Ego-Motion Estimate Corruption Due to Violations of the Range Flow Constraint

Abstract

Visual odometry methods are increasingly being used to estimate a vehicle's ego-motion from range data due to the decreasing cost of range sensors and the impressive speed and accuracy of visual odometry techniques. Dense geometry-based visual odometry methods are fundamentally based on the range flow constraint equation, an equation which depends on the temporal and spatial derivatives of range images. However, these derivatives are calculated with the fundamental assumption that the range flow is magnitude-limited. When scaling this method for faster vehicles, this assumption could be violated, invaliding the range flow constraint equation and thus corrupting the resulting ego-motion estimates. This paper derives the sensor, motion, environment, and sampling frequency conditions that would mathematically violate the range flow constraint. This information is useful for defining the operational limits of dense geometry-based visual odometry methods.