  Machine vision is an important sensing technology used in mobile robotic
systems. Advancing the autonomy of such systems requires accurate
characterisation of sensor uncertainty. Vision includes intrinsic uncertainty
due to the camera sensor and extrinsic uncertainty due to environmental
lighting and texture, which propagate through the image processing algorithms
used to produce visual measurements. To faithfully characterise visual
measurements, we must take into account these uncertainties.
  In this paper, we propose a new class of likelihood functions that
characterises the uncertainty of the error distribution of two-frame optical
flow that enables a heteroscedastic dependence on texture. We employ the
proposed class to characterise the Farneback and Lucas Kanade optical flow
algorithms and achieve close agreement with their respective empirical error
distributions over a wide range of texture in a simulated environment. The
utility of the proposed likelihood model is demonstrated in a visual odometry
ego-motion study, which results in performance competitive with contemporary
methods. The development of an empirically congruent likelihood model advances
the requisite tool-set for vision-based Bayesian inference and enables sensor
data fusion with GPS, LiDAR and IMU to advance robust autonomous navigation.
