The multi-line straight text segmentation test is based on a straight text reference line. Straight text is defined by the skew angle β. Typical values of β that correspond to the handwritten text are those up to 20°. Hence, it takes values from the set {5°, 10°, 15°, 20°} [9]. Furthermore, between line spacing is set to a standard value to 20% of the standard character height [12]. This corresponds to single line spacing. Multi-line straight text samples are shown in Figure 2.

The multi-line waved text segmentation test is based on a waved text reference line. Waved text is defined by the parameter ɛ, defined by the expression ɛ = h/l, where h is height, and l is half-width of the waved reference line (See Figure 3). Typical values of ɛ that correspond to the previously chosen values of skew angle β are from the set {1/12, 1/6, 1/4, 1/3} [9]. Between line spacing is set to 20% of the standard character height [12]. The resolution of the text samples is 150 and 300 dpi. Multi-line waved text samples are shown in Figure 3.

The multi-line fractured text segmentation test is based on a fractured text reference line. Fractured text is defined by the fractured skew angle φ. Typical values of φ that correspond to handwritten text are those up to 20°. Hence, it has values picked from the set {5°, 10°, 15°, 20°} [9]. Furthermore, between line spacing is set to 20% of the standard character height [12]. Resolution of the text samples is 150 and 300 dpi. Multi-line fractured text samples are shown in Figure 4.

The multi-line handwritten text segmentation test is based on freestyle handwritten text samples in Serbian Latin, Cyrillic as well as in English scripts [10]. This is a small document text database. The total number of handwritten text samples is 220 text lines. These text samples contain variable skew lines, multi-oriented text as well as mutually inserted words from different text lines. For the sake of conformity, the documents body is the only one considered in the analysis of the text line segmentation. Resolution of the text samples is 150 and 300 dpi. A few handwritten text fragments from the text database are shown in Figure 5.

It is assumed that during text segmentation a reference sample text containing text objects, called connected-components, is processed by the algorithm. This process leads to a new text object configuration. In an ideal circumstance the number of newly arranged objects corresponds to the correct number of text lines. To make a valid algorithm evaluation the following text elements should be defined [10]:

Initial objects number O_init,

Initial objects O_init represents the starting number of objects in the reference sample text. It is calculated as the counted number of text objects in the starting sample text. After applying the algorithm to the sample text, the number of text objects is changed. Consequently, many text objects are mutually merged by the influence of the text segmentation algorithm. Currently, the number of text objects is given as the number of detected objects O_det. The task of the text segmentation algorithm is to segment text lines hitting or missing this number of lines. Hence, this number of real text lines should be represented as the target number in reference sample text. It is called reference number of objects O_ref. The algorithm efficiency is evaluated by comparing the reference and detected number of objects per each text line.

Text pixels belonging to the initial objects O_init representing the same text line i form the reference object O_ref for the line i. If the detected object O_det for line i is integral and contains objects O_init from the reference object O_ref for the line i as subset, then the number of text objects in a distinct text line will be equal to one, which leads to a correctly segmented text line. The number of correctly detected text lines in the sample text is marked as O_clindet. However, all others are defined as error. These circumstances are illustrated in Figure 6.

Segmentation errors are present in the following circumstances:

Over-segmentation detected text lines O_ovlindet (split lines error i.e., SLE [7]),

Split lines errors represent the text lines which are wrongly divided by the algorithm into two or more components, i.e., text objects. This circumstance is known as over-segmentation. The joined lines error corresponds to the situation where the sequence of n consecutive lines is considered by the algorithm as a unique line. In that case, and if no other error happens, it is considered that one line in the sequence is correct and the other n−1 lines of the group are erroneous [7]. This phenomenon is called under-segmentation. Lines including outlier words correspond to lines containing words that are incorrectly assigned to two adjacent lines.

The algorithm efficiency means the evaluation of the text line segmentation process made by investigated algorithm. If the number of detected objects is closer to the number of reference objects, then the algorithm is more efficient. To evaluate the algorithm’s efficiency the following elements are introduced:

Segmentation line hit rate, i.e., SLHR,

SLHR represents the ratio of the number of correctly segmented text lines over the total number of text lines in the reference sample text. It is defined as: (1) SLHR = 1 − | RE | = 1 − | O ref − O clindet O ref |

Over-segmentation phenomena lead to an increased number of objects per text line. Hence, the boundary growing area created by algorithm hasn’t been successful in merging all objects of the text line into one. As previously stated, the number of the over-segmented lines is marked as O_ovlindet. OSHLR represents the ratio of the number of over-segmented text lines over the total number of text lines in the reference sample text. It is defined as: (2) OSLHR = 1 − | RE | = 1 − | O ref − O ovlindet O ref |

The under-segmentation process leads to a smaller number of objects than the number of text lines. Hence, two or more consecutive text lines are considered as a unique one. USHLR represents the ratio of the number of under-segmented text lines over the total number of text lines in the reference sample text. It is defined as: (3) USLHR = 1 − | RE | = 1 − | O ref − O unlindet O ref |

