Morphological Operations

Morphology Nədir?

Mathematical morphology şəkillərin forma və strukturunu analiz etmək və manipulyasiya etmək üçün istifadə olunan texnikalar toplusudur. Əsasən binary image-lər üçün təklif edilsə də, grayscale image-lərə də tətbiq oluna bilər.

Əsas konsepsiyalar:

Structuring element - Morfoloji əməliyyatda istifadə olunan kiçik forma (kernel)
Set operations - Binary image-lər üzərində riyazi çoxluq əməliyyatları
Shape analysis - Obyekt forması və topologiyası

Structuring Element

Structuring element (SE) morfoloji əməliyyatlarda istifadə olunan kiçik matrisdir - convolution-dakı kernel kimi.

Common Shapes

Misal strukturlar:

3×3 Rectangular:

┌─────────┐
│ 1  1  1 │
│ 1  1  1 │
│ 1  1  1 │
└─────────┘

3×3 Cross:

┌─────────┐
│ 0  1  0 │
│ 1  1  1 │
│ 0  1  0 │
└─────────┘

5×5 Ellipse:

┌─────────────┐
│ 0  1  1  1  0│
│ 1  1  1  1  1│
│ 1  1  1  1  1│
│ 1  1  1  1  1│
│ 0  1  1  1  0│
└─────────────┘

OpenCV-də SE yaratma:

import cv2
import numpy as np

# Rectangular
rect_kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (5, 5))

# Cross
cross_kernel = cv2.getStructuringElement(cv2.MORPH_CROSS, (5, 5))

# Ellipse
ellipse_kernel = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (5, 5))

# Custom
custom_kernel = np.array([[0, 1, 0],
                          [1, 1, 1],
                          [0, 1, 0]], dtype=np.uint8)

Basic Operations

1. Erosion (Aşınma)

Erosion foreground obyekti kiçildir, boundary pixel-lərini silir.

Prinsip:

Structuring element bütün image üzərində hərəkət edir
SE tam olaraq foreground-a fit olduqda, center pixel qorunur
Əks halda, center pixel background olur

Riyazi təsvir:

A ⊖ B = {z | (B)z ⊆ A}

A: Image
B: Structuring element
(B)z: B translated by z

Erosion A-nı B ilə: Yalnız SE tamamilə A-nın içinə fit olduğu nöqtələr

Implementation:

# Binary image
binary = cv2.imread('binary.jpg', cv2.IMREAD_GRAYSCALE)
_, binary = cv2.threshold(binary, 127, 255, cv2.THRESH_BINARY)

# Structuring element
kernel = np.ones((5, 5), np.uint8)

# Erosion
eroded = cv2.erode(binary, kernel, iterations=1)

# Multiple iterations
eroded_3 = cv2.erode(binary, kernel, iterations=3)

Effektlər:

Obyektlər kiçilir
Boundaries smooth olur
Thin connections qırılır
Small noise silinir

Misal:

Original:              Eroded (3×3):
┌──────────┐          ┌──────────┐
│ 0 0 0 0 0│          │ 0 0 0 0 0│
│ 0 1 1 1 0│          │ 0 0 0 0 0│
│ 0 1 1 1 0│    →     │ 0 0 1 0 0│
│ 0 1 1 1 0│          │ 0 0 0 0 0│
│ 0 0 0 0 0│          │ 0 0 0 0 0│
└──────────┘          └──────────┘

2. Dilation (Genişləmə)

Dilation foreground obyekti böyüdür, boundary-yə pixel əlavə edir.

