Matching Phase - Multi-plane Region Matching and Assembling Process

Chapter 3. Multi-plane Segmentation Approach for Complex Document Images

3.3 Multi-plane Region Matching and Assembling Process

3.3.2 Matching Phase

In the matching phase, each of the unclassified SRs in the Pool is respectively compared their connectedness and similarity with the already existing planes, to determine its best belonging plane. For this purpose, we employ two forms of "matching grades", the single-link matching grade, and the centroid-link matching grade, to evaluate their related connectedness and similarity. The single-link matching grade examines the degree of connectedness between a pair of two neighboring SRs, an unclassified SR and its neighboring classified SRs that already have belonging planes; while the centroid-link matching grade represents the degree of similarity between an unclassified SR and an already existing plane. Then the two matching grades are combined to provide an effective criterion to determine the best belonging plane for this unclassified SR among the existing planes. If an unclassified SR can obtain its best belonging plane during the current matching phase recursion, i.e. this SR reflects sufficient similarity and connectedness with one of the existing planes after examining their mutual matching grade, then this SR is classified and assembled into this best belonging plane and removed from the Pool afterward; otherwise, if there is no suitable

matching plane for an unclassified SR at this time, then this SR will remain in the Pool. Since new potential planes will be created in the following recursion of the plane constructing phase, SRs which cannot find matching planes in the current matching phase recursion will be re-analyzed in subsequent recursions until their best matching planes are determined.

The single-link matching grade is utilized for examining the degree of connectedness between an unclassified SR^{i j k}^{, ,} and an already existent plane in a local manner. It is determined by applying a connectedness measure on SR^{i j k}^{, ,} and its 4-adjacent SRs already belonging to this existent plane. To facilitate the computation of the single-link matching grade, two measures for evaluating the continuity and similarity between two 4-adjacent SRs – the side-match measure, denoted as DSM, and the region dissimilarity DRM, as computed using Eq. (3.8), are employed. Then both DSM and DRM measures are jointly considered to determine the single-link matching grade of a pair of two 4-adjacent SRs.

The side-match measure - DSM, which reveals the dissimilarity of the touching boundary between the two 4-adjacent SRs, is described as follows. Suppose that two SRs are 4-adjacent, they may have one of the two types of touching boundaries: 1) a vertical touching boundary mutually shared by two horizontally adjacent SRs, or 2) a horizontal boundary shared by two vertically adjacent SRs. For a pair of two horizontally adjacent SRs –SR^{i j k}¹^{, ,}¹ ¹ on the left, and

2, ,2 2

i j k

SR on the right, the pixel values on the rightmost side of SR^{i j k}¹^{, ,}¹ ¹ and the leftmost side of SR^{i j k}²^{, ,}² ² can be described as: g SR( ^{i j k}¹^{, ,}¹ ¹,M - y_H 1, ) and g SR( ^{i j k}²^{, ,}² ²,0, )y , respectively.

The sets of object pixels on the rightmost side and the leftmost side of an SR, denoted by (SR^{i j k}, , )

To facilitate the following descriptions of the side-match features, the denotations of SR^{i j k}¹^{, ,}¹ ¹ and SR^{i j k}²^{, ,}² ²are simplified as SR^l and SR^r, respectively. The vertical touching boundary of

SRl and SR^r, denoted as VB(SR SR^l, ^r), is represented by a set of side connections formed by pairs of object pixels that are symmetrically connected on their associated rightmost and leftmost sides, and is defined as follows,

( )

as SR^t and SR^b, respectively), their horizontal touching boundary can be represented as,

( )

and SR^b, respectively, and are defined as,

{ }

, , , , , , , ,

(SR^{i j k})= g SR( ^{i j k}, ,x M_v−1) g SR( ^{i j k}, ,x M_v− ∈1) (SR^{i j k}), and 0≤ ≤x M_H −1

BS OP ,

and ^TS⁽^SR^{i j k}^{, ,} ⁾⁼

{

^{g SR}⁽ ^{i j k}^{, ,} ^{, ,0)}^x ^{g SR}⁽ ^{i j k}^{, ,} ^{, ,0)}^x ^∈^OP⁽^SR^{i j k}^{, ,} ^{), and 0}^{≤ ≤}^{x M}^H ⁻¹

}

Also, the number of side connections of the touching boundary, i.e. the amount of connected pixel pairs in VB(SR^{i j k}^{1 1 1}^{, ,} ,SR^{i j k}²^{, ,}² ²) or HB(SR^{i j k}^{1 1 1}^{, ,} ,SR^{i j k}²^{, ,}² ²), should also be considered for the connectedness of the two 4-adjacent SRs, and is denoted by N SR_sc( ^{i j k}^{1 1 1}^{, ,} ,SR^{i j k}²^{, ,}² ²). Therefore, based on the above-mentioned side-match features of two 4-adjacent SRs, the side-match measure, DSM, of them when they are horizontally adjacent and vertically adjacent can be respectively computed as,

( ⁽ ^, ^{1, ), (} ^{,0, )}) ⁽ ^, ⁾ ⁽ ^, ^{1, )} ⁽ ^{,0, )} sufficiently low, then these two SRs are homogeneous with each other, and should belong to the same object plane P^.