The process of mutually injected objects from different text lines leads to mixed text lines. MLHR represents the ratio of the number of mixed text lines over the total number of text lines in the reference sample text. It is defined as: (4) MLHR = 1 − | RE | = 1 − | O ref − O mixlindet O ref |

At the end, the number of detected and reference text objects (per each text line) is compared. Hence, the number of reference text objects per line is equal to 1. The variance evaluation is given by the RMSE [9]: (5) RMSE seg = 1 N ∑ i = 1 N ( O i , ref − O i , est ) 2where N is the total number of lines in the reference sample text, O_i,ref is the number of reference objects in the text line i (equal to one per each line), and O_{i,est is} is the number of detected objects in the text line i.

Binary classification is based on the signal detection theory (SDT) postulate [13]. Its task is to classify the members of a given set of objects into two groups, based on whether they have some property or not. Suppose that we test the set of objects for the presence of a property. If some objects have a property and the test confirms it, then those objects are true positives (TP) [14]. In an unlikely scenario, some objects do not have a property, but the test confirms it. They are false negatives (FN) [14]. Some objects may have the property, but the test mistakenly does not confirm it. These are called false positives (FP) [14]. Finally, some objects do not have a property, and the test confirms it. These are true negatives (TN) [14]. In the context of classification tasks, the previous statements about the terms true positives, true negatives, false positives and false negatives are used to compare the given classification of an item. This is systemized in Table 1 in the so-called confusion matrix (CM) [14].

From these elements the common evaluation measures can be extracted [14]:

precision,

Precision is a measure of the ability of a system to present only relevant items. It is defined as [14]: (6) precision = TP TP + FPand it measures the exactness of a classification. A higher precision means less false positives, while a lower precision means more false positives. This is often at odds with recall, as an easy way to improve precision is to decrease recall.

Recall is a measure of the ability of a system to present all relevant items. It is defined as [14]: (7) recall = TP TP + FN

Recall measures the completeness, or sensitivity, of a classifier. Higher recall means less false negatives, while lower recall means more false negatives. Improving recall can often decrease precision because it gets increasingly harder to be precise as the sample space increases.

Precision and recall can be combined to produce a single metric known as f-measure, which is the weighted harmonic mean of precision and recall. It is defined as [14]: (8) f − measure = 2 * precision * recall precision + recall

These elements can be used as common evaluation measures. The following measures are correlated in the text line segmentation [15,16]:

TP represents segmented text line hits i.e., O_clindet,

The water flow algorithm proposed in [18] is also used. It will be just briefly explained. The algorithm assumes a hypothetical flow of water in a particular direction across an image frame in such a way that it faces obstruction from the characters of the text lines. As a result of water flow algorithm, unwetted image frames are extracted. These areas represent the triangle shadows that form the so-called unwetted regions. Seed points that activate the algorithm represent the isolated corner points of the text objects. Further, this hypothetical water flow is expected to fill up the gaps between consecutive text lines. Hence, unwetted areas are of major importance for text line segmentation. The circumstance where hypothetical water flows from left to right is shown in Figure 7.

Furthermore, the parameter water flow angle α is introduced. It widely affects the unwetted regions shape influencing the text line segmentation process. Hence, the selecting process of the water flow angle value is crucial to the quality of the text line segmentation. The complete process of the water flow algorithm applied on the text sample formed of the three letters I is shown in Figure 8.

Gray regions represent the unwetted areas incorporating initial text objects. The stripes of unwetted areas are labeled for the extraction of text lines. Once the labeling is completed, the image is divided into two different types of stripes. First one contains text lines, while the other one contains line spacing. It is shown in Figure 9.

An algorithm based on the anisotropic Gaussian kernel is also used for testing. It will be explained briefly. Its main principle is expanding black pixel areas of text by scattering every black pixel in its neighborhood. This way, distinct areas that mutually separate text lines are established. Hence, the primary purpose is joining only text elements from the same text line into the same distinct continuous areas. The Gaussian probability function is taken as a template that gives the probability of the random function. Consequently, it represents the probability of the hypothetical expansion around every black pixel representing a text element. Furthermore, around every black pixel, new pixels are non-uniformly dispersed.

These new pixels have lower black intensity. Because the level of probability expansion relates to distance from black pixel, their intensity depends completely on the distance from the original black pixel. However, after applying the Gaussian anisotropic kernel, equal to 2K + 1 in the x-direction and 2L + 1 in the y-direction, text is scattered forming an enlarged area around it. Newly created pixels are grayscale. Hence, document text image is a grayscale. Now, inside the kernel a “probability” sub-area is formed using the radius 3σ_x and 3σ_y of ellipse in x and y direction. σ represents standard deviation defining curve spread parameter. Converting all these pixels into black pixels as well as inverting image, forms the new black pixel expanded areas [7]. These areas are named boundary-growing areas. The algorithm’s application to the text sample is given in Figure 10.

