of both a representation and a family of algorithms for making inferences from examples, given suitable guidance from a user. The underlying computational paradigm taken consists of applying Hidden Markov Models to a wavelet representation of the curves of interest, each of which is presented as part of a pair of examples. The learning framework is exemplified by developing a gesture-based interface for two distinct applications: robot path planning and sketch beautification. For each, it is demonstrated that we can learn constraints on curves from a set of examples and apply them to augment rudimentary gesture information from a human operator. Further, it is demonstrated that we can identify what class of curves the human input belongs to, allowing us to automate the curve refinement process for unclassified inputs. Finally, in cases where gesture information is given in the form of an image, it is also shown that the same methodology can be used to detect and extract the most likely parametric curve from the image.; There are three key issues that are addressed for the classification and refinement of curves. First, we must establish the way in which the input, training and output curves look like one another. In the framework presented, this likeness is expressed statistically using Hidden Markov Models that extend over multiple curve attributes (such as curve thickness or color) and scales. Second, when attempting to infer a curve, we must also determine the way in which the surrounding curves should affect the inference. Using a hierarchy of Hidden Markov Models, we can impose and exploit probabilistic interactions between multiple curves that make up an entire scene. Finally, in addition to the learned constraints, we must also determine a method for combining user-defined constraints with the Hidden Markov Models. It is shown that we can reformulate the Hidden Markov Models using a regularization framework and allow for the seamless integration of ad hoc biases to the learned models. |
