A Generic Approach to Detect Edges, Corners and Junctions Simultaneously

1
A Generic Approach to Detect Edges, Corners and
Junctions Simultaneously

• Jiqiang Song
• The Chinese University of Hong Kong

2
Related work

• Low-level image features
• 1-D feature edge
• 2-D features corner, junction
• Edge detection surface model
• Gradient-based Sobel
• Derivative-based Canny, Zero-crossing, LoG
• Surface fitting
• Corner junction detection
• Edge-based
• Template-matching

3
Related work (contd)

• Two new models based on the statistic color
  distribution in a circular neighborhood
• SUSAN detector "USAN" principle.
• Handle edge, corner, and junction.
• Cannot handle textures.
• Compass operator color distributions of two
  parts.
• Handle edge, corner, and "Y"-junction in
  different passes.
• Using a group of colors to handle textures.
• Corner detection is very time-consuming.

4
Problems

• Existing methods have at least one of the
  following
• four disadvantages
• Requiring different passes or methods to detect
  edges, corners and junctions
• Unable to handle textured regions
• Unable to detect the boundary direction of
  corners and junctions
• Holding an assumption on the junction shape.

5
Our solutions

• Our objectives
• detect edges, corners, and junctions
  simultaneously
• handle textures
• detect free-shaped corners and junctions as well
  as their boundary directions.
• We emphasize
• the circular neighborhood to ensure the isotropy
• the statistic color distribution
• the spatial color distribution.

6
Generic neighborhood model

• NB(P) the circular neighborhood of any pixel P,
  NB(P) Sectori i1..n
• The sectors satisfy the following two conditions
  
• The global optimization conditions
• Each sector is of the most homogeneous color
  distribution inside
• Every two adjacent sectors are of the most
  significant difference in color distribution.

7
Pixel type classification

• After getting the best-divided sectors, the type
  of P can be classified according to the number
  and relationship of the sectors.

Table 1. Classification criteria of the pixel
type based on the best-divided sectors
8
Our detection approach

• A straightforward way design a proper function
  to represent the global optimization condition
  and then maximize/minimize it to get the best
  solution.
• Unknown number of variables
• Time-consuming
• Since this problem is similar to segmenting the
  neighborhood into several regions, the
  splitting-and-merging scheme is applied in our
  algorithm.

9
Step 1 Splitting

• NB(P) is split equally into n slices.
• n is even and is constrained by two conditions
  area condition and granularity condition.
• After n is determined, NB(P) is split as follows
• NB(P) Slicei i1..n (i-1)?? ? ?i lt
  i??, where ?i is the central angle subtended by
  Slicei

10
Step 2 Color distribution feature

• CDFi
• The color distribution feature of Slicei.
• Chosen according to the application demand.
• Dist(CDFi, CDFj)
• to calculate the distance between two CDFs, which
  returns a real number between 0,1.

11
Step 3 Integrated slice distance

• Adjacent Slice Distance (ASD)
• ASDi Dist( CDFi, CDFNext(i) )
• Global Slice Distance (GSD)
• GSDi Dist( CDFi, CDFmin_inx )
• Relative GSD (RGSD)
• Integrated Slice Distance (ISD)
• ISDi MAX(ASDi, RGSDi)

12
Step 4 Boundary detection

• If a point in the ISD profile ? Td, it is called
  a peak.
• A peak ? a boundary slice.
• The conditions for one boundary slice ? one peak
  
• Each region covers at least two slices, where
  "cover" means the pixels of this region occupies
  more than 90 area of a slice.
• The real boundary of two regions is near the
  border of the boundary slice.

13
Step 4 (contd)

• Combinations of "Yes" or "No" responses to the
  two conditions indicate four typical cases.
• Real Sector Strength (RSS) discriminate between
  Case 2 and Case 3.
• RSS Dist (2?CDFk, CDFPrev(k)CDFNext(k)).

14
Step 4 (contd)

• The final number of boundary slices is
• 0 "Plain" type,
• 2 "Edge" or "Corner" type
• more than 2 "Junction" type
• If it is "Plain" type, all the following steps
  are skipped. Otherwise, the best-divided sectors
  are formed by merging the slices between every
  two adjacent boundary slices.

15
Step 5 False junction elimination

• Junction strength
• Edge (or corner) strength

Strength MAX Dk(g1, g2), if MIN Sk(g1),
Sk(g2) gt Th , k1,2,..,.
16
Step 6 Boundary refinement

• A boundary Slicei ? the real boundary is within
  Slicei
• The real boundary is between the bisectors of
  Slicei and SliceNext(i), i.e., x??1, ?2.
• DR changes monotonously when x moves from ?1 to
  ?2.

17
Step 7 Classification

• With the best-divided sectors and their accurate
  boundaries, edges, corners and junctions are
  classified clearly according to the criteria
  listed in Table 1.
• With the accurate boundary information, the edge
  strength and the corner strength as follows

18
Step 8 Localization

• Directional non-maximal suppression
• to localize edges and to eliminate false corners.
  
• Regional non-maximal suppression
• to localize both corners and junctions.
• Integrity verification.
• to match the branches of corners and junctions
  with edges.
• to eliminate false junctions.

19
Implementation techniques

• Weighting the circular neighborhood.
• Rayleigh distribution with a central hole.
• CDF is represented by the Color Signature.
• (x1,v1), (x2,v2),..., (xn,vn), where vi is a
  vector in a color space to which the weight xi is
  assigned.
• Dist(CDFi, CDFj) is calculated by the Earth
  Mover's Distance (EMD).
• The saturating distance between two colors (vi
  and vj) is calculated by distij 1 - exp-Eij
  /14.

20
Experimental results

• Our experiments focus on the localization
  accuracy, the boundary accuracy, the ability of
  detecting the junctions with many boundaries, the
  ability of handling textured regions, and the
  speed.

21
Experimental results (contd)
22
Experimental results (contd)
23
Experimental results (contd)

• Table 2 shows their processing time (in seconds)
  on a 512?512 real image with different ?.
• for Compass operator and our detector, the radius
  of circular neighborhood is 3??,
• for SUSAN detector, the radius is ?.

24
Conclusions

• Solved the problem of detecting edges, corners
  and junctions from color images simultaneously,
  while handling textured regions.
• A generic neighborhood model to classify edges,
  corners and junctions clearly by their color
  distributions.
• A low-level feature detection approach which is
  the first one with all the following four
  capabilities
• detecting edges, corners and junctions in the
  same pass
• handling both uniform-colored regions and
  textured regions
• able to detect free-shaped corners and junctions
  
• producing the accurate boundary direction for
  corners and junctions.