Prinsip:

SE-nin center-i foreground pixel-də olduqda
SE-nin shape-i foreground-a əlavə olunur

Riyazi təsvir:

A ⊕ B = {z | (B̂)z ∩ A ≠ ∅}

B̂: B-nin reflection
Dilation: SE-nin heç olmasa bir elementi A ilə overlap olduqda

Implementation:

# Dilation
dilated = cv2.dilate(binary, kernel, iterations=1)

# Multiple iterations
dilated_3 = cv2.dilate(binary, kernel, iterations=3)

Effektlər:

Obyektlər böyüyür
Holes fill olur
Gaps bağlanır
Close objects birləşir

Misal:

Original:              Dilated (3×3):
┌──────────┐          ┌──────────┐
│ 0 0 0 0 0│          │ 0 1 1 1 0│
│ 0 0 0 0 0│          │ 0 1 1 1 0│
│ 0 0 1 0 0│    →     │ 1 1 1 1 1│
│ 0 0 0 0 0│          │ 0 1 1 1 0│
│ 0 0 0 0 0│          │ 0 1 1 1 0│
└──────────┘          └──────────┘

Erosion vs Dilation

Compound Operations

3. Opening

Opening = Erosion → Dilation

Məqsəd:

Small noise silinir
Thin connections qırılır
Obyekt ölçüsü approximate qorunur

Riyazi təsvir:

A ∘ B = (A ⊖ B) ⊕ B

∘: Opening operator

Implementation:

# Opening
opening = cv2.morphologyEx(binary, cv2.MORPH_OPEN, kernel)

# Manual
eroded = cv2.erode(binary, kernel, iterations=1)
opening_manual = cv2.dilate(eroded, kernel, iterations=1)

Effektlər:

Small white noise silinir
Thin protrusions (çıxıntılar) silinir
Smooth outline
Internal structure qorunur

Practical use case:

# Salt noise (ağ nöqtələr) təmizləmək
noisy = binary.copy()
opening = cv2.morphologyEx(noisy, cv2.MORPH_OPEN, kernel)

4. Closing

Closing = Dilation → Erosion

Məqsəd:

Small holes fill olur
Small gaps bağlanır
Obyekt ölçüsü approximate qorunur

Riyazi təsvir:

A • B = (A ⊕ B) ⊖ B

•: Closing operator

Implementation:

# Closing
closing = cv2.morphologyEx(binary, cv2.MORPH_CLOSE, kernel)

# Manual
dilated = cv2.dilate(binary, kernel, iterations=1)
closing_manual = cv2.erode(dilated, kernel, iterations=1)

Effektlər:

Small black holes fill olur
Small gaps bağlanır
Broken contours bərpa olunur
Smooth outline

Practical use case:

# Pepper noise (qara nöqtələr) və gaps-i təmizləmək
broken = binary.copy()
closing = cv2.morphologyEx(broken, cv2.MORPH_CLOSE, kernel)

Opening vs Closing

Side-by-side comparison:

Original:           Opening:           Closing:
┌────────────┐     ┌────────────┐     ┌────────────┐
│ 1 0 1 1 1 │     │ 0 0 1 1 1 │     │ 1 1 1 1 1 │
│ 0 1 1 0 1 │     │ 0 1 1 0 1 │     │ 1 1 1 1 1 │
│ 1 1 0 1 1 │  →  │ 0 1 0 1 1 │  →  │ 1 1 1 1 1 │
│ 1 1 1 1 0 │     │ 0 1 1 1 0 │     │ 1 1 1 1 1 │
│ 1 0 1 1 1 │     │ 0 0 1 1 1 │     │ 1 1 1 1 1 │
└────────────┘     └────────────┘     └────────────┘

Advanced Operations

5. Morphological Gradient

Gradient = Dilation - Erosion

Məqsəd:

Obyekt outline-ını tap
Edge detection

Implementation:

# Morphological gradient
gradient = cv2.morphologyEx(binary, cv2.MORPH_GRADIENT, kernel)

# Manual
dilated = cv2.dilate(binary, kernel, iterations=1)
eroded = cv2.erode(binary, kernel, iterations=1)
gradient_manual = dilated - eroded

Effekt:

Object boundary (outline)
Edge thickness SE size-a bağlı

6. Top Hat (White Top Hat)

Top Hat = Original - Opening

Məqsəd:

Bright obyektləri tap (background-dan bright)
Small bright features

Implementation:

# Top hat
tophat = cv2.morphologyEx(gray, cv2.MORPH_TOPHAT, kernel)

# Manual
opening = cv2.morphologyEx(gray, cv2.MORPH_OPEN, kernel)
tophat_manual = gray - opening

Use case:

