One of the main cues we use in our everyday life when interacting with the environment is shape.
For example, we use shape information to recognise a chair, grasp a cup, perceive traffic signs and
solve jigsaw puzzles. We also use shape when dealing with more sophisticated tasks, such as the
medical diagnosis of radiographs or the restoration of archaeological artifacts. While the perception
of shape and its use is a natural ability of human beings, endowing machines with such skills is
not straightforward. However, the exploitation of shape cues is important for the development of
competent computer methods that will automatically perform tasks such as those just mentioned.
With this aim, the present work proposes computer methods which use shape to tackle two important
tasks, namely packing and object recognition.
The packing problem arises in a variety of applications in industry, where the placement of a set
of two-dimensional shapes on a surface such that no shapes overlap and the uncovered surface area
is minimised is important. Given that this problem is NP-complete, we propose a heuristic method
which searches for a solution of good quality, though not necessarily the optimal one, within a reasonable
computation time. The proposed method adopts a pictorial representation and employs a greedy
algorithm which uses a shape matching module in order to dynamically select the order and the pose
of the parts to be placed based on the “gaps” appearing in the layout during the execution.
This thesis further investigates shape matching in the context of object recognition and first considers
the case where the target object and the input scene are represented by their silhouettes. Two distinct
methods are proposed; the first method follows a local string matching approach, while the second
one adopts a global optimisation approach using dynamic programming. Their use of silhouettes,
however, rules out the consideration of any internal contours that might appear in the input scene,
and in order to address this limitation, we later propose a graph-based scheme that performs shape
matching incorporating information from both internal and external contours. Finally, we lift the assumption
made that input data are available in the form of closed curves, and present a method which
can robustly perform object recognition using curve fragments (edges) as input evidence. Experiments
conducted with synthetic and real images, involving rigid and deformable objects, show the
robustness of the proposed methods with respect to geometrical transformations, heavy clutter and
substantial occlusion.