Robotics Computer Vision & Physical AI Studio

In-Browser Robotics Vision & Optical Calibration Lab

Interactive computer vision workstation for robotics engineers: calibrate HSV color segmentation with live centroid tracking, generate metric ArUco & AprilTag fiducial markers with 3D pose estimation, and calculate lens FOV, GSD, and optical matrices in real time.

Image Source: 📁 Upload Image

● BUILT-IN TEST SCENE

Tuning Presets:

Threshold Sliders OpenCV Scale (H: 0-179, S,V: 0-255)

Hue Min (H_min): 22 (44°)

Hue Max (H_max): 38 (76°)

Saturation Min (S_min): 100

Saturation Max (S_max): 255

Value / Brightness Min (V_min): 100

Value / Brightness Max (V_max): 255

Auto Red Wrap-Around (when H_min > H_max) Invert Binary Mask (NOT gate) Morphological Filter (3x3 Erode / Dilate noise reduction)

Target HUD Telemetry LOCKED

Centroid (cx, cy)

(320, 240)

Offset: ΔX: 0px, ΔY: 0px

Bounding Box

140 × 140

Aspect Ratio: 1.00

Segmented Area

15,394 px²

5.0% of camera frame

Steering Heading Error

0.0°

CENTERED (ON TARGET)

1. Original Feed 640 × 480

2. Binary Threshold Mask 0 px

3. Contour & Tracking HUD HUD Active

1-Click Robotics Code Exporter

Fiducial Family:

Marker ID (0 - 49):

Print Size (mm):

Fiducial Marker & Metric Scale

4×4 • ID 7

                0 mm
                25 mm
                50 mm Scale Ruler
              

Measure with calipers after printing to verify 1:1 scale

              Family: DICT_4X4_50 | ID: 7 | Physical Size: 100 mm × 100 mm
            

💡 Printing Advice: Set printer scaling to "100% / Actual Size" (do not select "Fit to Page") for millimeter-accurate computer vision ground truth.

Interactive 3D Pose Estimation Simulator solvePnP Raytracer

              Drag mouse on 3D viewport to orbit camera • Red = X, Green = Y, Blue = Normal Z
              Distance: 1.00 m
            

Distance Z (m): 1.00 m

Lateral X (m): 0.00 m

Vertical Y (m): 0.00 m

Pitch (θ): 15°

Yaw (ψ): -20°

Roll (φ): 0°

Rodrigues Vector rvec [rx, ry, rz]

-0.245, 0.321, 0.042 rad

Rotation Matrix Det(R) = +1.000

Translation Vector tvec [tx, ty, tz]

[0.000, 0.000, 1.000] m

Projected Corners: (220,160) … (420,320) px

OpenCV solvePnP & Camera Geometry Derivation

Perspective-n-Point (PnP) Formulation: Given 3D object points in the tag's local coordinate frame $P_i = [X_i, Y_i, 0]^T$ and their observed 2D image projections $p_i = [u_i, v_i]^T$, OpenCV solves for rotation $R$ and translation $ec{t}$ minimizing reprojection error:

                s · [u, v, 1]ᵀ = K · [R | t] · [X, Y, Z, 1]ᵀ
              

import cv2
import numpy as np

# 1. Physical 3D Object Points in Marker Frame (Corners at Z=0)
marker_size = 0.10  # 100mm = 0.10m
obj_points = np.array([
    [-marker_size/2,  marker_size/2, 0],
    [ marker_size/2,  marker_size/2, 0],
    [ marker_size/2, -marker_size/2, 0],
    [-marker_size/2, -marker_size/2, 0]
], dtype=np.float32)

# 2. Camera Intrinsic Matrix K and Distortion Vector D
camera_matrix = np.array([
    [967.0,   0.0, 320.0],
    [  0.0, 967.0, 240.0],
    [  0.0,   0.0,   1.0]
], dtype=np.float64)
dist_coeffs = np.zeros((5, 1), dtype=np.float64)  # [k1, k2, p1, p2, k3]

# 3. Estimate 3D Pose via Levenberg-Marquardt
success, rvec, tvec = cv2.solvePnP(obj_points, img_corners, camera_matrix, dist_coeffs, flags=cv2.SOLVEPNP_IPPE_SQUARE)

# 4. Convert Rodrigues rvec to 3x3 Rotation Matrix
R, _ = cv2.Rodrigues(rvec)

# 5. Draw 3D Coordinate Axes on Image (X=Red, Y=Green, Z=Blue)
cv2.drawFrameAxes(frame, camera_matrix, dist_coeffs, rvec, tvec, 0.05)  # 50mm axis

Optical & Sensor Parameters

Sensor Optical Format:

Camera Resolution:

Lens Focal Length (f): 2.80 mm

Working Distance / Altitude (Z): 1.50 m

Intrinsic Matrix K & ROS 2 Info

Horizontal FOV (HFOV)

89.7°

Wide-Angle Lens

Vertical FOV (VFOV)

58.4°

Diagonal: 99.8°

Ground Sampling (GSD)

1.55 mm/px

0.16 cm per pixel

Focal Length (Pixels)

fx: 967 px

fy: 967 px

Interactive Optical Frustum & Coverage Visualizer

              Viewing Cone from Camera Focal Point • Scale indicates ground coverage footprint at Z
              Coverage: 2.98 m × 1.68 m
            

Optical Resolution & Detectability Criteria

Optical Property	Computed Value	Robotics & Physical AI Significance
Physical Pixel Pitch	2.90 μm × 2.90 μm	Microscopic pixel cell size on silicon die
Field Coverage at Distance	2.98 m (W) × 1.68 m (H)	Total rectangular optical footprint visible to robot
Min Object Detection (2 px)	3.1 mm	Nyquist spatial sampling threshold for target detection
Min Object Recognition (6 px)	9.3 mm	Feature classification & contour centroid tracking
ArUco Tag Decode (60 px)	93.0 mm (min tag size)	Reliable fiducial barcode decoding & 3D solvePnP