Uneven illumination correction
Small bright object detection

7. Black Hat

Black Hat = Closing - Original

Məqsəd:

Dark obyektləri tap (background-dan dark)
Small dark features

Implementation:

# Black hat
blackhat = cv2.morphologyEx(gray, cv2.MORPH_BLACKHAT, kernel)

# Manual
closing = cv2.morphologyEx(gray, cv2.MORPH_CLOSE, kernel)
blackhat_manual = closing - gray

Use case:

Dark line detection
Small dark object extraction

Grayscale Morphology

Morfoloji əməliyyatlar grayscale image-lərə də tətbiq oluna bilər.

Grayscale Erosion

(A ⊖ B)(x,y) = min{A(x+i, y+j) - B(i,j)}

Hər position-da local minimum tap

Grayscale Dilation

(A ⊕ B)(x,y) = max{A(x-i, y-j) + B(i,j)}

Hər position-da local maximum tap

Implementation:

# Grayscale image
gray = cv2.imread('image.jpg', cv2.IMREAD_GRAYSCALE)
kernel = np.ones((5, 5), np.uint8)

# Grayscale operations
eroded_gray = cv2.erode(gray, kernel)
dilated_gray = cv2.dilate(gray, kernel)
opening_gray = cv2.morphologyEx(gray, cv2.MORPH_OPEN, kernel)
closing_gray = cv2.morphologyEx(gray, cv2.MORPH_CLOSE, kernel)

Practical Applications

1. Noise Removal

def remove_noise(binary_image, kernel_size=5):
    """Salt and pepper noise təmizləmə"""
    kernel = np.ones((kernel_size, kernel_size), np.uint8)
    
    # Opening: ağ noise
    opening = cv2.morphologyEx(binary_image, cv2.MORPH_OPEN, kernel)
    
    # Closing: qara noise
    result = cv2.morphologyEx(opening, cv2.MORPH_CLOSE, kernel)
    
    return result

2. Text Extraction

def extract_text_regions(image):
    """Document-dən text region-ları tap"""
    gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
    _, binary = cv2.threshold(gray, 0, 255, cv2.THRESH_BINARY_INV + cv2.THRESH_OTSU)
    
    # Horizontal kernel: text line-ları birləşdirmək
    kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (25, 1))
    dilated = cv2.dilate(binary, kernel, iterations=1)
    
    # Find contours
    contours, _ = cv2.findContours(dilated, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
    
    return contours

3. Skeleton Extraction

def skeletonize(binary_image):
    """Obyektin skeleton-unu tap"""
    skeleton = np.zeros(binary_image.shape, np.uint8)
    element = cv2.getStructuringElement(cv2.MORPH_CROSS, (3, 3))
    
    while True:
        eroded = cv2.erode(binary_image, element)
        temp = cv2.dilate(eroded, element)
        temp = cv2.subtract(binary_image, temp)
        skeleton = cv2.bitwise_or(skeleton, temp)
        binary_image = eroded.copy()
        
        if cv2.countNonZero(binary_image) == 0:
            break
    
    return skeleton

4. Boundary Extraction

def extract_boundary(binary_image, kernel_size=3):
    """Obyekt boundary-sini tap"""
    kernel = np.ones((kernel_size, kernel_size), np.uint8)
    
    # Erosion
    eroded = cv2.erode(binary_image, kernel)
    
    # Boundary = Original - Eroded
    boundary = cv2.subtract(binary_image, eroded)
    
    return boundary

5. Hole Filling

def fill_holes(binary_image):
    """Binary image-də hole-ları fill et"""
    # Invert
    inverted = cv2.bitwise_not(binary_image)
    
    # Flood fill from (0,0)
    h, w = binary_image.shape[:2]
    mask = np.zeros((h+2, w+2), np.uint8)
    cv2.floodFill(inverted, mask, (0, 0), 255)
    
