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Analysing a visual scene by inferring the configuration of a generative model is widely considered the most flexible and generalizable approach to scene understanding. Yet, one major problem is the computational challenge of the inference procedure, involving a combinatorial search across object identities and poses. Here we propose a neuromorphic solution exploiting three key concepts: (1) a computational framework based on vector symbolic architectures (VSAs) with complex-valued vectors, (2) the design of hierarchical resonator networks to factorize the non-commutative transforms translation and rotation in visual scenes and (3) the design of a multi-compartment spiking phasor neuron model for implementing complex-valued resonator networks on neuromorphic hardware. The VSA framework uses vector binding operations to form a generative image model in which binding acts as the equivariant operation for g eo me tric t ra nsformations. A scene can therefore be described as a sum of vector products, which can then be efficiently factorized by a resonator network to infer objects and their poses. The hierarchical resonator network features a partitioned architecture in which vector binding is equivariant for horizontal and vertical translation within one partition and for rotation and scaling within the other partition. The spiking neuron model allows mapping the resonator network onto efficient and low-power neuromorphic hardware. Our approach is demonstrated on synthetic scenes composed of simple two-dimensional shapes undergoing rigid geometric transformations and colour changes. A companion paper demonstrates the same approach in real-world application scenarios for machine vision and robotics. 

Visual odometry (VO) is a method used to estimate self-motion of a mobile robot using visual sensors. Unlike odometry based on integrating differential measurements that can accumulate errors, such as inertial sensors or wheel encoders, VO is not compromised by drift. However, image-based VO is computationally demanding, limiting its application in use cases with low-latency, low-memory and low-energy requirements. Neuromorphic hardware offers low-power solutions to many vision and artificial intelligence problems, but designing such solutions is complicated and often has to be assembled from scratch. Here we propose the use of vector symbolic architecture (VSA) as an abstraction layer to design algorithms compatible with neuromorphic hardware. Building from a VSA model for scene analysis, described in our companion paper, we present a modular neuromorphic algorithm that achieves state-of-the-art performance on two-dimensional VO tasks. Specifically, the proposed algorithm stores and updates a working memory of the presented visual environment. Based on this working memory, a resonator network estimates the changing location and orientation of the camera. We experimentally validate the neuromorphic VSA-based approach to VO with two benchmarks: one based on an event-camera dataset and the other in a dynamic scene with a robotic task.