2.1.1

Skew Correction.

The text lines of Tibetan historical documents are arranged horizontally and distributed in parallel, so the standard variance of the one-dimensional array obtained by horizontal projection is certain to be the largest. On the contrary, when the document image is tilted, the standard variance of the array obtained by horizontal projection will decrease. Based on the above analysis, the calculation of the document tilt Angle is equivalent to determining the maximum variance of the document projection at different rotation angles.

Generally, the tilt angle of Tibetan historical document images is small. Thus, the oblique angle of the document image is determined in the range of minus 5 degrees to plus 5 degrees by two decimal places. Rotate the document image by different angles, and then calculate the variance of the one-dimensional array obtained by horizontal projection. The angle corresponding to the maximum variance is the tilt correction angle of the document image.

2.1.2

Estimation of Character.

Stroke width (SW) is an important parameter in document analysis. Calculation of stroke width is shown in equation (1):

where, W and H represent the width and height of the image, I is the document image, and I_SK is the foreground skeleton of the document image.

The width of the Character also needs to be estimated. The calculation formula of Average Character width (ACW) is shown in equation (2):

where, CCW_i is the width of the ith connected component in the document image, n is the number of connected components whose width is greater than 2 times SW.

2.1.3

The Number of Text Lines.

The number of text lines in the document image is determined by foreground horizontal projection method. The peak number of foreground horizontal projection in the local area is equal to the number of text lines, denoted as TLNum, and the position of the peak point of horizontal projection is recorded as Ppos. The blue histogram in Figure 3 shows the horizontal projection result, and the red line shows the baseline location of the horizontal projection in Figure 3.

Figure 3.

Document image overall projection.

2.2.1

Upper Edge Detection.

A morphological open operation is used to obtain the horizontal component of characters. The morphological operator is defined as a rectangle with SW as its height and SW as its width twice. The horizontal component is shown in Figure 4. A gradient operator is used to obtain the gradient of the horizontal component in the vertical direction, where the gradient of the upper edge is positive and the gradient of the lower edge is negative. The upper edge of the character is obtained by preserving all pixels with a positive gradient, as shown in red part in Figure 5.

Figure 4.

Horizontal component of characters.

Figure 5.

Upper edge local connection.

2.2.2

Local Connection.

The upper edge is locally connected to form a longer baseline. The rules for connecting the upper edge lines are as follows: for each upper edge, subsequent edge lines are selected by calculating horizontal and vertical distances and then connected to get longer baselines. The horizontal distance of the upper edge is defined as equation (3):

where, x_A and x_B represent the column coordinates of edges A and B, as shown in Figure 6a. Because Tibetan syllables usually consist of no more than 4 characters, the horizontal distance threshold is set to 4 times the ACW.

Figure 6.

The horizontal and vertical distances between the upper edges.

The vertical distance between upper edge line segments is shown in equation (4), the threshold value of vertical distance is 2 times of SW.

where, Y_{A_right} and у_{B_left} represent the row coordinates of the right endpoint of edge A and the left endpoint of edge B, as shown in Figure 6b.

After the upper edge is connected locally, the short upper edges form a long baseline, as shown in Figure 5. The green line is the connecting line between the upper edges.

2.3.1

Baseline Group.

Baselines are clustered according to row coordinates, and seeds are the baseline positions obtained by horizontal projection. By clustering, baselines belonging to the same text line are marked. The number of document image text lines has been confirmed by horizontal projection, and the baseline is divided into TLNum sets, denoted as BaselineSets. Each set contains one or more elements, and each element is a baseline. Grouping results of baselines are shown in Figure 7a, different colors represent different sets.

Figure 7.

Baseline groups and text line baselines.

The baselines in each set are analyzed to find the line pairs that are mutually exclusive. The line pairs that are mutually exclusive cannot be in the baseline combination at the same time. If the horizontal distance from line A to line B is negative, that is, the two lines overlap vertically, then line A and B are mutually exclusive.

Finally, the baselines in the same set are arranged. According to the mutual exclusion of baselines, the permutations with mutual exclusion are excluded and only reasonable line combinations are retained.

2.3.2

Baseline Combination Evaluation.

A reasonable baseline should have three characteristics: the longest length of the baseline, the highest number of pixels where the baseline intersects the foreground character, and the lowest horizontal fluctuation of the baseline. Therefore, the following three parameters are given to evaluate the baseline combination:

(1) Baseline Maximum Length (ML): the Maximum Length that can be reached after all lines are connected in a combination, as shown in equation (5):

where, y_{BLgroup_k} represents the column coordinates of all baseline segments in the Kth baseline combination.

(2) Crossed pixels between baseline and character: the number of Crossed pixels between baseline and character foreground in baseline combination is shown in equation (6):

where, x _{BLgmup_k} , y _{BLgroup_k} represent the row and column coordinates of all lines in the Kth baseline combination.

(3) Horizontal Fluctuation Ratio (HFR) of baseline: the Fluctuation degree of baseline combination in the Horizontal direction, as shown in equation (7):

where, x_L represents the row coordinates of the L baseline in the baseline combination.

After obtaining the three parameters of each combination connection, the baseline combination is evaluated, and the evaluation function is shown in equation (8):

where, LenMax represents the maximum length of text line in the current document image, that is, the maximum horizontal distance of the document foreground character, and ε is a small positive number to prevent the occurrence of denominator 0.

The combination with the highest score is selected, and the baselines in the combination are connected from left to right to get the baseline of the text line. Baselines of text line are shown in Figure 7b, where different colors represent different baselines.

3.2.1

Evaluation Indicators.

In order to evaluate the results of baseline detection, the deviation distance of baseline (DDb) is proposed, as shown in equation (9):

where, DDb_L represents the deviation distance of baseline L, n represents the length of baseline, y_Li represents the abscissa of the ith point in baseline L detected by the algorithm, and у_MLi represents the abscissa of the corresponding pixel point in the data set.

If the deviation between the detected baseline and the labeled baseline is less than the Vertical Distance threshold (VDT), the current baseline detection result is considered correct.

Let N is the total number of baselines in the data set, and M is the number of correct Detection results. The definition of Base line Detection Accuracy (BDA) is shown in equation (10).

Table 1 shows the accuracy of the baseline detection method proposed at different vertical distance thresholds.

Table 1.

The BDA of the method proposed.

3.2.2

Comparison with Other Methods.

The horizontal projection⁵, piecewise projection⁷, local connection⁸ methods and the proposed method were tested on data sets. DDb was taken as the evaluation index, and VDT was set to 3. Table 2 lists the indicators of different baseline detection algorithms.

Table 2.

The algorithm comparison results.

Table 2 shows the performance of the proposed method and others. Compared with other methods, the method proposed in this paper is superior to other methods in the evaluation index. It shows that the proposed method can well adapt to the distribution of text lines in Tibetan historical documents and can effectively overcome the distortion of text lines and extract the accurate baseline of text lines.