    # Invert back
    inverted = cv2.bitwise_not(inverted)
    
    # Combine
    filled = cv2.bitwise_or(binary_image, inverted)
    
    return filled

6. Connected Component Analysis

def analyze_components(binary_image):
    """Connected component analysis"""
    # Opening: noise təmizlə
    kernel = np.ones((3, 3), np.uint8)
    cleaned = cv2.morphologyEx(binary_image, cv2.MORPH_OPEN, kernel)
    
    # Label connected components
    num_labels, labels, stats, centroids = cv2.connectedComponentsWithStats(cleaned)
    
    # Filter by area
    min_area = 100
    result = np.zeros_like(binary_image)
    
    for i in range(1, num_labels):  # 0 is background
        area = stats[i, cv2.CC_STAT_AREA]
        if area > min_area:
            result[labels == i] = 255
    
    return result, num_labels - 1

Structuring Element Size Selection

Guidelines:

3×3: Minimal effect, fine control
5×5: Standard choice, balanced
7×7+: Stronger effect, smooth results
Custom size: Feature size-a uyğun seç

Iteration Count

Operations Summary

Operation	Formula	Purpose	Use Case
Erosion	A ⊖ B	Shrink objects	Noise removal, separate objects
Dilation	A ⊕ B	Grow objects	Fill holes, connect objects
Opening	(A ⊖ B) ⊕ B	Remove white noise	Clean background
Closing	(A ⊕ B) ⊖ B	Remove black noise	Fill holes, connect
Gradient	(A ⊕ B) - (A ⊖ B)	Extract boundary	Edge detection
Top Hat	A - (A ∘ B)	Bright features	Uneven illumination
Black Hat	(A • B) - A	Dark features	Dark line detection

Performance Considerations

Best practices:

OpenCV built-in funksiyalardan istifadə et
Large kernels yavaşdır - lazım olduqda istifadə et
Multiple iterations əvəzinə larger kernel consider et
Binary operations grayscale-dən sürətlidir
GPU acceleration for real-time

Əsas Nəticələr

Erosion - Obyekti kiçildir, noise silir
Dilation - Obyekti böyüdür, hole-ları fill edir
Opening - Erosion+Dilation, white noise təmizləyir
Closing - Dilation+Erosion, black noise təmizləyir
Structuring element - Shape və size effektə təsir edir
Morphological gradient - Boundary extraction
Top/Black hat - Feature extraction, illumination correction
Grayscale morphology - Local min/max əməliyyatları
Applications - Noise removal, text extraction, skeleton, boundary
Iteration count - Effect strength-i control edir

Morphology Nədir?​

Structuring Element​

Common Shapes​

Basic Operations​

1. Erosion (Aşınma)​

2. Dilation (Genişləmə)​

Erosion vs Dilation​

Compound Operations​

3. Opening​

4. Closing​

Opening vs Closing​

Advanced Operations​

5. Morphological Gradient​

6. Top Hat (White Top Hat)​

7. Black Hat​

Grayscale Morphology​

Grayscale Erosion​

Grayscale Dilation​

Practical Applications​

1. Noise Removal​

2. Text Extraction​

3. Skeleton Extraction​

4. Boundary Extraction​

5. Hole Filling​

6. Connected Component Analysis​

Structuring Element Size Selection​

Iteration Count​

Operations Summary​

Performance Considerations​

Əsas Nəticələr​

Morphology Nədir?

Structuring Element

Common Shapes

Basic Operations

1. Erosion (Aşınma)

2. Dilation (Genişləmə)

Erosion vs Dilation

Compound Operations

3. Opening

4. Closing

Opening vs Closing

Advanced Operations

5. Morphological Gradient

6. Top Hat (White Top Hat)

7. Black Hat

Grayscale Morphology

Grayscale Erosion

Grayscale Dilation

Practical Applications

1. Noise Removal

2. Text Extraction

3. Skeleton Extraction

4. Boundary Extraction

5. Hole Filling

6. Connected Component Analysis

Structuring Element Size Selection

Iteration Count

Operations Summary

Performance Considerations

Əsas Nəticələr