🏗️ Sampling & Quantization

(Understanding Image Resolution and Bit Depth) :contentReference[oaicite:0]{index=0}

When we digitise a real-world scene, we convert a continuous image into a grid of discrete pixels with discrete intensity (or colour) values. This process involves two key steps:

1. Sampling – breaking the image into individual pixels
2. Quantization – assigning each pixel a finite set of intensity values based on bit depth

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1. Sampling: Breaking the Image into Pixels

Definition:
Sampling refers to how frequently we measure light intensity across the spatial dimensions of the image.

Why it matters:

• A high-resolution image (e.g. 1920×1080) has many pixels → finer detail
• A low-resolution image (e.g. 100×100) has fewer pixels → blocky appearance

Think of it like zooming in on a LEGO™ photo — more pieces = more detail.

Code Example: Simulating Sampling

import cv2
import matplotlib.pyplot as plt

# Load and convert to RGB
img = cv2.imread("bird.jpg")
img_rgb = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)

# Preserve aspect ratio
h, w = img_rgb.shape[:2]
new_w = 50
new_h = int(h * (new_w / w))

# Downsample then upsample
low_res = cv2.resize(img_rgb, (new_w, new_h), interpolation=cv2.INTER_NEAREST)
upscaled = cv2.resize(low_res, (w, h), interpolation=cv2.INTER_NEAREST)

# Plot side by side
plt.figure(figsize=(15, 5))
for i, (title, im) in enumerate([
    ("Original", img_rgb),
    (f"Downsampled ({new_w}×{new_h})", low_res),
    ("Upscaled to Original Size", upscaled)
]):
    plt.subplot(1, 3, i+1)
    plt.imshow(im)
    plt.title(title)
    plt.axis("off")
plt.tight_layout()
plt.show()

2. Quantization: Assigning Values to Pixels

Definition:
Quantization maps the continuous range of light intensities to a finite set of discrete values determined by the bit depth of the image sensor or format.

• 8-bit quantization: each channel can take values from 0 to 255
• Higher bit depth (e.g. 10–16 bits) allows smoother tonal transitions (reducing banding)

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🔄 Summary

Concept	Meaning	Key Impact
Sampling	Number of pixels in the image	Affects spatial resolution
Quantization	Range of values a pixel can take	Affects intensity/grayscale levels
Bit Depth	Number of bits used per pixel/channel	Higher bit depth → smoother gradients