5. Results

iPhone 4S with Olloclip 3 in one (mm) Nikon Coolpix8700 with Nikon FC-E9 (mm)

Figure 9. Three-dimensional position of projection points with regard to antenna; three-dimensional co-ordinates of the camera as the result of balancing (left image shows values for iPhone 4S camera with Olloclip 3 in one; and right image

shows values for Nikon Coolpix8700 camera with Nikon FC-E9 fisheye lens).

ck 2.23950000 0.00161000 8 1.69005000 0.00203000 8 x0 0.05886000 0.00397000 8 0.03987000 0.00259000 8 y0 0.10471000 0.00399000 8 0.11442000 0.00240000 8 A1 0.00080228 0.00027401 8 0.00118750 0.00038919 6 A2 0.00386240 0.00007329 8 0.00067814 0.00005062 8 B1 0.00105490 0.00016903 8 0.00026227 0.00012548 4 B2 0.00137450 0.00015347 8 0.00021274 0.00011927 3 C1 0.00050562 0.00032783 1 0.00009505 0.00029182 1 C2 0.00038251 0.00030980 6 0.00031644 0.00028458 1

Table 3. Calibration parameters calculated for equidistant model.

42 Smartphones from an Applied Research Perspective

Value rms Significance Value rms Significance

At the end of the application designed for testing, numerical values of calibration parameters and rms of those parameters that were calculated according to equidistant model were compared between the 'Olloclip 3 in one' fisheye lens used with iPhone 4S mobile phone and standard 'Nikon FC-E9' fisheye lens used in Nikon Coolpix8700. This comparison is given in Table 3 and the resulting graphics are shown in Figures 10 and 11.


Figure 10. Distortion parameters for two different camera-fisheye lens combinations.


Figure 11. Rms values of distortion parameters for two different camera-fisheye lens combinations.

Since A3 distorsion parameter was a so small value that can be ignored, it was not analysed and written in Table 3 [87]. Table 3 shows that the significance values of the iPhone are higher than that of Nikon because of smaller pixel (it is given in Table 1 in Section 3) structure of iPhone's camera.

When Figure 11 is examined, it is seen that distortion parameters of iPhone 4S camera and Olloclip 3 in one fisheye lens equipment is larger, although it has a larger focal length. It does not show a significant difference than Nikon Coolpix8700 camera and FC-09 fisheye lens equipment. (ck: focal length after calibration process, x0: image co-ordinate of principle point in X direction, y0: image co-ordinate of principle point in Y direction).

Figures 10 and 11 illustrate that when x0, y0 principal image point co-ordinate values and focal lengths of two different fisheye lenses are ignored for the cameras with same resolution and same pixel size, a meaningful approximation is obtained. In consideration of these results, current technology developed for Olloclip 3 in one lens that is improved for mobile phones, is particularly great. Nikon FC-E9 mounted on bulky Nikon Coolpix8700 is difficult to use. Olloclip 3 in one lens mounted on iPhone 4S is considered to be used in studies done with photogrammetric fisheye lens instead of Nikon FC-E9. The conclusion part compares the advantages and disadvantages of two different fisheye images.

Nine of 112 control points are considered as passing points, while 103 of them are full control points. One hundred and three point co-ordinates from testing area are considered errorless and used in bundle block adjustment. Three-dimensional position data derived from the bundle block adjustment are compared to the errorless points. Nikon Coolpix8700 camera and FC-09 fisheye lens combination give accuracy on 85 points under the sub-pixel level. IPhone 4S camera and Olloclip 3 in one fisheye lens combination gives accuracy on 89 points under the sub-pixel level. This means that there is 82.52% accuracy for Nikon Coolpix8700 camera and FC-09 fisheye lens combination and 86.40% accuracy for iPhone 4S camera and Olloclip 3 in one fisheye lens combination. The co-ordinates of three-dimensional object co-ordinates of 103 points are subtracted from the points that derived from bundle block adjustment process. If the difference values are greater than sub-pixel level in any axis then they are eliminated consequently. Figures 12 and 13 are depicted from the obtained differences, respectively, for iPhone 4S camera and Olloclip 3 in one fisheye lens combination and Nikon Coolpix8700 camera and FC-09 fisheye lens combination. Delta X is the difference between three-dimensional point co-ordinate that measured before adjustment in X direction and three-dimensional point co-ordinate, which derived after adjustment in X direction. Delta Y and delta Z were calculated similarly.

The standard deviations of co-ordinate differences have been calculated for three different axes from the data contributing to depict Figures 12 and 13. The standard deviation values on the X, Y and Z axes are 0.763, 0.558 and 0.638 mm, respectively, for Olloclip 3 in one lens kit. By using similar derivation, the standard deviation values on the X, Y and Z axes are 0.748, 0.699 and 0.517 mm, respectively, for Nikon FC-09 lens kit. As presented, the standard deviation values of identical axes are found approximately close to each other from the calculations. Moreover, when the distribution of the co-ordinate differences were evaluated for three identical axes (X, Y, Z) of these two kinds of lens kits, it was calculated that they have the same maximum difference value which is approximately 2 mm. From these graphics, root mean square error of point positions has

Since A3 distorsion parameter was a so small value that can be ignored, it was not analysed and written in Table 3 [87]. Table 3 shows that the significance values of the iPhone are higher than that of Nikon because of smaller pixel (it is given in Table 1 in Section 3) structure of

Figure 11. Rms values of distortion parameters for two different camera-fisheye lens combinations.

