JPH02302880A - Method for matching outline graphic - Google Patents

Abstract

PURPOSE:To attain the matching of each partial outline at the optimum scale by using a segment of an upper scale corresponding to the plural segments of the lowermost scale also as an object to be matched by using hierarchical property of rugged segments. CONSTITUTION:Convolution operation with a Gaussian function having a different scale sigma in each outline graphic is executed while increasing the scale sigmain stages, the outline graphics are sequentially smoothed, the rugged structure of sequentially obtained smoothed graphics are matched and the rugged structure is expressed in stages by the multiplex scale relating to the scale sigma. Then the ruggedness at the optimum scales of respective partial outlines is matched so that the sum of differences is minimized. Consequently, the optimum combination out of the combinations of all rugged partial outlines can be efficiently found out in the multiplex scale expression relating to the scale sigma.

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical field to which the invention pertains] The present invention relates to a method for matching contour figures obtained by tracing the contours of a silhouette image or the like.

[Prior Art] Conventionally, many methods have been proposed for pattern recognition, focusing on the uneven structure of the outline of a 07 figure and matching the figures. However, most of these only describe the uneven structure at one scale σ.

It is not possible to grasp the global structure and local structure of a figure at the same time, and it is therefore difficult to match two figures that are highly deformed.

On the other hand, the two contour figures are scaled σ (an example of scale is "
CMokhtari devised a multi-scale representation method that hierarchically describes the uneven structure of a figure by smoothing it with a Gaussian function (which can be considered as "dispersion").
an,, et, al, ”5ca1e,-bas
e,ddescription and recognition
ition of plan+ir curves,+
nd two dimensional 5hapes,
+IEEE Trans.

PAMI, Vol. PAMI-8, No. 1. pp
, 34-43 (, 1986)), several matching methods between two figures using the multi-scale representation have been proposed. □ [Problem to be solved by the invention] However, the conventional technology is very l'ff (method targeting 12 figures (Mokhtarian, e
t, al, +5cale-based descri
ption and recognition of ption and recognition
lanar curves and two dimes
nsional 5hapes,”IEE[!Tra
ns, PAMI, Vol, PAMI-8, No. 1
．． pp. 34-43 (1986)) or a method of matching from the big picture to the details (Sakawa et al., "Matching algorithm for deformed waveforms using multi-resolution", Transactions of the Institute of Electronics and Communication Engineers (D).

□ J-71-D, 11. pp, 1019-1022.
(1983-11)) However, none of these methods can be applied between figures with large uneven deformations and low reliability of global matching.

The present invention aims to solve the above-mentioned conventional problems. That is, the object of the present invention is to provide a method for efficiently finding an optimal set from among all combinations of uneven partial contours in multi-scale representation regarding σ.

[Means for Solving the Problems] In the present invention, attention is paid to the uneven segments of two contour figures, and the unevenness matching between the two figures is determined by the lowest scale σ of each.
. ,σ°. Concave (convex) segment (al”' + l
=1.2. ”'+ N+ tlJ(0' + j=
1+L''+M) is the basic unit.The subscript I+j is the order of the segments obtained by tracing the outline from a certain starting point segment while looking inside the figure with your left hand, because it is a closed figure.

a, +01 and a, to+, b, 4to+
It goes without saying that and (0) are adjacent to each other.

Now, if we focus on one contour figure, in multi-scale representation, the adjacent odd number of segments are 1 in the upper scale.
may correspond to one segment. The present invention does not match only the above ai (01, bjl), but also uses the hierarchical nature of uneven segments to match one segment of an upper scale corresponding to multiple segments of the lowest scale. The main feature is that. At this time,
The degree of dissimilarity of concave and convex segments on multiple scales is expressed by the formula fl)
Defined by

d(j(0), n, j(01:m)=d(i”'
, j(V) ) 10e(i10' : n)+e(j
”': m) (Formula 11 + 11 is 2
The lowest scale σ of the figure. ,σ゛. each (2n
+1) segments (a 1-2n ”ゝ.

a 1-2n+I ”' + ”'+ ' ” i ”
) and (2m+1) segments (b J-
1m (O' + b J-Zi,, (0),...
.

bJ′. represents the degree of dissimilarity of many-to-many segments with l). 5-2. (01, etc. refers to the 2nth segment when tracing from a, ++1+ in the opposite direction to the above tracing direction.The first term on the right side of the equation (1+ is the upper scale σ corresponding to each multiple segment, σ, It is the degree of difference between segments of 1 to 1 at , and is given by (2) using the rotation angle θ from the start point to the end point of the segment and the contribution A/L to the peripheral length (L). still.

In equation (2), the subscript representing the scale is omitted.

The second term on the right side of equation (1) is the cost of replacing the above multiple segments with one segment at the higher scale,
It is given by equation (3) as the sum of the dissimilarities of adjacent segments. The same applies to the third term on the right side of equation (1). In addition, when n or m is O in Formula 1 (1), u.

■ is each O.

d(i,j)=(lθi−θj 1barθ1)θj))*
l Q i/L, -j2j/Lal
(2) e(i (01:n)= Then, the set of uneven segments (inn, J: m
) is obtained from all combinations, and the unevenness is matched on an optimal scale for each partial contour, which is different from the conventional technology.