Accordingly, the DSM measure can reflect the continuity of two 4-adjacent SRs, and the DRM value, as obtained by Eq. (3.8), assesses the similarity between them. Hence the homogeneity and connectedness of two 4-adjacent SRs can be evaluated by considering the dominant effect of the DSM and the DRM values. Therefore, based on the above definitions, the single-link matching grade of two 4-adjacent SRs, denoted by m_s, is determined as,

( )

(3.14) serves as the normalization factor. Besides, it must be noted that the DSM measure becomes invalid when N SR_sc( ^{i j k}^{1 1 1}^{, ,} ,SR^{i j k}²^{, ,}² ²) 0= . Therefore, in the determination of the single-link matching grade in Eq. (3.14), the DSM can be disabled by setting the DSM to zero using the “max” operation, so as to allow the DRM having the dominant effect.

Next, we describe the centroid-link matching grade to assess the degree of similarity between SR^{i j k}^{, ,} and an already existing plane _P_q in a global manner. Let μ( )P_q and

2( )_q

σ _P denote the mean and variance of the existing plane P , respectively, and they are _q given by,

( )

The above-mentioned two matching grades are then combined to form a composite matching grade, denoted by M(SR^{i j k}^{, ,} , )P_q , to complimentarily evaluate the degree of connectedness and similarity of an unclassified SR and an already existing plane in both local and global manners. As a result, this composite matching grade can provide a more effective criterion for determining the best belonging plane for each of the unclassified SRs.

Accordingly, in each recursion of the matching phase, each of the unclassified SRs, i.e.

, , i j k

SR in the Pool, is analyzed by evaluating the composite matching grade of SR^{i j k}^{, ,} associated with each of its neighboring existent planes _P_q, to seek for the best matching plane into which SR^{i j k}^{, ,} should be grouped.

Since the evaluating process of the composite matching grades of SR^{i j k}^{, ,} is performed on its neighboring planes, a plane _P_q must have at least one of its own SRs 4-adjacent to

, ,

(SR^{i j k}, , , )P_q

where w_c and w_s are the weighting factors to control the weighted contributions of the centroid-linkage and single-linkage strengths of the composite matching grade, respectively, and w_c +w_s=1. By applying the weighting factors w_c and w_s in the composite matching grade, the centroid-linkage and single-linkage can be combined by taking advantage of their related strengths. Because textual regions mostly reveal obvious spatial connectedness, we reasonably strengthen the single-linkage weight of the composite matching grade, and thus the values of the weighting factors are chosen as w_c =0.45 and w_s =0.55, respectively.

Besides, if SR^{i j k}^{, ,} has no neighboring SR s_q in _P_q, i.e. AS(SR^{i j k}^{, ,} , )P_q =φ, then _P_q is excluded from the consideration for matching with SR^{i j k}^{, ,} , that is, the evaluation process of their composite matching grade is skipped.

As a result, the best candidate belonging plane for SR^{i j k}^{, ,} , i.e. the plane having the lowest composite matching grade associated with SR^{i j k}^{, ,} among all existing planes, denoted by P , can be determined by, _m

If the determined value of M(SR^{i j k}^{, ,} ,P_m) is too large, SR^{i j k}^{, ,} is not likely to have sufficient connectedness and similarity to P . The following matching criterion is applied to _m check whether the currently selected candidate plane P and _m ^SR^{i j k}^{, ,} are sufficiently matched, and then the suitability of SR^{i j k}^{, ,} for belonging to P can be determined well. _m This matching criterion is defined as follows,

(SR ^{i j k}, , ,P_m)≤

τ

M (3.23)

where τ_m is a predefined threshold which represents the acceptable tolerance of dissimilarity for SR^{i j k}^{, ,} to be grouped into P . The matching criterion has a moderate effect _m on the number of resultant object planes, and the value choice of τ_m =1.2 is experimentally determined to obtain sufficiently distinct planes and avoid excessive splitting of planes.

Accordingly, if SR^{i j k}^{, ,} and its associated P satisfy the matching criterion, then _m

, , i j k

SR is merged into P , and removed from the Pool. If the matching criterion cannot be _m satisfied, this reflects that SR^{i j k}^{, ,} is distinct from all its existent adjoining planes, and there is no appropriate belonging plane for SR^{i j k}^{, ,} during this current matching phase recursion.

Therefore, SR^{i j k}^{, ,} will remain in the Pool, until its suitable matching plane emerges or it begins its own plane in the following recursions of the plane construction phase. After a belonging determination has been made for SR^{i j k}^{, ,} , the matching process is in turn applied on the subsequent unclassified SRs in the Pool, until all the rest unclassified SRs have been processed one time in the current matching phase recursion.

在文檔中影像處理與電腦視覺技術應用於複雜文件影像分析、夜間駕駛輔助、以及視訊監控系統之研究 (頁 88-95)