Empirical Capacity of a Recognition Channel for Single- and Multipose Object Recognition Under the Constraint of PCA Encoding

The ability of practical recognition systems to recognize a large number of objects is constrained by a variety of factors that include choice of a feature extraction technique, quality of images, complexity and variability of underlying objects and of collected data. Given a feature extraction technique generating templates of objects from data and a resolution of the original images, the remaining factors can be attributed to distortions due to a recognition channel. We define the recognition channel as the environment that transforms reference templates of objects in a database into templates submitted for recognition. If templates in an object database are generated to be statistically independent and the noise in a query template is statistically independent of templates in the database, then the abilities of the recognition channel to recognize a large number of object classes can be characterized by a number called recognition capacity. In this paper, we evaluate the empirical recognition capacity of PCA-based object recognition systems. The encoded data (templates) and the additive noise in query templates are modeled to be Gaussian distributed with zero mean and estimated variances. We analyze both the case of a single encoded image and the case of encoded correlated multiple images. For this case, we propose a model that is orientation and elevation angle (pose) dependent. The fit of proposed models is judged using statistical goodness of fit tests. We define recognition rate as the ratio
R
=log(
M
)/
n
, where
M
is the number of objects to recognize and
n
is the length of PCA templates. The empirical capacity of PCA-based recognition systems is numerically evaluated. The empirical random coding exponent is also numerically evaluated and plotted as a function of the recognition rate. With these results, given a value of the recognition capacity and the length of templates (assume large), we can predict the number of distinct object classes that can be stored in an object library and be identified with probability of error close to zero.