We present a general scheme for segmenting a radiographic image into polygons that correspond to visual features. This decomposition provides a vectorized representation that is a high-level description of the image. The polygons correspond to objects or object parts present in the image. This characterization of radiographs allows the direct application of several shape recognition algorithms to identify objects. In this paper we describe the use of constrained Delaunay triangulations as a uniform foundational tool to achieve multiple visual tasks, namely image segmentation, shape decomposition, and parts-based shape matching. Shape decomposition yields parts that serve as tokens representing local shape characteristics. Parts-based shape matching enables the recognition of objects in the presence of occlusions, which commonly occur in radiographs. The polygonal representation of image features affords the efficient design and application of sophisticated geometric filtering methods to detect large-scale structural properties of objects in images. Finally, the representation of radiographs via polygons results in significant reduction of image file sizes and permits the scalable graphical representation of images, along with annotations of detected objects, in the SVG (scalable vector graphics) format that is proposed by the world wide web consortium (W3C). This is a textual representation that can be compressed and encrypted for efficient and secure transmission of information over wireless channels and on the Internet. In particular, our methods described here provide an algorithmic framework for developing image analysis tools for screening cargo at ports of entry for homeland security.