When Figure 11 is examined, it is seen that distortion parameters of iPhone 4S camera and Olloclip 3 in one fisheye lens equipment is larger, although it has a larger focal length. It does not show a significant difference than Nikon Coolpix8700 camera and FC-09 fisheye lens equipment. (ck: focal length after calibration process, x0: image co-ordinate of principle point

Figures 10 and 11 illustrate that when x0, y0 principal image point co-ordinate values and focal lengths of two different fisheye lenses are ignored for the cameras with same resolution and same pixel size, a meaningful approximation is obtained. In consideration of these results, current technology developed for Olloclip 3 in one lens that is improved for mobile phones, is particularly great. Nikon FC-E9 mounted on bulky Nikon Coolpix8700 is difficult to use. Olloclip 3 in one lens mounted on iPhone 4S is considered to be used in studies done with photogrammetric fisheye lens instead of Nikon FC-E9. The conclusion part compares the advantages and

Nine of 112 control points are considered as passing points, while 103 of them are full control points. One hundred and three point co-ordinates from testing area are considered errorless and used in bundle block adjustment. Three-dimensional position data derived from the bundle

in X direction, y0: image co-ordinate of principle point in Y direction).

disadvantages of two different fisheye images.

iPhone's camera.

44 Smartphones from an Applied Research Perspective

Figure 12. Subpixel graphic for the combination of iPhone 4S camera with Olloclip 3 in one fisheye lens.

Figure 13. Subpixel graphic for the combination of Nikon Coolpix8700 camera with Nikon FC-E9 fisheye lens.

been determined as 3.556 mm for Olloclip 3 in one and 3.401 mm for Nikon FC-09 lens kit. These values show us the internal reliability of these two kinds of fisheye lens kits is similar for threedimensional point co-ordinate determination.

When the difference of image co-ordinates derived before and after adjustment are analysed in vectorial form, Figures 14 and 15 are achieved for the two different fisheye lenses. If the difference

Figure 14. Image co-ordinates residuals for iPhone 4S camera and Olloclip 3 in one fisheye lens combination (between measured and after adjustment).

Figure 15. Image co-ordinates residuals for Nikon Coolpix8700 camera and FC-09 fisheye lens combination (between measured and after adjustment).

between the measured images co-ordinates and the adjusted image co-ordinates are analysed in vectorial form, Figures 14 and 15 are achieved for the two different fisheye lenses. As can be seen from these two figures, residuals decrease while approaching to the image principal point for the two fisheye lens cameras, but increase proportionally to the sides due to distortion. The standard deviation results of the above-mentioned experiment are 0.000814 for iPhone 4S camera and Olloclip 3 in one fisheye lens combination and 0.000890 for Nikon Coolpix8700 camera and FC-09 fisheye lens combination. It can be said that according to above explained results, although there is not a significant difference, iPhone 4S camera and Olloclip 3 in one fisheye lens combination has lower distortion on the total image surface than Nikon Coolpix8700 camera and FC-09 fisheye lens combination. Therefore, iPhone 4S camera and Olloclip 3 in one fisheye lens combination could also be used for photogrammetric applications instead of Nikon Coolpix8700 camera and FC-09 fisheye lens combination.

Advantages and disadvantages of using fisheye lenses for the above-mentioned equipments can be listed as follows:

Advantages

been determined as 3.556 mm for Olloclip 3 in one and 3.401 mm for Nikon FC-09 lens kit. These values show us the internal reliability of these two kinds of fisheye lens kits is similar for three-

Figure 13. Subpixel graphic for the combination of Nikon Coolpix8700 camera with Nikon FC-E9 fisheye lens.

**points**

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85

Delta X Delta Y Delta Z

**Nikon Coolpix8700 and Nikon FC-E9** 

When the difference of image co-ordinates derived before and after adjustment are analysed in vectorial form, Figures 14 and 15 are achieved for the two different fisheye lenses. If the difference

Figure 14. Image co-ordinates residuals for iPhone 4S camera and Olloclip 3 in one fisheye lens combination (between

dimensional point co-ordinate determination.


measured and after adjustment).





**meter**

0.0005

0.001

0.0015

0.002

0.0025

46 Smartphones from an Applied Research Perspective

0


• There is no significant difference between the image centre point co-ordinates of iPhone 4S camera and Olloclip 3 in one fisheye lens equipment and Nikon Coolpix8700 camera and FC-09 fisheye lens.

Disadvantages

