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Machine Vision

Rectangle Detection using Hough Transform Techniques

By Jan on 03/13/2025

Learn how to efficiently detect rectangles in images using the powerful Hough transform algorithm.

Rectangle Detection using Hough Transform Techniques

Table of Contents

Introduction

Detecting rectangles in an image is a common task in computer vision, often used in object detection, image analysis, and document scanning. This article outlines a step-by-step approach to detecting rectangles in an image using OpenCV, a popular computer vision library in Python. The process involves leveraging edge detection, line detection, and geometric analysis to identify and extract rectangular shapes from an image.

Step-by-Step Guide

  1. Preprocess the image: Apply edge detection techniques like Canny edge detection (cv2.Canny()) to highlight the boundaries of potential rectangles.

    edges = cv2.Canny(image, threshold1, threshold2)

  2. Apply Hough Line Transform: Use the Hough Line Transform (cv2.HoughLines()) to detect lines in the edge-detected image. This will give you a set of lines represented by their rho and theta values.

    lines = cv2.HoughLines(edges, 1, np.pi/180, threshold)

  3. Group lines: Iterate through the detected lines and group them based on their slopes and distances. Lines with similar slopes and a certain distance threshold can be considered as potential rectangle sides.

  4. Find intersections: Calculate the intersection points of the grouped lines. These intersections represent the potential corners of rectangles.

  5. Verify rectangles: Check if the detected corners form a valid rectangle by verifying the angle between the lines and the distance between opposite corners.

  6. Refine and filter: You can further refine the detected rectangles by considering factors like area, aspect ratio, and proximity to other rectangles. Filter out any false positives based on your specific application requirements.

Code Example

This Python code detects rectangles in an image using the Hough Line Transform. It first preprocesses the image by converting it to grayscale and detecting edges. Then, it applies the Hough Line Transform to detect lines in the image. The detected lines are grouped based on their slope and distance. Intersection points of the grouped lines are calculated and verified to form rectangles. Finally, the detected rectangles are drawn on the original image and displayed.

import cv2
import numpy as np

def detect_rectangles(image):
    """
    Detects rectangles in an image using Hough Line Transform.

    Args:
        image: Input image.

    Returns:
        A list of detected rectangles, each represented as a list of four corner points.
    """

    # 1. Preprocess the image
    gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
    edges = cv2.Canny(gray, 50, 150)

    # 2. Apply Hough Line Transform
    lines = cv2.HoughLines(edges, 1, np.pi / 180, 100)

    # 3. Group lines
    grouped_lines = group_lines_by_slope_and_distance(lines)

    # 4. Find intersections
    intersections = find_intersections(grouped_lines)

    # 5. Verify rectangles
    rectangles = verify_and_filter_rectangles(intersections)

    return rectangles


def group_lines_by_slope_and_distance(lines):
    """
    Groups lines based on their slopes and distances.
    """
    grouped_lines = []
    for i in range(len(lines)):
        for j in range(i + 1, len(lines)):
            rho1, theta1 = lines[i][0]
            rho2, theta2 = lines[j][0]

            # Check if slopes are similar
            if abs(theta1 - theta2) < 0.1:
                # Check if lines are close enough
                if abs(rho1 - rho2) < 20:
                    grouped_lines.append([lines[i], lines[j]])
    return grouped_lines


def find_intersections(grouped_lines):
    """
    Calculates intersection points of grouped lines.
    """
    intersections = []
    for line1, line2 in grouped_lines:
        rho1, theta1 = line1[0]
        rho2, theta2 = line2[0]

        A = np.array([[np.cos(theta1), np.sin(theta1)],
                      [np.cos(theta2), np.sin(theta2)]])
        b = np.array([[rho1], [rho2]])
        x0, y0 = np.linalg.solve(A, b)
        x0, y0 = int(np.round(x0)), int(np.round(y0))
        intersections.append((x0, y0))
    return intersections


def verify_and_filter_rectangles(intersections):
    """
    Verifies if detected corners form valid rectangles and filters out false positives.
    """
    rectangles = []
    for i in range(len(intersections)):
        for j in range(i + 1, len(intersections)):
            for k in range(j + 1, len(intersections)):
                for l in range(k + 1, len(intersections)):
                    # Check if points form a rectangle
                    if is_rectangle(intersections[i], intersections[j], intersections[k], intersections[l]):
                        rectangles.append([intersections[i], intersections[j], intersections[k], intersections[l]])
    return rectangles


def is_rectangle(p1, p2, p3, p4):
    """
    Checks if four points form a rectangle.
    """
    # Check if angles are approximately 90 degrees
    if not all(abs(angle(*p) - 90) < 5 for p in [(p1, p2, p3), (p2, p3, p4), (p3, p4, p1), (p4, p1, p2)]):
        return False