For the purpose of testing the algorithm, the parameter water flow angle α from the reduced set {10°, 12°, 14°} is used [19,20]. Text samples are converted to 300 dpi resolution. Testing of the algorithm is performed on the example of 96 lines of multi-line straight, waved, and fractured text as well as 220 lines of diverse handwritten text, consisting of a variety of different scripts (over 500 lines of text).

For the purpose of testing the algorithm based on anisotropic Gaussian kernel, its parameters K and L are under consideration. The main purpose of testing is the optimization of these parameters. Because of the size of the letters, K is picked from the reduced set {5, 8, 10} [12,21]. Furthermore, corresponding the parameter λ is used instead of L. It is defined as λ = K/L. λ is selected from the reduced set {3, 4, 5} [21,22]. All text samples are converted to 300 dpi resolution. Testing of the algorithm is performed on the example of 96 lines of multi-line straight, waved, and fractured text as well as 220 lines of diverse handwritten text, which consist of different variety of scripts (over 500 lines of text).

The evaluation based on error type contains five distinct measures: SLHR, OSLHR, USLHR, MLHR, and RMSE. Their interpretation is clear and unmistakable. The fifth measure is RMSE, which is clearly distinct in fine tuning segmentation results (See Example #1, and 2 in the Appendix). Obviously, the evaluation based on error type is more clear and remarkable. In contrast, the evaluation based on the binary classification has only three distinct measures: precision, recall, and f-measure. Consequently, the third one is the harmonic mean of the other two. Nevertheless, this evaluation process includes more statistical measures. In [10] evaluation based on binary classification is improved by additional measurement extension. However, both methods have different capabilities and convenience, and they can be used mutually as well. Still, the method with five measures has certain advantages. Hence, it is chosen in the decision-making procedure.

From the obtained results, the decision-making procedure is performed. It results as the set of algorithm parameter values, which are the starting point for choosing the algorithm’s optimal parameters. Hence, each test, according to the obtained results, gives the optimal subset of parameter values. These values offer the best response of the algorithm to the specific text samples. Each test experiment is referring as i. Furthermore, it means that for the test framework i = 1, ..., N, where N represents the total number of tests. In our case N = 4. For each test i, the best parameters subset is given as P_i. Finally, the final set of parameters is given as P_f: (9) P f = ∩ P i

The final word in testing efficiency is represented by the comparison of the obtained results between the optimal parameter values of both algorithms. For the water flow algorithm (WF algorithm) the optimal parameter α is equal to 10° [20]. Furthermore, for the algorithm based on anisotropic Gaussian kernel (AGK algorithm) the optimal parameter pair is given by the (10, 4). Comparative analysis based on error type classification is given in Tables 36–39.

From Table 36, the WF algorithm affords more uniform SLHR results, irrespective of different text types. This is confirmed by better results in the multi-line handwritten text test by a margin of up to 10%.

From Table 37, the AGK algorithm has no problem with over-segmentation phenomena. On the contrary, the WF algorithm has to be improved. However, these circumstances can be overcome by additional morphological post-processing. In addition, in a real situation such as with handwritten text both algorithms are equal.

From Table 38, it is obvious that the AGK algorithm has clear problems with under-segmentation. This is a key which leads to better results of the WF algorithm in a complex and diverse test such as the handwritten text.

The RMSE measure of the WF and AGK algorithms just confirms the previous statements, i.e., the slight advantage of the WF over the AGK algorithm. Figure 11 shows the SLHR (%) comparison between the WF and AGK algorithms.

From Figure 11, the WF algorithm can process the various type of text by the SLHR margin of over 65%, while the AGK algorithm cannot. Hence, the WF algorithm has a clear advantage over the AGK algorithm. Similar evaluations can be used for the comparison of algorithms by the methodology based on binary classification. However, it has only three measures and some circumstances are not clearly distinct [10] (See Appendix). Furthermore, comparative analysis based on binary classification of errors is given in Tables 40–42.

From Table 40, the AGK algorithm has a clear advantage over WF algorithm in three synthetic-like tests. However, all advantages vanish in a complex test like the multi-line handwritten text.

From Table 41, WS algorithm has more uniform results. Furthermore, this means less under-segmentation elements. Particularly, this is true for multi-line handwritten text testing.

F-measure is criteria that reflect all bad and good results of testing. Hence, the evaluation process of the algorithm should be very sensitive to this measure [10]. From Table 42, WF algorithm has been characterized by more uniform level of f-measure value. Figure 12 shows f-measure comparison between WF and AGK algorithms.

From Figure 12, the WF algorithm can process the various type of text by the f-measure margin of around and over 80%, while the AGK algorithm can do so only up to 75%. Again, the WF algorithm has a clear advantage over the AGK algorithm. However, the interpretation process of the binary classification of errors is not so obvious as the error type classification.