Coordinate Systems & Pixel Access

If there is one topic that causes 90% of bugs for beginners, it is Coordinate Systems.

OpenCV and NumPy speak slightly different languages when it comes to coordinates. One talks in Geometry (x, y), and the other talks in Matrices [row, col]. mixing them up will crash your code or—worse—silently edit the wrong pixels.

This guide is your Rosetta Stone.

The Coordinate System

In standard mathematics (Cartesian), the origin (0, 0) is usually at the bottom-left or center.

In Computer Vision (and most computer graphics), the origin (0, 0) is at the Top-Left.

• X-axis: goes from Left to Right.
• Y-axis: goes from Top to Bottom.

  (0,0) ------> X (Width)
    |
    |
    v
    Y (Height)

The Great Divide: (x, y) vs [y, x]

Here is the rule you must memorize:

1. Function Arguments use (x, y).
   • Example: cv2.resize(img, (width, height))
   • Example: cv2.circle(img, (x, y), ...)
2. Matrix Access uses [y, x] (or [row, col]).
   • Example: pixel = img[y, x]
   • Example: crop = img[y1:y2, x1:x2]

Danger

The “Shape” Trap: img.shape returns (Height, Width, Channels). But cv2.resize expects (Width, Height). This means cv2.resize(img, img.shape[:2]) is WRONG! It flips the dimensions.

Accessing & Modifying Pixels

Since images are NumPy arrays, accessing a pixel is just array indexing.

Python

import cv2
import numpy as np

img = cv2.imread("photo.jpg")

# 1. Access a pixel
# Remember: [y, x]
y, x = 50, 100
pixel = img[y, x]
print(f"Pixel at y={y}, x={x} is {pixel}")

# 2. Modify a pixel
# Make it White (255, 255, 255)
img[y, x] = [255, 255, 255]

Tip

Looping over every pixel with a for loop is extremely slow in Python. Always prefer Slicing or Vectorized operations (NumPy) whenever possible.

Regions of Interest (ROI) & Slicing

A ROI is just a sub-section of an image. You might want to detect a face and then just work on that square face region.

In NumPy, we use Slicing: array[start:stop:step].

Basic Crop

To crop a rectangular region, you need the start and end coordinates for both Y (Rows) and X (Cols).

Python

# Defined coordinates
x_start, y_start = 100, 50
x_end, y_end = 300, 250

# Crop logic: [y_start:y_end, x_start:x_end]
roi = img[y_start:y_end, x_start:x_end]

cv2.imshow("Cropped ROI", roi)

ROI arithmetic

Here is a practical example: “I want to put a black square in the center of the image”.

Python

# 1. Create a blank canvas
img = np.zeros((400, 400, 3), dtype="uint8")

# 2. Define the region
# Center 100x100 square
center_y, center_x = 200, 200
offset = 50

# 3. Modify the region directly
# We are selecting a range of pixels and assigning a value to ALL of them at once
img[center_y-offset:center_y+offset, center_x-offset:center_x+offset] = [255, 255, 255] # White square

Copy vs View

This is a critical Python concept. When you slice an array, NumPy usually returns a View, not a Copy.

• View: If you modify the roi, the original img ALSO changes.
• Copy: If you modify the roi, the original img stays the same.

Python

# VIEW example
roi = img[0:100, 0:100]
roi[:] = [0, 0, 255] # Make the ROI Red
# Result: Top-left of 'img' is now Red!

# COPY example
roi_copy = img[0:100, 0:100].copy()
roi_copy[:] = [0, 255, 0] # Make the copy Green
# Result: 'img' is NOT changed.

Advanced Indexing

Negative Indexing

Just like standard Python lists, you can use negative numbers to count from the end.

Python

# Get the last row
last_row = img[-1, :]

# Crop the bottom-right 10x10 corner
corner = img[-10:, -10:]

Striding (Stepping)

The third argument in slicing is the step. You can use this to downsample an image trivially (though without anti-aliasing).

Python

# [start:end:step]
# Take every 2nd pixel in both directions (half size)
small_img = img[::2, ::2]

Summary Reference

Operation	Syntax	Logic
Pixel Access	img[y, x]	Matrix Row/Col
Drawing	cv2.line(img, (x, y), ...)	Cartesian Point
Resizing	cv2.resize(img, (w, h))	Cartesian Dimensions
Shape	(h, w, c)	Matrix Dimensions
Cropping	img[y1:y2, x1:x2]	Matrix Slicing

References

1. NumPy Indexing Documentation
2. OpenCV Core Functionality