Image Segmentation Techniques

Pattern Recognition - Segmentation

• Segmentation divides an image into segments or regions to simplify representation and enhance analysis.
• It identifies and isolates regions of interest (ROI) like objects and boundaries.

Edge-Based Segmentation

• This technique identifies objects or regions in an image by detecting edges.
• It finds boundaries with significant changes in intensity or color.

Concept of Edge-Based Segmentation

• Edges are locations in an image marked by significant pixel intensity changes due to variations in color, brightness, or texture.
• Edge detection identifies these locations using operators like the Sobel, Canny Edge Detector, and Prewitt Operator.
• Pixels within the same boundaries are grouped to segment the image.
• It separates them from other groups, highlighting edges to differentiate objects or regions.

Region-Based Segmentation

• It partitions images into regions with similar characteristics based on intensity, color, or texture for meaningful analysis.

Key Concepts in Region-Based Segmentation

• Homogeneity involves grouping pixels into regions sharing similar properties like pixel intensity, color, or texture.
• Connectivity assumes neighboring pixels within a region are connected, either 4-connected (cross pattern) or 8-connected (cross and diagonal pattern).

Region Growing

• Region growing is a method starting with a "seed" pixel and adding neighboring pixels with similar properties, like intensity or color, until no more can be added.

Mathematical Explanation of Region Growing

• Image: Image I is of size M x N, where each pixel I(x, y) has an intensity value.
• Seed Points: Set of seed points S = {s1, s2, ..., sk} are identified as starting points.
• Homogeneity Criteria
  • A pixel p = (xp, yp) is added to a region if it meets a condition relative to the seed point or growing region and R is the current region.
  • If R represents the current region and I(p) represents the intensity of a pixel p,
  • The homogeneity criterion can be defined as the absolute value of I(p) - I(s) less than or equal to T where I(s) is the intensity of the seed pixel and T is a threshold.
  • A criterion based on the region's mean intensity µR can be expressed as the absolute value of I(p) - µR, which should be less than or equal to T, where µR is the mean intensity of the pixels within region R. Algorithm
  • Initialize: Begin with seed points S, where each seed point initiates a region, and initialize a region list R = S.
  • Check Neighboring Pixels: For pixel p in region R, assess its 4-connected or 8-connected neighbors N(p).
  • Homogeneity Test: For each neighboring pixel q ∈ N(p), verify if it meets the homogeneity criterion: absolute value of (I(q) – µR) ≤ T.
  • If the condition stands, include q in region R and update the region's mean intensity using the formula.
  • Repeat: Continue the process of evaluating and incorporating neighboring pixels while the homogeneity condition is satisfied.
  • Termination: The algorithm concludes when no more pixels can be included in the region, resulting in a segmented region R that meets the homogeneity criteria.

Example for Region Growing Algorithms

• For a grayscale image, take a seed point s = (xs, ys), and assign its intensity I(s) as 120, setting a threshold T at 10.
• For a neighboring pixel q that has an intensity I(q) of 115: |I(q) – 120| = |115 – 120| = 5 ≤ 10.
• Since 5 ≤ 10, pixel q gets incorporated into the region.
• This process continues expanding until no more neighboring pixels can be included.

Region Splitting and Merging

• This technique treats the entire image as one region.
• The algorithm recursively splits the image into smaller regions based on a homogeneity criterion.
• Adjacent regions that meet a merging criterion are combined.
• This process repeats until no more splits or merges occur.

