In this paper, we propose a continuous-domain version of principal-component analysis, with the constraint that the underlying family of templates appears at arbitrary orientations. We show that the corresponding principal components are steerable. Our method can be used for designing steerable filters so that they best approximate a given collection of reference templates. We apply this framework to the detection and classification of micrometer-sized particles that are used in a microfluidic diagnostics system. This is done in two steps. First, we decompose the particles into a small number of templates and compute their steerable principal components. Then we use these principal components to automatically estimate the orientation and the class of each particle.