# Depth from 2D Images: Development and Metrological Evaluation of System Uncertainty Applied to Agricultural Scenarios

## TL;DR

This paper presents a model for estimating depth from 2D images using optical flow, validated in agricultural settings with low-cost cameras.

## Contribution

The paper introduces a practical model for depth estimation and provides guidelines for optimizing camera settings in agricultural scenarios.

## Key findings

- Higher image speeds (500–800 px/s) reduce depth estimation uncertainty.
- Optimal camera movement is 0.50–0.75 m/s with a 60 fps frame rate.
- Two validation methods are proposed to account for the model's exponential nature.

## Abstract

This article describes the development, experimental validation, and uncertainty analysis of a simple-to-use model for monocular depth estimation based on optical flow. The idea is deeply rooted in the agricultural scenario, for which vehicles that move around the field are equipped with low-cost cameras. In the experiment, the camera was mounted on a robot moving linearly at five different constant speeds looking at the target measurands (ArUco markers) positioned at different depths. The acquired data was processed and filtered with a moving average window-based filter to reduce noise in the estimated apparent depths of the ArUco markers and in the estimated optical flow image speeds. Two methods are proposed for model validation: a generalized approach and a complete approach that separates the input data according to their image speed to account for the exponential nature of the proposed model. The practical result obtained by the two analyses is that, to reduce the impact of uncertainty on depth estimates, it is best to have image speeds higher than 500–800 px/s. This is obtained by either moving the camera faster or by increasing the camera’s frame rate. The best-case scenario is achieved when the camera moves at 0.50–0.75 m/s and the frame rate is set to 60 fps (effectively reduced to 20 fps after filtering). As a further contribution, two practical examples are provided to offer guidance for untrained personnel in selecting the camera’s speed and camera characteristics. The developed code is made publicly available on GitHub.