How Run-Length Encoding (RLE) is used in Image Compression

Let’s see how Run-Length Encoding (RLE) — the same logic as the String Compression problem — is applied in image compression.

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🧩 What Is Run-Length Encoding (RLE)?

Run-Length Encoding is a lossless compression algorithm that reduces file size by storing consecutive repeating values as one value + count.

It’s used in formats like:

• BMP, TIFF, and PDF
• Fax machines
• Early video game graphics
• Simple icons, pixel art, and mask images

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🖼️ Example: A Tiny 2D Black & White Image

Let’s imagine a 6×6 image made of only black (1) and white (0) pixels:

Image matrix:
0 0 0 1 1 0
0 0 1 1 1 0
0 0 0 0 0 0
1 1 0 0 0 0
1 1 1 0 0 0
1 0 0 0 0 0

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🧠 Step 1 — Flatten the image into a 1D sequence:

000110 001110 000000 110000 111000 100000
→ 000110001110000000110000111000100000

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🧮 Step 2 — Apply Run-Length Encoding (count consecutive runs):

Value	Count	Encoded
0	3	03
1	2	12
0	1	01
0	2	02
1	3	13
0	1	01
0	6	06
1	2	12
0	4	04
1	3	13
0	3	03
1	1	11
0	5	05

So the RLE encoded sequence is:

[(0,3), (1,2), (0,1), (0,2), (1,3), (0,1), (0,6), (1,2), (0,4), (1,3), (0,3), (1,1), (0,5)]

Or, compact form:

03 12 01 02 13 01 06 12 04 13 03 11 05

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🧩 Step 3 — Decoding (Decompression)

To reconstruct the image:

• Read pair by pair
• Expand each (value, count) → e.g., (1,3) → 111
• Rebuild into the original 6×6 grid

Result → Exactly same image! ✅ That’s why RLE is called lossless.

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⚙️ Real-World Example in Code

Python Implementation

def rle_encode(data):
    encoding = []
    count = 1

    for i in range(1, len(data)):
        if data[i] == data[i - 1]:
            count += 1
        else:
            encoding.append((data[i - 1], count))
            count = 1
    encoding.append((data[-1], count))
    return encoding


def rle_decode(encoded):
    result = []
    for value, count in encoded:
        result.extend([value] * count)
    return result


pixels = [0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0]
encoded = rle_encode(pixels)
decoded = rle_decode(encoded)

print("Encoded:", encoded)
print("Decoded == Original:", decoded == pixels)

✅ Output:

Encoded: [(0, 3), (1, 2), (0, 1), (0, 2), (1, 3), ...]
Decoded == Original: True

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🧠 Why It Works Well

RLE works best when:

• There are lots of consecutive identical values
• e.g. black-and-white icons, drawings, QR codes, barcodes, etc.

But it fails (i.e., no compression benefit) when:

• Data is highly varied (like photos with noise or color gradients)

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🖌️ Visual Analogy

Imagine describing a line of pixels to someone:

👩‍💻 “There are 5 white pixels, then 3 black pixels, then 10 white pixels.”

That’s RLE — it saves space by describing runs, not listing every pixel.

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