Image Representation & Description

1. Introduction

• Course: CoE4TN4 Image Processing
• Chapter: 11 - Image Representation & Description
• Institution: McMaster University

2. Image Representation & Description: Basics

• After segmentation, regions are represented and described in a form suitable for computer processing using descriptors.
• Representing a Region:
  1. External Characteristics: Focus on the boundary. Example: Length of the boundary.
  2. Internal Characteristics: Focus on properties like color and texture.
• Goal: Descriptors should ideally be insensitive to rotation and translation.

3. Chain Code

• Definition: Represents a boundary by a connected sequence of straight-line segments.

• Uses either 4 or 8 connectivity.

• Method:

  1. Follow the boundary (e.g., clockwise).
  2. Assign a direction code to each segment connecting pixel pairs.

• Direction Codes (Mermaid Diagram):

Exp: 003333232212111001

• Problems:

  • Dependent on the starting point.
  • Changes with rotation.

• Solutions:

  1. Circular Sequence: Treat the chain code as circular; find the minimum magnitude representation.
  2. First Difference: Count counterclockwise the number of direction changes between adjacent elements.
     • take difference between two consecutive direction number (the latter - the former), and if it is negative, add 4.
  • Example, chain code: $10103322$
  • First difference code: $33133030$

• Shape Number: is the first difference of smallest magnitude.

4. Signature

• Definition: A 1-D functional representation of a boundary.

• Generation Methods:

  • Plot distance from centroid to boundary as a function of angle.

• Example Signatures:

• Other methods can also be used, such as by plotting the angle between the tangent to the boundary at a specific location and a reference line.

• Invariance:

  • Translation: Signatures are inherently invariant to translation.
  • Rotation: Choose a consistent starting point (e.g., farthest from centroid).
  • Scaling: Normalize to a specific range.

• Slope-Density Function: A histogram of tangent-angle values. Peaks correspond to straight segments.

6. Simple Boundary Descriptors

• Length: Number of pixels along the contour.
• Diameter: $Diam(B)=\max [D(p_i,p_j)]$, where $p_i$ and $p_j$ are points on the boundary.
• Curvature: Rate of change of slope. (For digital images, difference between slopes of adjacent segments).
• Major Axis: Straight line segment joining the two farthest points on the boundary.
• Minor Axis: Perpendicular to the major axis, forming a bounding box.
• Eccentricity: $\frac{\text{Major Axis}}{\text{Minor Axis}}$
• Basic Rectangle (Bounding Box): Rectangle formed by major and minor axes. chapter11 (1), p.16

7. Fourier Descriptor

• Given an N-point boundary represented by coordinates: $(x_0,y_0),(x_1,y_1),...,(x_{N-1},y_{N-1})$.

• Represent the boundary coordinates as a complex sequence: $s(k)=x_k+j{y}_k$

• Calculate N point DFT of s(k): $a(u)=\frac{1}{N}{\sum }_{k=0}^{N-1}s(k)\exp (-j2\pi uk/N)$

  • $a(u)$ are the Fourier Descriptors.

• By using P of the Fourier descriptors, we can find the following: $\hat{s}(k)={\sum }_{u=0}^{P-1}a(u)\exp (j2\pi uk/N)$

  • If $P<N⟹$ High frequency details of the boundary will be removed.

• Properties:

  • Not directly insensitive to translation, rotation, and scaling.
  • Magnitude of Fourier descriptors is insensitive to rotation.

8. Regional Descriptors

• Area: Number of pixels within a region.
• Compactness: $(\text{Perimeter}{)}^2/\text{Area}$
• Min/Max Gray Levels: Minimum and maximum pixel values in the region.
• Mean and Median Gray Levels: Average and median pixel values.