Point Operators in Image
Processing
Unit 2 - Image Processing &
Computer Vision
Definition of Point Operators
• Point operators (or point processing
techniques) are operations applied
individually to each pixel of an image.
• The new pixel value depends only on the
original value of that pixel, not on its
neighbors.
• General form: g(x,y) = T[f(x,y)]
• where𝑓(𝑥,𝑦)= input pixel intensity,
• 𝑔(𝑥,𝑦)=output pixel intensity,
• 𝑇 = transformation function.
Characteristics
• Operates at single pixel level.
• Simple & fast compared to neighborhood-
based processing.
• Mainly used for contrast enhancement,
thresholding, brightness adjustment.
Types of Point Operators
• 1. Image Negation
• 2. Logarithmic Transformation
• 3. Power-Law (Gamma) Transformation
• 4. Piecewise Linear Transformations
• 5. Thresholding
Common Types of Point Operators
1.Image Negation:
Transformation:
𝑔(𝑥,𝑦)=𝐿−1−𝑓(𝑥,𝑦)
where 𝐿 = number of gray levels, e.g. 256 for 8-bit
images).
Effect: Dark areas → bright,
bright areas → dark.
Use: Medical imaging (X-rays), highlighting white
structures on dark backgrounds.
Image Negation
• Formula: g(x,y) = L - 1 - f(x,y)
• Converts dark areas to bright and vice versa
• Used in medical imaging and highlighting
structures
Logarithmic Transformation
• The log transformation is defined as:
• 𝑔(𝑥,𝑦)=𝑐⋅log(1+𝑓(𝑥,𝑦))
• 𝑓(𝑥,𝑦) = input pixel (0–255 for 8-bit)
• 𝑐=scaling constant, usually
• 𝑐=255 / log(1+max(𝑓))
• This enhances dark regions while
compressing bright values.
• The left image shows a normal gradient (0 →
255).
• The right image shows the log-transformed
gradient:
Dark regions (left side) are brightened.
Bright regions (right side) are compressed.
• The curve confirms this: it rises quickly for low
values (enhancing dark areas) and flattens for
high values (compressing bright areas).
2. Purpose
• Enhances low-intensity (dark) regions of an image.
• Compresses high-intensity (bright) regions.
• Useful for images with large variations in brightness.
3. Intensity Curve
At low input values → curve rises quickly → dark pixels
brighten.
At high input values → curve flattens → bright pixels
compressed.
Scenario Why Log Transform Helps
Reveals soft tissues hidden by bone
Medical X-ray
brightness
Brings out shadow details while saving
Outdoor HDR Landscape
highlights
Enhances dark cloud or water details
Satellite Imagery
without losing bright regions
Gamma (Power-Law) Transformation
• Power-Law (Gamma) Transformation in Image
Processing
• The Power-Law (Gamma) Transformation is defined
as:
• s=c⋅ r^gamma
• s=c⋅rγ
• where:
• r → input pixel intensity (normalized, 0–1 or 0–255).
• s → output pixel intensity.
• c → scaling constant (usually 1).
• γ gammaγ → gamma value (the key parameter).
• Effect of Gamma (γ)
• γ < 1 → Expands dark regions, brightens the
image.
• γ > 1 → Compresses dark regions, darkens the
image.
• γ = 1 → No change (linear).
• Applications
• Correcting lighting conditions (too dark or too
bright images).
• Display correction (because monitors and
cameras often have gamma non-linearities).
• Enhancing details in medical, astronomical,
and low-light images.
Piecewise Linear Transformations
• Contrast Stretching: Expands intensity range
• Gray-Level Slicing: Highlights specific ranges
• Bit-plane Slicing: Separates bit contributions
Thresholding
• Formula: g(x,y) = 1 if f(x,y) > T, else 0
• Converts grayscale image to binary
• Used in segmentation, OCR, and object
extraction
Applications
• Enhancement of images
• Compression (bit-plane slicing)
• Segmentation (thresholding)
• Medical imaging (tumor/bone highlighting)
• Display correction for devices
Neighborhood Operators in Image
Processing
• Neighborhood operators are image processing
techniques where the output value of a pixel
is determined by considering its neighboring
pixels. Unlike point operators (which only use
the pixel’s own intensity), neighborhood
operators analyze the local region to perform
operations like smoothing, sharpening, and
edge detection.
A pixel’s new value depends on the values of
pixels around it.
The local region is often represented as a mask
(kernel or filter), usually of size 3×3, 5×5, etc.
Common operations: averaging, median
filtering, edge detection, Laplacian, Sobel,
Prewitt, etc.
Types of Neighborhood Operators
• Smoothing (Noise Reduction)
• Sharpening
• Edge DetectionReplace each pixel with the
mean of its neighbors.
• Morphological Operators (for binary images)
Types of Neighborhood Operators
• Smoothing (Noise Reduction)
• Removes noise and blurs the image.
• Example: Averaging Filter
• Replace each pixel with the mean of its
neighbors.
