  The detection of landmarks or patterns is of interest for extracting features
in biological images. Hence, algorithms for finding these keypoints have been
extensively investigated in the literature, and their localization and
detection properties are well known. In this paper, we study the complementary
topic of local orientation estimation, which has not received similar
attention. Simply stated, the problem that we address is the following:
estimate the angle of rotation of a pattern with steerable filters centered at
the same location, where the image is corrupted by colored isotropic Gaussian
noise. For this problem, we use a statistical framework based on the
Cram\'{e}r-Rao lower bound (CRLB) that sets a fundamental limit on the accuracy
of the corresponding class of estimators. We propose a scheme to measure the
performance of estimators based on steerable filters (as a lower bound), while
considering the connection to maximum likelihood estimation. Beyond the general
results, we analyze the asymptotic behaviour of the lower bound in terms of the
order of steerablility and propose an optimal subset of components that
minimizes the bound. We define a mechanism for selecting optimal subspaces of
the span of the detectors. These are characterized by the most relevant angular
frequencies. Finally, we project our template to a basis of steerable functions
and experimentally show that the prediction accuracy achieves the predicted
CRLB. As an extension, we also consider steerable wavelet detectors.
