• visit these notes over here on github!

Knowing both the Field of View (FoV) of a camera’s lens and the dimensions of the object we’d like to measure (Region of Interest, ROI) seems like more than enough to get a distance.

Note, opencv has an extensive suite of actual calibration tools and utilities here.

…But without calibration or much forethought, could rough measurements of known objects even be usable? Some notes from a math challenged individual:

# clone:
git clone https://github.com/Jesssullivan/misc-roi-distance-notes && cd misc-roi-distance-notes

Most webcams don’t really provide a Field of View much greater than ~50 degrees- this is the value of a MacBook Pro’s webcam for instance. Here’s the plan to get a Focal Length value from Field of View:

Focal Length = (ImageDimension / 2) * tan(FieldOfView / 2)

So, thinking along the lines of similar triangles:

• Camera angle FoV / 2 forms the angle between the hypotenuse side (one edge of the FoV angle) and the adjacent side
• Dimension ImageDimension / 2 is the opposite side of the triangle we are using to measure with.
• ^ This makes up the first of two “similar triangles”
• Then, we start measuring: First, calculate the opposite ROI Dimension using the arbitrary Focal Length value we calculated from the first triangle- then, plug in the Actual ROI Dimensions.
• Now the adjacent side of this ROI triangle should hopefully be length, in the the units of ROI’s Actual Dimension.

source a fresh venv to fiddle from:

# venv:
python3 -m venv distance_venv
source distance_venv/bin/activate

# depends are imutils & opencv-contrib-python:
pip3 install -r requirements.txt

The opencv people provide a bunch of prebuilt Haar cascade models, so let’s just snag one of them to experiment. Here’s one to detect human faces, we’ve all got one of those:

mkdir haar
wget https://raw.githubusercontent.com/opencv/opencv/master/data/haarcascades/haarcascade_frontalface_alt2.xml  -O ./haar/haarcascade_frontalface_alt2.xml

Of course, an actual thing with fixed dimensions would be better, like a stop sign!

Let’s try to calculate the distance as the difference between an actual dimension of the object with a detected dimension- here’s the plan:

Distance = ActualDimension * (FocalLength / ROIDimension)

YMMV, but YOLO:

# `python3 measure.py`
import math
from cv2 import cv2

DFOV_DEGREES = 50  # such as average laptop webcam horizontal field of view
KNOWN_ROI_MM = 240  # say, height of a human head

# image source:
cap = cv2.VideoCapture(0)

# detector:
cascade = cv2.CascadeClassifier('./haar/haarcascade_frontalface_alt2.xml')

while True:

Capture & resize a single image:

_, image = cap.read() image = cv2.resize(image, (0, 0), fx=.7, fy=0.7, interpolation=cv2.INTER_NEAREST)

Convert to greyscale while processing:

gray_conv = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY) gray = cv2.GaussianBlur(gray_conv, (7, 7), 0)

get image dimensions:

gray_width = gray.shape[1] gray_height = gray.shape[0]

focal_value = (gray_height / 2) / math.tan(math.radians(DFOV_DEGREES / 2))

run detector:

result = cascade.detectMultiScale(gray)

for x, y, h, w in result:

dist = KNOWN_ROI_MM * focal_value / h dist_in = dist / 25.4

update display:

cv2.rectangle(image, (x, y), (x + w, y + h), (255, 0, 0), 2) cv2.putText(image, ‘Distance:’ + str(round(dist_in)) + ’ Inches’, (5, 100), cv2.FONT_HERSHEY_SIMPLEX, 1, (255, 255, 255), 2) cv2.imshow(‘face detection’, image)

if cv2.waitKey(1) == ord(‘q’): break

run demo with:

python3 measure.py

Results:

…With only Field of View and a ROI of known dimensions, the accuracy of this “similar triangles” solution thus far has only been limited by image resolution and the quality of the detector- pretty cool!

This image has been lost to time. The original was hosted on WordPress.

-Jess