A Survey of Different Shape Analysis Techniques

1
A Survey of Different Shape Analysis Techniques

• -- Huang Nan

2
Abstract

• Shape analysis methods play an important role in
  the computer vision
• applications. It is used for object recognition,
  matching, registration and analysis
• This paper we will describe two major shape
  analysis categories, one is focus on the shape
  boundary (or contour) points and the other one is
  focus on the global (or interior) method.

3
Introduction

• Retrieving images by their contents, instead of
  by other characters, is more and more becoming a
  operation strategy.
• Two general methods for image comparison
• Intensity-based (color and texture)
• Geometry-based(shape)

4
Introduction

• Common criteria need to be followed when develop
  or evaluate the shape description algorithms
• Accessibility( cost of memory and running time)
• Scope (how many kinds of shapes can be represent)
• Uniqueness(result match to unique or multiple
  image)

5
Boundary Based Image Retrieval Algorithms

• Boundary scalar transform techniques
• Concept Use one-dimensional function to
  represent the two-dimensional shape boundary.
• ---The result is scaleable but not a graph, an
  image or other values which like the shape.

6
Boundary Based Image Retrieval Algorithms

• Algorithms
• Shape Centroid Select acentroid point of the
  shape, the values of the 1-D function are the
  distances between shape centroid point and
  boundary points. The boundary points are selected
  based on the criteria that the central angles are
  equal. (Refer to the Figure 1)

a4
a3
a2
a1
a0
0
Figure 1
7
Boundary Based Image Retrieval Algorithms

• Algorithms
• Arc Height Function
• An arc chord AB with a predefined length is
  insert on the boundary.
• A vertical line OC is cross the arc chord and
  separate AB to two same length parts. AB also
  reach the boundary at point OC.
• The length of OC is called the arc height at
  position A. As the arc chord is moved along the
  curve, a mapping between arc length and arc
  height defined the AHF.

C
A
B
O
arc
8
Boundary Based Image Retrieval Algorithms

• Algorithms
• Turing Function Used a tangent angle versus arc
  length, the tangent angle at some point is
  measured relative to the tangent angle at the
  initial point.
• Line segmentationLine segments are obtained by
  partitioning the radial line form the center of
  the mass to the boundary point. Segments are
  partitioned into parts within the shape and parts
  outside the shape.

9
Boundary Based Image Retrieval Algorithms

• Boundary Space Domain Techniques
• Concept The Boundary space domain technique use
  shape boundary as input and produce the result as
  the format of graph or pictorial
• --- The result is a image, a graph, instead of
  scalar results

10
Boundary Based Image Retrieval Algorithms

• Algorithms
• Chain Code Developed by Freeman, an arbitrary
  boundary image is represented by a sequence of
  small vectors of unit length and limited set of
  possible directions.

2
1
3
0
4
5
6
7
11
Boundary Based Image Retrieval Algorithms

• Algorithms
• Chain Code

12
Boundary Based Image Retrieval Algorithms

• Algorithms
• Pairwise object recognition
• Use the consecutive edgepoints to define the line
  segments which organizing the shape boundary.
• Let each line segment be a reference line on its
  turn., then comparing the reference line to all
  other lines and calculate the relative angle ?
  between the reference line and each line, and the
  perpendicular minimum and maximum distance(dmin
  and dmax )
• The histogram values are increased by one on the
  indexes corresponding to the angle ? and the line
  segment from the dmin to dmax
• ---Used for the recognition of polygonal shapes

13
Boundary Based Image Retrieval Algorithms

• Algorithms
• Pairwise object recognition

Li
dmax
dmin
?
Lref
14
Boundary Based Image Retrieval Algorithms

• Other Algorithms
• Polygonal approximation Use the polygonal line
  to approximately representing the boundary image.
• Boundary Decomposition Estimate the
  orientational, scaling, and transnational data
  between the target image and model shape by using
  a small number of control points extracted from
  both shapes

15
Boundary Based Image Retrieval Algorithms

• Summary
• - The choice of the proper shape recognition
  method is always a compromise between recognition
  power and computational complexity
• Chain Code
• Fast to calculate and it needs only a small
  amount of space
• Can not preserve information on the exact shape
  of a boundary image
• Pairwise histogram
• Computationally heavy and it requires more memory
  space
• Polygonal approximation
• typically suitable for images which contain
  polygonal objects