G - [Embodiment] Fig. 1 is a diagram showing the configuration of an embodiment of the present invention, in which 1 is a concave-convex structure matching processing unit for the same figure, and 2 is a concave-convex structure matching unit between two figures, which is the core of the present invention. This is the processing section.

The concavo-convex structure matching processing unit 1 for the same figure can be realized using the technique disclosed in "Method for matching concave-convex structures of closed curves", Japanese Patent Application No. 1-56182. Fig. 2 shows the process for matching concave-convex structures for the same figure. This figure shows an example of the processing result of part 1. The black dots in figure 1 are inflection points, and the matching results are shown by a group of line segments connecting two inflection points. The smoothed figure is translated in parallel.

The unevenness matching processing unit 2 between the two figures uses the dynamic programming method to perform the following steps (steps 1 to 8).
This can be achieved by

First, concave (convex) segments I/group □ between adjacent inflection points in the lowest scale in multi-scale representation are expressed below for figures A and B, respectively.

A = (a i ”l l i =112.・IN)
(4) B= (b; (0' l
j・1,2. ..., M)
(5) In the following, the subscript tel indicating the lowest scale will be omitted to avoid confusion. MX
Two 2-dimensional tables (arrays) of N (g(i+jLT(
LD), and 2MXNX2 3D table (array)
Prepare one (L (i, 3.2)) and perform the following procedure. In the following procedure, executing an expression means assigning the value on the right side to the left side.

(Step 1) If the polarity (concave or convex) of al and are the same,
Set C to 0, otherwise set to 1.

(Step 2) j-c+2+c+4+c+ y7・+2(M-1)+c
Execute equations (6) and (7) for .

g (0,j)=O(6) T(9,J)=? l
(7) (Step 3) Execute equation (8) for i=2-c, 4-c, -, (N-2)-c.

T(i,0)=O(8) (Step 4) i・1,2. ..., execute step 5 for N.

(Step 5) If i is an odd number, set C to 0. Otherwise, let C′ be 1,
j=1+c+c'+ 3+c+c', ・, 2M-
Execute step 6 for 1+c+c'.

(Step 6) Execute equations (9), 03), 04).

g(i,j)=min (g(i-(2n+1),j-
(2m+1))l + d(i:n,j:m)nkoRn
, IIICRIll Here, the sets Rn and Rm are given by 2〇OL (11).

Rn=(nll≦n≦[(i-1＞/2] V
Go) Rm=(mll≦m≦min ([(j-1)
/2 ].

[T(i-(2n+1), j-(2m+1))] )
jl (If) [] represents a Gaussian symbol.

T(i,j)=T(i-(2n"+1), j-(2
m" +1)) - (2m" +1) (12)L (i
, j, 0) = i − (2n” +1)
θ3)L(i, j, 1)=j −(2m”
+1) θ brown where n", m" is n that minimizes the right side of equation (9)
, is the value of m.

(Step 7) Execute equation aω for j=2+c, 4+c+kawa, 2M-24cj"=argmin (g(N,j)l
05) (Step 8) L (i, j, 0), L (i, j, 1) obtained in Step 5
) and 2. By tracing back L from jl obtained in step 6, the optimal alignment of the concavo-convex segments is found.

□ The variables c and c' in the above procedure are used to prevent segments with different polarities (concave or convex) from being candidates for correspondence. And T (i.

j) such that there are no duplicate matches of segments (i.

gives the maximum value of the difference of j that can be transitioned from j). Also,
L is a value in a table that stores partial optimal correspondences.

For example, when two contour figures 101 and 102 are given as shown in FIGS. 3A and 3B, respectively, uneven structure matching processing unit 1 and the unevenness matching between the two figures in the same figure shown in FIG. When processing is performed by the processing section 2, the matching result shown by the straight line in FIG. 3 is obtained. In FIG. 3, both end points of the matched partial contours are connected with a straight line.

〔Effect of the invention〕

According to the present invention, matching at an optimal scale can be realized for each partial contour. In other words, microscopic matching can be achieved for very similar partial contours, and more macroscopic matching is possible for partial contours that are not very similar by 1 m.
It can be a useful tool for figure recognition, etc. It should be noted that conventional matching methods using multi-scale representations cannot deal with shapes with large uneven deformations and low reliability of global matching.

[Brief explanation of drawings]

FIG. 1 is a diagram showing the configuration of an embodiment of the present invention. FIG. 2 is an example of the processing results of the concavo-convex structure matching processing unit for the same figure. FIG. 3 is an example of the result of processing performed in the unevenness matching processing section between two figures. 1... Concave and convex structure matching processing unit for the same figure. 2... Concave/convex matching processing section between two figures. Figure 1 (A) (B) 3rd

Claims (1)

[Claims] A method for matching contour figures consisting of two arbitrary closed curves, in which a convolution operation with a Gaussian function having a different scale σ is performed for each contour figure while increasing σ stepwise. and a first process of sequentially smoothing the contour figure and at the same time matching the uneven structure between the sequentially obtained smoothed figures and hierarchically expressing the uneven structure on multiple scales with respect to σ; In the hierarchical uneven structure representation regarding σ in each obtained contour figure, the degree of dissimilarity is calculated from the rotation angle of the partial contour consisting of concave segments or convex segments and the degree of contribution to the perimeter length, and the sum of the degrees of dissimilarity is the minimum. and a second step of matching the unevenness at an optimal scale for each partial contour so that the contour figures match.