The automatic understanding of human activity is probably one of the most challenging problems for the scientific community. Several application domains would benefit of such an analysis, from context-aware computing, to area monitoring and surveillance, to assistive technologies for elderly or disabled, and more. In a broad sense, we can define the activity analysis as the problem of finding an explanation coherent with a set of observations. These observations are typically influenced by several factors from different disciplines, such as sociology or psychology, but also mathematics and physics, making the problem particularly hard. In the last years, also the computer vision community focused its attention on this area, producing the latest advances in the acquisition and understanding of human motion data from image sequences. Despite the increasing effort spent in this field, there still exists a consistent gap between the numerical low-level pixel information that can be observed and measured, and the high abstraction level of the semantic that describes a given activity. In other words, there exist a conceptual ambiguity between the image sequence observations and their possible interpretations. Although several factors are involved, the activity modeling and the comparison strategy play crucial roles. In this proposal, a correlation between activity and corresponding path has been assumed. In light of this, the work carried out tackles two strictly related issues: (i) obtaining a proper representation of human activity; (ii) define an effective tool for reliably measuring the similarity between activity instances. In particular, the object activity is modeled with a signature obtained through a symbolic abstraction of its spatio-temporal trace, allowing the application of particular high-level reasoning for computing the activity similarity. This representation is particularly effective since it provides a smart way to compensate the noise artifacts coming from low-level modules (i.e., tracking algorithms), allowing also the possibility of considering interesting properties, such as the invariance to shift, rotation, and scale factors. Since any complex task may be decomposed in a limited set of atomic units corresponding to elementary motion patterns, the key idea of this representation is to catch the object activities by suitably representing their trajectories through symbols. This syntactic activity description relies on the extraction and on the symbolic coding of meaningful samples of the path, while the similarity between trajectories is computed using the so-called approximate-matching, thus casting the trajectory comparison problem to a string matching one. Also another representation scheme has been adopted, coding the signature according some relevant spots in the environment: in this case, the structural pattern information is coded in ad-hoc Context-Free Grammars, and the matching problem is solved through the parsing of the incoming string according the defined rules.