    # Check if opposite sides are approximately equal
    if not all(abs(distance(*p1) - distance(*p2)) < 10 for p1, p2 in [((p1, p2), (p3, p4)), ((p2, p3), (p4, p1))]):
        return False

    return True


def angle(p1, p2, p3):
    """
    Calculates the angle between three points.
    """
    v1 = np.array(p2) - np.array(p1)
    v2 = np.array(p3) - np.array(p2)
    cosine_angle = np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))
    angle_rad = np.arccos(cosine_angle)
    return np.degrees(angle_rad)


def distance(p1, p2):
    """
    Calculates the distance between two points.
    """
    return np.sqrt(((p2[0] - p1[0]) ** 2) + ((p2[1] - p1[1]) ** 2))


# Load image
image = cv2.imread('image.jpg')

# Detect rectangles
rectangles = detect_rectangles(image)

# Draw rectangles on the image
for rect in rectangles:
    cv2.polylines(image, [np.array(rect)], True, (0, 255, 0), 2)

# Show the result
cv2.imshow('Rectangles', image)
cv2.waitKey(0)
cv2.destroyAllWindows()

Explanation:

  1. Preprocessing: The image is converted to grayscale and Canny edge detection is applied to extract edges.
  2. Hough Line Transform: The cv2.HoughLines() function detects lines in the edge image.
  3. Line Grouping: The group_lines_by_slope_and_distance() function groups lines that have similar slopes and are within a certain distance threshold.
  4. Intersection Calculation: The find_intersections() function calculates the intersection points of the grouped lines.
  5. Rectangle Verification: The verify_and_filter_rectangles() function checks if the detected intersections form valid rectangles by verifying the angles and side lengths.
  6. Output: The detected rectangles are drawn on the original image and displayed.

Note: This code provides a basic framework for rectangle detection using Hough Line Transform. You may need to adjust the parameters and thresholds based on your specific image and application requirements.

Additional Notes

Parameter Tuning:

  • Canny edge detection thresholds: These values significantly impact the quality of edge detection. Experiment with different values to find what works best for your images.
  • HoughLines threshold: This parameter determines the minimum number of votes needed to consider a line. A higher threshold reduces noise but might miss faint lines.
  • Line grouping thresholds: The thresholds for slope difference and distance between lines influence how lines are grouped. Adjust these based on the expected size and orientation of rectangles in your images.

Optimizations:

  • Region of Interest (ROI): If you know the approximate location of the rectangle, process only that ROI to save computation time.
  • Probabilistic Hough Transform: Consider using cv2.HoughLinesP() for faster line detection, especially in images with many lines.
  • Data Structures: Efficient data structures like k-d trees can speed up the process of finding lines with similar slopes and distances.

Handling Complexities:

  • Overlapping rectangles: The code might struggle with heavily overlapping rectangles. You might need additional logic to separate or merge detected rectangles based on overlap and context.
  • Perspective distortion: If rectangles are viewed at an angle, apply perspective correction techniques before rectangle detection.
  • Non-perfect rectangles: The code assumes rectangles with near-perfect right angles. For irregular quadrilaterals, explore contour-based approaches or more advanced shape detection algorithms.

Alternative Approaches:

  • Contour Detection: Use cv2.findContours() to find contours in the image and then filter for contours that resemble rectangles based on properties like aspect ratio and number of sides.
  • Template Matching: If you have a template image of the rectangle, use template matching techniques (cv2.matchTemplate()) to find instances of the template in the image.
  • Machine Learning: Train a machine learning model (e.g., using YOLO or SSD) to detect rectangles directly. This approach requires labeled training data but can be more robust and adaptable to variations in rectangle appearance.

Summary

This article outlines a method for detecting rectangles within images using OpenCV in Python. The process can be summarized in six key steps:

  1. Edge Detection: The image is preprocessed using edge detection techniques like Canny edge detection (cv2.Canny()), highlighting potential rectangle boundaries.

  2. Line Detection: The Hough Line Transform (cv2.HoughLines()) is applied to the edge-detected image, identifying lines based on their rho and theta values.

  3. Line Grouping: Detected lines are grouped based on similar slopes and distances, indicating potential rectangle sides.

  4. Intersection Calculation: Intersection points of grouped lines are calculated, representing potential rectangle corners.

  5. Rectangle Verification: Corners are analyzed to confirm if they form valid rectangles by checking line angles and distances between opposite corners.

  6. Refinement and Filtering: Detected rectangles are refined and filtered based on criteria like area, aspect ratio, proximity to other rectangles, and application-specific requirements to eliminate false positives.

Conclusion

This article provides a comprehensive overview of detecting rectangles in images using the Hough Line Transform in OpenCV with Python. By understanding the principles of edge detection, line detection, and geometric analysis, developers can effectively implement this technique for various applications. The code example demonstrates the step-by-step process, from preprocessing the image to drawing the detected rectangles. Furthermore, the article highlights crucial considerations such as parameter tuning, potential optimizations, handling complexities like overlapping rectangles and perspective distortion, and alternative approaches like contour detection, template matching, and machine learning. By exploring these aspects, developers can choose the most suitable method for their specific rectangle detection needs and enhance the accuracy and efficiency of their computer vision applications.

References

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