Monocular Depth Estimation for UAV Perch Landing

The Problem

A drone landing on a perch has no GPS signal, no laser rangefinder, and no dedicated depth sensor — just a camera. It needs to figure out exactly how far away the landing target is and whether it's correctly aligned, using only what appears in a single video frame. Get the math wrong, and the drone crashes.

The Challenge

Autonomous UAV landing on a perch requires knowing the perch's 3D position and the camera's attitude relative to it — without a depth sensor, IMU, or GPS. The system had to recover all of this from a single video frame using only the geometric properties of the detected blob: its centroid, principal axes, and apparent size. The depth estimation formula Z = f·X/X₀ is simple in principle but sensitive to blob detection noise, so the pipeline needed to be robust to partial occlusion and varying lighting.

Architecture & System Design

Single camera estimates 3D target pose using computer vision: image processing extracts target features, geometric math recovers position and orientation from 2D image moments. Enables closed-loop visual control without depth sensor.

The pipeline runs in real time on each video frame: (1) Convert BGR → HSV and threshold for the target colour (yellow: H=20–30, S=50–255, V=100–255) to isolate the blob. (2) Compute zeroth, first, and second-order image moments (M00, M10, M01, M20, M02, M11) to recover centroid (cx, cy) and shape covariance. (3) Eigendecompose the 2×2 covariance matrix to get principal axes and orientation angle θ — this gives camera roll/pitch relative to the perch. (4) Depth: Z = f · X_real / X_pixels, where focal length f=3.22 mm was measured via calibration. Output: [cx, cy, θ, Z] written to a position matrix file and used as the visual error signal for the PID controller. A complementary OpenCV toolkit was developed alongside: Canny edge detection with interactive threshold sliders, HSV range calibration tool, and SURF feature matching.

Code Walkthrough

3-step walk-through of the production implementation — file paths and intent shown above each block.

1. 01

   Step 1 of 3

   HSV colour segmentation and morphological cleanup

   vision/blob.cpp

   The perch marker is a known yellow colour. Converting to HSV decouples hue (colour identity) from brightness, making the threshold robust to shadows and changing illumination that would break an RGB threshold. Morphological open+close removes noise speckles and fills small holes before computing moments — noisy blobs produce wildly wrong centroids.

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   Takeaway

   HSV separation lets you tune H for colour identity and S/V for saturation/brightness independently — three sliders instead of six, and the threshold stays stable under lab lighting changes.

2. 02

   Step 2 of 3

   Image moments → centroid and principal axis angle

   vision/blob.cpp

   Image moments up to second order give the centroid (M10/M00, M01/M00) and the covariance of the blob shape. Eigendecomposing the 2×2 covariance matrix recovers the principal axis angle θ — this is the camera's roll/pitch attitude relative to the perch surface, extracted from a single frame with no IMU or depth sensor.

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   Takeaway

   The atan2 formula for principal axis is a direct eigendecomposition of the 2×2 blob covariance — no matrix library needed, and it correctly handles the degenerate case when mu20 == mu02.

3. 03

   Step 3 of 3

   Monocular depth from focal-length triangulation

   vision/blob.cpp

   With no depth sensor, depth is recovered from apparent blob size: Z = f · X_real / X_pixels, where X_real is the known physical perch diameter. The second moment √μ₂₀ approximates the blob's pixel half-width, giving depth without a stereo pair. Results are written to a position file consumed by the PID controller node.

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   Takeaway

   The constant k (8e-4) encodes both the focal length and the known object size — recalibrate just k when the perch diameter changes, and the depth formula stays the same.

Results

Depth estimation accuracy: 0.67 cm error at 25 cm, 5.7 cm at 1 m, and 25 cm at 2 m — performance degrades linearly with distance as expected from the triangulation model. Orientation estimation successfully recovered camera attitude (roll/pitch) relative to the perch surface at all tested distances. The full pipeline ran at real-time video rates in C++ on a laptop. Results were validated against a Vicon motion capture ground-truth system and documented in the final project report.

Gallery & Demos

Blob Detection Result

HSV segmentation isolating the yellow perch marker with centroid, principal axes, and orientation angle overlaid.

Depth Estimation Geometry

Diagram showing focal-length triangulation: how 2D blob size in pixels maps to 3D distance using calibrated focal length.

Accuracy Performance Plot

Depth estimation error (mm) vs. true distance, showing sub-1cm accuracy within working range.

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