Early in the 20th century it could be observed that the finger lengths of second (2D) and fourth digit (4D) represents a sexually dimorphic feature, whereby in general the second digit is longer than the fourth digit for men and vice versa for women. In the early 1980s first studies could show a correlation between the 2D:4D ratio and the concentration of androgens one is exposed to during a short window within the prenatal development phase. Therefore, the 2D:4D digit ratio can serve as an additional marker for certain physiological and psychological traits like fertility, assertiveness, aggressiveness and alcohol addiction. Manual measurements are the established method to retrieve the finger lengths e.g. by using a ruler on printed scans of hands. For higher reliability these extremely time-consuming procedures have to be done multiple times. In this contribution two automated procedures are proposed to reduce the time for measurements whilst maintaining the accuracy. A deviation of maximal 2% from the manual measurement could be achieved for more than 75% of the 22 participants.
The 2D:4D ratio describes the length ratio of the second digit (index finger - 2D) to the fourth digit (ring finger - 4D). First studies relating to the ratio date back to the end of the 19th century which revealed a difference between women and men. In 1930 R. George could confirm the 2D:4D ratio as a sexually dimorphic feature by measuring the finger lengths of 620 hands (two out of three were men) . In a short period during the prenatal development phase the ratio of second to fourth digit takes shape and does not change throughout life . It could be shown that the ratio itself depends on the concentration of androgens one is exposed to in this phase ,. A first correlation between the 2D:4D ratio and a psychological trait could be established by G. Wilson in 1982. Furthermore, it could be proven that women with a longer ring finger considered themselves as more assertive in comparison to other women. Further studies revealed a correlation between fertility , physical competitiveness , homosexuality for men , attention deficit hyperactivity disorder (ADHD) , alcohol addiction and video game addiction .
Up to now measurements are performed manually in order to retrieve the necessary data. In most of the cases the hands of test persons were scanned in a first step. Depending on the scanning device used, the images of these hands were printed out or digitalized. In the first case the finger lengths are determined using rulers  or vernier calipers . In the second case, measuring is done using appropriate software tools which includes virtual rulers . To assure a certain degree of reliability, the measurements have to be revised multiple times and often by distinct experts. This approach is both cumbersome and time-consuming. Therefore, a method is proposed to automatize the image acquisition and measuring of finger lengths in order to provide a standardized and robust way to obtain the 2D:4D digit ratio.
This paper is structured as follows. The proposed method is explained in detail in Section 2. This includes the segmentation method and two different approaches to measure the finger lengths. In Section 3 the results of the automatized measurements of 22 participants are compared to the manual measurements using a graphics editor. The results are discussed and concluded in Section 4.
The left and right hands of the participants were scanned with the multifunction printer at a resolution of 200 dpi (dots per inch). This digital images are the basis for the method proposed in this section to automatically segment images of hands. These images are processed to detect the position of the second and fourth digit and furthermore to determine their lengths. In general, the distance of the last finger crease (between finger and palm) to the fingertip defines the digit length. This definition is used for both presented methods to determine the finger lengths. The accuracy of the results depends highly on the used segmentation approach. Besides that a background of arbitrary complexity should be taken into account to provide higher flexibility. Therefore, an algorithm is proposed which uses color structure code as described by Priese et al.  in combination with a brute-force approach to achieve a segmented image fulfilling the necessary requirements.
A region segmentation that was proposed for color images is the so–called color structure code, CSC . The color structure code is used in a pre-processing step in order to segment the image into several uniform areas with unique color. The number of areas building up the mosaic-like image depends on a single threshold, which is used to determine whether certain areas are fused or split. Each area is assigned to a unique number to generate a label image (see Figure 1, right).
Afterwards the hand is segmented from the background by using a brute-force approach, where regions with same label are hidden subsequently and in all possible combinations (see Figure 2). Finally, the remaining regions are checked if they build up the shape of a hand. Generally, this is a very time-consuming step, but with respect to some restrictions (e.g., consider only bigger regions or merge adjacent regions) the segmented image can be achieved within a finite amount of time (a few minutes at maximum).
Furthermore, meaningless combinations can be discarded if regions are not connected (directly or indirectly) to each other. This can be done by arranging the labels in a graph data structure and applying a depth-first search which results in combinations of connected regions. Using a fixed label as searching root, which definitely belongs to the hand, can further reduce the amount of combinations to be considered.
