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Terrain Sensing with Smartphone Structured Light: 2D Dynamic Time Warping for Grid Pattern Matching

Tanaka Nobuaki

TL;DR

The paper tackles dense terrain sensing for small mobile rovers using a smartphone-based structured-light system. It introduces a topology-constrained 2D-DTW algorithm that matches a projected grid by performing column-wise DTW under a global grid-consistency constraint, balancing robustness and computational efficiency. The method yields dense local 3D ground reconstructions from a single frame and fuses them along the rover path to form a continuous ground profile, with favorable performance on texture-poor surfaces compared to feature-based approaches. The work demonstrates a practical, low-cost alternative to LiDAR for ground profiling and suggests broader applicability of grid-pattern matching in image processing tasks.

Abstract

Low-cost mobile rovers often operate on uneven terrain where small bumps or tilts are difficult to perceive visually but can significantly affect locomotion stability. To address this problem, we explore a smartphone-based structured-light system that projects a grid pattern onto the ground and reconstructs local terrain unevenness from a single handheld device. The system is inspired by face-recognition projectors, but adapted for ground sensing. A key technical challenge is robustly matching the projected grid with its deformed observation under perspective distortion and partial occlusion. Conventional one-dimensional dynamic time warping (1D-DTW) is not directly applicable to such two-dimensional grid patterns. We therefore propose a topology-constrained two-dimensional dynamic time warping (2D-DTW) algorithm that performs column-wise alignment under a global grid consistency constraint. The proposed method is designed to be simple enough to run on resource limited platforms while preserving the grid structure required for accurate triangulation. We demonstrate that our 2D-DTW formulation can be used not only for terrain sensing but also as a general tool for matching structured grid patterns in image processing scenarios. This paper describes the overall system design as well as the 2D-DTW extension that emerged from this application.

Terrain Sensing with Smartphone Structured Light: 2D Dynamic Time Warping for Grid Pattern Matching

TL;DR

The paper tackles dense terrain sensing for small mobile rovers using a smartphone-based structured-light system. It introduces a topology-constrained 2D-DTW algorithm that matches a projected grid by performing column-wise DTW under a global grid-consistency constraint, balancing robustness and computational efficiency. The method yields dense local 3D ground reconstructions from a single frame and fuses them along the rover path to form a continuous ground profile, with favorable performance on texture-poor surfaces compared to feature-based approaches. The work demonstrates a practical, low-cost alternative to LiDAR for ground profiling and suggests broader applicability of grid-pattern matching in image processing tasks.

Abstract

Low-cost mobile rovers often operate on uneven terrain where small bumps or tilts are difficult to perceive visually but can significantly affect locomotion stability. To address this problem, we explore a smartphone-based structured-light system that projects a grid pattern onto the ground and reconstructs local terrain unevenness from a single handheld device. The system is inspired by face-recognition projectors, but adapted for ground sensing. A key technical challenge is robustly matching the projected grid with its deformed observation under perspective distortion and partial occlusion. Conventional one-dimensional dynamic time warping (1D-DTW) is not directly applicable to such two-dimensional grid patterns. We therefore propose a topology-constrained two-dimensional dynamic time warping (2D-DTW) algorithm that performs column-wise alignment under a global grid consistency constraint. The proposed method is designed to be simple enough to run on resource limited platforms while preserving the grid structure required for accurate triangulation. We demonstrate that our 2D-DTW formulation can be used not only for terrain sensing but also as a general tool for matching structured grid patterns in image processing scenarios. This paper describes the overall system design as well as the 2D-DTW extension that emerged from this application.

Paper Structure

This paper contains 29 sections, 33 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Two-dimensional DTW for images and matrices
  4. Rotation- and affine-invariant DTW
  5. System Overview
  6. Hardware configuration.
  7. High-contrast grid UI and heading constraint.
  8. Image acquisition and grid extraction.
  9. 2D-DTW-based grid matching.
  10. Local 3D reconstruction.
  11. Pose refinement and ground profile accumulation.
  12. 2D-DTW for Grid Pattern Matching
  13. Setting
  14. One-dimensional DTW distance
  15. Column-wise DTW distance matrix
  16. ...and 14 more sections

Figures (1)

  • Figure 1: Cross-sectional view of the smartphone-based triangulation setup. The smartphone display is modeled as a plane above the ground. The vertical segment (depth) represents the distance $h$ between the display and the ground, and the slanted segment $p$ is a ray connecting a display pixel to a point on the surface.