Abstract. 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.

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.