Session 03📈

Intensity Transformations

Point-wise gray-level transformations: negative, logarithm, and power-law (gamma).

Learning Objectives

✓Apply negative transformation to invert intensity
✓Use logarithmic transform to expand dark regions
✓Apply power-law (gamma) transform to control brightness

Negative Transformation

The negative of an image is obtained by $s = L - 1 - r$ , where $L = 256$ . This inverts intensities — dark becomes bright and vice versa. Useful for displaying X-rays or enhancing detail in dark areas.

s = L - 1 - r \qquad (L = 256)

r

= original intensity,

s

= transformed intensity

Ex3_1a — Negative transformationPython

import cv2
import numpy as np

img = cv2.cvtColor(cv2.imread('input.jpg'), cv2.COLOR_BGR2RGB)
L = 256
negative = (L - 1) - img

Logarithmic Transformation

The log transform maps a narrow range of dark input values into a wider range of output values, where $c$ is a scaling constant. Great for images with large dynamic range (e.g. Fourier spectra).

s = c \cdot \log(1 + r)

c = \dfrac{255}{\log(1 + \max(r))}

is the usual choice, mapping the result into

[0, 255]

Ex3_1b — Log transformationPython

img_f = img.astype(np.float64)
c = 255 / np.log(1 + np.max(img_f))
log_img = np.uint8(c * np.log(1 + img_f))

Power-Law (Gamma) Transformation

When $\gamma < 1$ , the image is brightened (expands dark values). When $\gamma > 1$ , the image is darkened (compresses dark values). $\gamma = 1$ is the identity transformation.

s = 255 \cdot \left(\frac{r}{255}\right)^{\gamma}

\gamma < 1

brightens ·

\gamma > 1

darkens ·

\gamma = 1

leaves the image unchanged

Ex3_1c — Power (gamma) transformationPython

img_f = img.astype(np.float64) / 255.0

gamma_values = [0.3, 0.5, 1.0, 2.0, 3.0]

for gamma in gamma_values:
    result = np.uint8(np.clip((img_f ** gamma) * 255, 0, 255))

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