Measurement method of ICDAR2013 text detection algorithm (II.) Rectangle matching and Deteval

This is the second part, the first part please click the measurement method of ICDAR2013 text detection algorithm (a) Evaluation levels

Main content:

ICDAR2013 method for Rectangle Matching, or bbox Matching foucsed evaluation Image Text detection task

If not specifically stated, the following:

The evaluation/measurement method is only for the text localization algorithm; text detection is not distinguished from text localization bounding box, bbox, rectangle do not differentiate Det Ection with Bbox

As already mentioned, the evaluation method has four Level:pixel feature discriminace pixel classification detection at rectangle target oriented

In the field of text detection, 3 and 4 (end2end evaluation) are the most commonly used.

For text detection tasks that are subject to horizontal text and general's object detection tasks, it is the most convenient, practical, and extensive method to use a rectangular box to represent the test results. ICDAR2013 is so. (but ICDAR2015 not) evaluation problem Description

Evaluation the input of the problem: D D, the Bbox collection to measure the output of the detection algorithm. G G, Ground Truth bbox collection. Di,gj D_i, G_j represents an element of D,g D and G, respectively.
Output: Evaluation of the quality of D D.

So far, the evaluation methods I've learned (object detection and text detection) have recall and precision calculations. When these two values are obtained, the evaluation of the object detection calculates the map, and the evaluation of the text detection calculates F-mean.

So, for the evaluation of text detection, the difference of different methods is mainly how to calculate recall and precision, and the key of recall and precision is how to decide whether the two bbox match. Matching of Bboxes

Judging whether the two Bbox match is a simple problem that can be simplified but not. There are three match modes, as shown in the following illustration:

The solid wireframe represents the ground truth, and the dashed box represents the output of the detection algorithm. One-to-one match, as shown in (a). A one-to-many match, as shown in (b), ground Truth when the granularity is greater than detection granularity. Many-to-one match, as shown in (c), detection is larger than the granularity of ground truth. Many-to-many match, not in the picture.
The difference between the different Evaluation methods is that the three kinds of match are handled differently Evaluation in ICDAR2003, only one-to-two match is considered

Just considering that one-to-one match is the simplest, simplest and most brutal way, ICDAR2003 is using this approach.

The formula (6) in the figure calculates recall and precision, both of which are used in the Bestmatch bestmatch.
Given a bbox b b, such as Gi g_i, and a bbox list (which is the previous set, note, not a mathematical unordered set) b b, for example D, Bestmatch Bestmatch method outputs a value between 0 and 1, representing b b in b b's match score. If b b has a fully coincident with b b bbox, the output is the maximum value of 1, if b b bbox and b b does not have any overlap, the output of the minimum value of 0.

(7) The fractional calculation form of Bestmatch Bestmatch looks very similar to F-mean. In fact, it is a f-mean/harmonic average (Harmonic mean). You can define an area-based, bbox-applicable recall and precision:
R (GI,DJ) =area (GI∩DJ) area (Gi) R (g_i, D_j) = \frac {Area (g_i \cap d_j)}{area (g_i)}

P (G