The check for hand shape is done by considering each combination of regions as a binary image and examining a generated contour signal representing the shape. This signal can be achieved by rotating a line around the centroid (PS). The distance between the centroid and the first intersection of the line with the contour of the binary image expresses a data point in the contour signal. The signal can then be examined for the characteristic sequence of maxima in the contour signal generated by the hand-shaped binary image (see Figure 3). These sequence also helps to distinguish between the right and left hand. Are there two local maxima to the left and one to the right of the global maximum (= middle finger) it is the right hand; for the left hand it is vice versa.
2.2 Length measurement using finger creases
The first approach is making use of the contour signal generated in previous the segmentation step (cf. Figure 3). The borders of the region of interests (ROI) for the second and fourth digit can be deduced from the local minima and maxima. In general, the highest maximum represents the third digit (middle finger). Therefore, the second and fourth digits are represented by the local maxima on the left and right side of the global maximum. The finger gaps can be directly taken from the local minima besides the respective maxima. These gaps also serve as the right and left boundary of the corresponding region of interest. The upper border is determined by the location of the finger tip. The lower border is determined by the smaller minimum of the ones representing the finger gaps. Converting the ROI in the color image of the separated finger to a gray-scale image allows the direct detection of the creases by establishing a brightness profile. A longitudinal portion of the ROI is taken. In this portion the grey-scale values for each row are summed up building a one dimensional signal (brightness profile). The local minima in this signal corresponds to finger creases whereas the uprising flank starting by zero represents the fingertip(see red arrows in Figure 4). The distance of the fingertip and the last crease expresses the length of the finger.
2.3 Length measurement using geometry
As the second approach the shape of the finger itself is used to estimate its length. This method is more robust against artifacts caused by skin irritations and rings worn which would disturb the brightness profile used for the direct detection of the finger creases. The position of the finger gaps are used as reference points in order to define the finger length. For the fourth digit this can be done by connecting the gaps on the left and right side through a straight line. The center of this line is then used as an approximation of the corresponding finger crease. Due to the missing second gap for the second digit, a straight line is constructed which intersects the existing gap and is oriented orthogonal to the finger itself. A second line parallel to the finger and running through the tip intersects the first line at some point. Finally, this point serves as an approximation for the finger crease of the second digit (see Figure 5).
The left and right hands of the 22 participants (5 female and 17 male) were scanned with the multifunction printer Typs Xerox WorkCentre 7120 at a resolution of 200 dpi (dots per inch). The participants were advised to place their hands in the same relaxed position such that neighboring digits did not touch each other and to ensure the correct detection of the finger gaps. Both approaches, the direct detection of the finger crease and the approximation of the creases based on the geometry, were compared to the manual measurements using a virtual ruler in the image editing tool GIMP (GNU Image Manipulation Program). Hereby, the measured finger lengths and the results for the 2D:4D digit ratios of the three methods were compared. The direct detection of finger creases revealed a high accuracy against the manual measurement. A deviation of up to 2% from the manual measurement could be reached for about 75% of all participants for the second and fourth digit. In comparison, the approximations of the creases using the geometric approach, only ∼33% of all measured index fingers and ∼55% of all measured ring fingers yielded a derivation of up to 2% from the manual measurements (see Table 1).
|1 − 2%
|2 − 3%
The geometric approximation as well as the direct detection of the creases provided a similar 2D:4D ratio for each participant. For both approaches nearly 40% of the measurements differ up to 2% from the 2D:4D ratios calculated using the manual measurements.
The goal was the automatization and standardization of the process of retrieving the 2D:4D ratio of a person, which has to be done manually until today. In order to achieve accurate results the images have to be segmented robustly. This was achieved by applying color structure code in conjunction with a brute-force approach. Finally, two differently methods were proposed to measure the finger lengths. The direct detection of the finger creases corresponds to the manual measurement. This approach is accurate, but is susceptible against artifacts caused by e.g., noise, skin irritations or rings. Approximating the creases using a geometric approach is more robust but less accurate. This is due to the high differences in finger creases between humans. An improved model using natural fixed proportions in the human hand could increase the accuracy of the geometric approach. This work also showed up that using more suitable hardware can improve the performance of the brute-force segmentation step.
Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.
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