# Non-Iterative SLAM

## TL;DR

This paper introduces a novel non-iterative dense SLAM framework suitable for micro-robot systems, significantly reducing computational costs while maintaining high-resolution 3D mapping accuracy.

## Contribution

It proposes the first non-iterative, online trainable data association method for visual SLAM using Fourier domain matching and decoupling techniques.

## Key findings

- Faster runtime compared to state-of-the-art methods
- Higher resolution 3D maps with comparable accuracy
- Reduced computational complexity to O(n log n)

## Abstract

The goal of this paper is to create a new framework for dense SLAM that is light enough for micro-robot systems based on depth camera and inertial sensor. Feature-based and direct methods are two mainstreams in visual SLAM. Both methods minimize photometric or reprojection error by iterative solutions, which are computationally expensive. To overcome this problem, we propose a non-iterative framework to reduce computational requirement. First, the attitude and heading reference system (AHRS) and axonometric projection are utilized to decouple the 6 Degree-of-Freedom (DoF) data, so that point clouds can be matched in independent spaces respectively. Second, based on single key-frame training, the matching process is carried out in frequency domain by Fourier transformation, which provides a closed-form non-iterative solution. In this manner, the time complexity is reduced to $\mathcal{O}(n \log{n})$, where $n$ is the number of matched points in each frame. To the best of our knowledge, this method is the first non-iterative and online trainable approach for data association in visual SLAM. Compared with the state-of-the-arts, it runs at a faster speed and obtains 3-D maps with higher resolution yet still with comparable accuracy.