Stochastic Geometry for Image Analysis

Chapter 9

Shape Recognition 1

In this chapter, we consider applications that aim to recognize shapes starting from a dictionary or a library. A library is a set of object classes, each object characterizing a parametric object. So, here it is a question of not only finding the objects that compose the scene, and of estimating their parameters, but also of associating them with a precise class. We will see two examples, which concern the choice of a particular distribution to model each of the modes of a light detection and ranging (LIDAR) signal and the choice of a building type according to the geometry of the roof. Our target applications therefore no longer relate only to the detection of objects, but also to pattern recognition.

9.1. Modeling of a LIDAR signal

We describe a model that represents waveforms acquired with LIDAR systems using a sum of parametric functions where the most suited function is chosen, from a given library, for each mode of the LIDAR waveform. Indeed, the latest generation of airborne or spatial full-waveform LIDAR no longer provides an unstructured cloud of three-dimensional points, as was previously the case. Instead for each emitted laser pulse, the received signal, called waveform, is recorded. This signal is digitized at constant frequency: LIDAR waveforms are therefore a one-dimensional sequence of samples (between 60 and 200) of the amplitude of the received signal. Such a sequence represents the progress of the laser beam as it interacts with ...