Edge Detection in Computer Vision

Edge Detection

• Edge recognition is a fundamental image processing concept for identifying boundaries between image regions.
• Line drawing recognition extracts structural outlines, simplifying images into object shapes.
• Image derivatives measure changes in pixel intensity.
• The first-order derivative detects rapid intensity changes, highlighting edges where the gradient is highest.
• The second-order derivative detects variations in the gradient, revealing finer edge details and transitions.
• Recognition using line drawings simplifies images to essential lines and edges, focusing on shape and structure.
• This technique is useful in applications such as sketch-based recognition and augmented reality.
• Edge detection involves steps:
  • Smoothing using a Gaussian filter to reduce noise and high-frequency variations.
  • Calculating derivatives (gradients) to measure intensity change rates and highlight regions with significant intensity variations.
  • Identifying maxima of the derivative (locations of the highest intensity change) which mark boundaries between image regions.
• Goals of edge detection include accurate edge identification, while minimizing noise and errors.

Goals of Edge Detection

• Accurate identification of significant intensity changes.
• Minimizing errors from noise or artifacts.
• Robust detection to differentiate between true edges and random noise.
• Precise location of edges where intensity change occurs.
• Single response; detecting each edge only once.

Edge Detection Issues

• Poor localization (shifted edges due to filtering or interference).
• Too many responses (multiple edge detections for a single edge).

1D Edge Detection Steps

• Analyzing intensity variations along a single image dimension (row or column) isolates boundaries or transitions. This method simplifies edge detection to a single dimension.
• Analyzing intensity profiles using derivatives or gradient-based methods detects peaks and troughs (representing edges).

Preprocessing the Image with Gaussian Smoothing

• Smoothing an intensity profile reduces noise and emphasizes significant intensity transitions for enhanced edge detection in one dimension.
• Gaussian smoothing reduces high-frequency components and noise in intensity profiles.
• Smoother curves are easier to analyze and highlight significant changes in intensity that represent edges or boundaries in images.

First Derivative (Gradient)

• Measures the rate of intensity change across the image.
• Quantifies pixel value changes.
• Large first derivative values indicate rapid intensity changes; marking edges.
• Gradient operators such as Sobel or Prewitt can compute the first derivative efficiently, enhancing boundary detection and emphasizing significant changes.

Second Derivative (Laplacian)

• Measures the rate at which the first derivative changes, revealing the curvature of the intensity profile.
• Identifying changes in the shape of the intensity curve is key; useful for locating edges or inflection points.
• Zero-crossing points, where the second derivative switches from positive to negative (or vice versa), represent peaks in the intensity profile; identifying fine edge details.
• Methods such as the Laplacian of Gaussian (LoG) filter enhance this, further improving edge localization.

Simplified Edge Detection

• Combination of smoothing and differentiation processes to identify edges in a single step, minimizing computational complexity.
• Derivative of Gaussian filter combines both operations, providing a single filter which smooths the image concurrently while detecting edges.

Hysteresis

• Technique for continuous edge detection, accounting for minor intensity fluctuations, creating robust edge detection.
• High threshold initializes an edge segment only when the gradient exceeds a certain value.
• Low threshold continues edge segments of points with gradients under the high threshold value but above the low threshold (to remain connected).

Color Recognition Advantages

• Consistent color representation under geometric transformations (translation, rotation, scaling).
• Local feature, defined at each pixel, highly localized, and resistant to partial object occlusion.

Color Histograms

• A distribution representation of colors in an image.
• Each pixel's (RGB) values are counted for each color channel (R, G, B).
• Histogram counts for each color channel indicates how many pixels have a specific color intensity.
• Luminance histograms provide brightness levels without considering color.
• Describe color distribution in images; compared against other histograms to identify similar objects or patterns.

3D Color Histograms

• More precise representations of color combinations by considering RGB values (Red, Green, and Blue) together.
• An entry in 3D space represents a color combination; the histogram count indicates how frequently that combination appears.

Color Normalization by Intensity

• Removes lighting/shading variation effects and standardizes color representation.
• Dividing each color component (R, G, B) by the total pixel intensity normalizes the colors; handles the variations of pixel color intensity due to lighting or shading differences which can give a different visual perception of the same color.

Recognition Using Histograms

• A method of identifying objects based on their color distributions.
• Histogram comparison step: compares a test image's color distribution with color distributions from known objects in a database to find the closest match.
• Multiple views per object: a database stores various views and lighting conditions for the same object; leading to enhanced object recognition accuracy.
• Histogram-based retrieval: retrieves objects with color histograms close to the query object's histogram, identifying similar objects.

Histogram Comparison Techniques

• Method for measuring similarities or differences between two histograms.
• Histogram intersection method: quantifies overlapping parts of two histograms to measure similarities.
• Euclidean distance: measures distances between corresponding bins in two histograms, focusing on absolute differences.
• Chi-Square distance: weighs bins' differences in proportion to their values; more sensitive to differences among bins.

Performance Evaluation

• Methods used to assess a model's performance in object recognition tasks.
• Accuracy: the proportion of correctly classified instances out of the total number of predictions.
• Precision: the measure that evaluates the accuracy of positive predictions.
• Recall: the measure that evaluates the ability to identify all positive instances or cases.
• F1 Score: balances Precision and Recall to create a more comprehensive measure.
• ROC/AUC (Receiver Operating Characteristic/Area Under the Curve): distinguishes between classes across various thresholds.