Mathematical Explanation of Region Splitting and Merging

• Image: An image I of size M×N and each pixel I(x, y) has an intensity value.
• Region: The whole image is initially considered a single region, R0 which is then split into regions and adjacent ones are merged that meet homogeneity standards.
• Homogeneity Criterion
• For each region Ri homogeneity is tested to decide if a split should occur with µi and σi signifying pixel intensities in region Ri.
  • A region Ri is homogenous if σi ≤ T where T is a threshold.
    • If the standard deviation σi is small (below the threshold), the region is homogeneous and should not be split.
    • A region is non-homogeneous and split because the standard deviation σi is above the defined threshold.
• Region Splitting
  • Quadtree Decomposition: The region splitting method is a quadtree decomposition that splits each region into quadrants if it does not meet the split homogeneity criterion.
  • Starting with the entire image R0, the area is split into quadrants denoted as R1, R2, R3, R4.
  • Homogeneity is assessed for each quadrant.
• For a quadrant that is inhomogeneous, it is split into smaller regions recursively.
  • Mathematically, the splitting can be denoted by Split Ri into {Ri1, Ri2, Ri3, Ri4} if σi > T,
  • Subregions are expressed by Rij when Ri gets split.
• Region Merging
  • Adjoining areas are merged after the split when they fulfill the combined homogeneity standard.
• Two regions Ri and Rj go into a combined region Rij if: σίj ≤T; σij signifies standard deviation of the region Rij.
• The mean intensity of the merged region denoted as µij is: µij = (|Ri|· µi + |Rj|·μj)/ (|Ri|+|Rj|) with ∣Ri∣ and ∣Rj∣ stating counts pertaining pixels in Ri and Rj sections.

Explanation of Variables

• I(x, y): represents the illumination (or color) value at point (x, y) in the image.
• M,N: image dimensions (number of rows and columns).
• R0: the total area dedicated to an image at its inception.
• Ri: area segment coming directly off the source image.
• µi: average illumination degree with respect to a regional area.
• σi: measures the dispersal of assigned values across that section's data.
• T: represents the tolerance level defining limits before changing homogenization methods.

Algorithm

• Step 1: Initialize: Define an images initial state is set by identifying a region.
• Step 2: Splitting: Splitting processes take place across quadtree based partitions to keep homogeneity at its maximum value.
• Step 3: Merging: Merging sees adjacent segments grouped together if that provides the region with homogeneous continuity.
• Step 4: Repeat: Perform further splitting or merging until operations are exhausted as much as practically permissible.

Example

• Start with a grayscale image using the whole picture segment and presume 100 to be light intensity levels μ0 setting variance to set threshold limit at standard deviation of 30 σ0.
• Because 30 σ0, surpasses limit given by benchmark variance (T = 20) segment will be further partition down quadrants.
• In each of those segmented portions’ evaluations, one sees some segments lacking light intensity uniformity that requires further sectioning.

Thresholding

• Thresholding is the initial step in segmentation.
• Single value thresholding is mathematically represented as:
• g(x,y) = 1 if f(x, y) > T; or 0 if f(x, y) ≤ T

Basic Global Thresholding

• Based on the histogram of an image
• Partitions an image histogram using a single global threshold.
• The success depends on how well the histogram can be partitioned.
• The histogram has distinct and well-defined peaks and global thresholding works exceptionally well, such as images with high contrast between the foreground and background.
• If the histogram has overlapping distributions (unclear intensity gradients), global thresholding has inaccurate segmentations.

Basic Global Thresholding Algorithm

• Calculates T
  • Select an initial estimate for T (typically the average grey level in the image).
  • Segment the image using T to produce two groups of pixels: G1 (grey levels >T) and G2 (grey levels ≤ T).
  • Compute the average grey levels of pixels in G1 to give µ1 and G2 to give µ2.
  • Compute a new threshold value T = µ1 + µ2/2.
  • Repeat steps 2 – 4 until the difference in T in successive iterations is less than a predefined limit very small T∞.
• This algorithm is effective thresholds when the histogram is suitable.

Applications of Segmentation

• Medical Imaging: segmenting organs, tumors, or lesions based like in MRI or CT scans.
• Object Detection: identifying and isolating objects within an image.
• Remote Sensing: segmenting land cover types like forests, water bodies, or urban areas in imagery.

Explore edge-based and region-based image segmentation methods. Understand Prewitt and Canny operators for edge detection. Learn about connectivity in region-based segmentation to enhance image analysis.