This paper presents two contributions. We first introduce a continuous-domain version of Principal-Component Analysis (PCA) for designing steerable filters so that they best approximate a given set of image templates. We exploit the fact that steerability does not need to be enforced explicitly if one extends the set of templates by incorporating all their rotations. Our results extend previous work by Perona to multiple templates. We then apply our framework to the automatic detection and classification of micro-particles that carry biochemical probes for molecular diagnostics. Our continuous-domain PCA formalism is particularly well adapted in this context because the geometry of the carriers is known analytically. In addition, the steerable structure of our filters allows for a fast FFT-based recognition of the type of probe.