Image correlation has proven useful for image filtering, matching, pattern recognition, and image registration over many decades. The two classical correlation forms, amplitude and phase correlation, display different properties. Amplitude correlation often provides a low, broad peak in the correlation domain. The broadness of the peak provides robustness to matching imagery exhibiting non-translational geometric offsets, such as rotation or scale differences. By contrast, phase correlation tends to provide a high, narrow peak. The high peak signifies high matching confidence while the narrow peak width provides accurate shift localization. However, the phase correlation peak degrades rapidly when matching against images with non-translational geometric offset. To provide tradeoffs between properties of these traditional correlation forms, in this paper we present a general, flexible form of correlation called Spectrally-Shaped Correlation (SSC). SSC provides control over the Fourier domain normalization of the correlation components. We apply SSC to the problem of image registration. We show how SSC contains the classical amplitude, phase, and phase-only correlation forms as special cases. First, we present the general theory of Fourier transforms for multi-channel imagery, modeled as hypercomplex-valued imagery. We present mathematical details of the transform techniques and develop the SSC approach. We then present numerical results demonstrating registration of real image data, acquired from a UAV operating in an urban environment, to reference imagery. We demonstrate a performance improvement of the SSC over the classical forms of correlation.