RECONSTRUCTION OF PANORAMIC IMAGE 360ᵒ BASED ON 3D COORDINATES SYSTEM (CASE STUDY: INTERIOR ROOM)

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1 RECONSTRUCTION OF PANORAMIC IMAGE 360ᵒ BASED ON 3D COORDINATES SYSTEM (CASE STUDY: INTERIOR ROOM) Siti Hajar Aswad 1, Deni Suwardhi 2, Agung Budhi H Institut Teknologi Bandung, Bandung, West Java 40116, Indonesia ogutpoenya@gmail.com; denisuwardhi@gmail.com; abh.geodesi@gmail.com KEY WORDS: Panoramic Image, Geometric, 3D Projection. ABSTRACT : Panomaric image is one kind of image which has a large FOV (field of view). It can cover the view 360ᵒ horizontally and 180ᵒ vertically. Many field of study use panoramic image, such as history, construction, and safety or security. Panoramic image is also used to create any virtual reality of building and architecture object. Many kind of methods to create panoramic image only show us the information about texture and color of the panoramic image. In a few field of study, it will be more usefull if the panoramic image can also show the geometric information. This research will use the photogrammetric method, expecially colinearity which combine with spherical projection to create a panoramic image from 3D model of interior room. The result of this final project, the accuracy of the distance, angle and wide of the object can be used in practical, but it still need many development. The development must be focus in a way to make an easy way for user to use it. 1.INTRODUCTON Panoramic image is an image which have wide field of view. It could be 180ᵒ, 360ᵒ until 720ᵒ. The advantages from this kind of image can give more information about texture, colour, and shape from the object. Any field of study work with panoramic image, but it is only working with visualization from this image. Metric information such as distance, wide and angle from the object on the image is never shown. Texture range image is a fusion result process from 3D lascanner and panoramic image which can inform provides more reliable information about the investigated object for conservators and historians, than using both datasets separately (Bila, Reznicek, & Pavelka, 2013). In this research would be discuss about panoramic image reconstruction based on 3D coordinate system. The expectation result from this research hope would give same result as texture range image which can make any calculation of size, wide, and angle from the object. 2.METHOD AND DATA Panoramic image reconstruction in this research be divided into there process which were translasion, projectioan, and evaluation of visualitation and metric from panoramic image 360ᵒ. Data used in this entire process was 3D data of Interior room. This data was the result of photogramtry process with main data consist of image which cover all of entire room. The fist step is transformation of 3D object would be transformation. This process is to define the center of camera coordinate system that the center of coordinate is the center of 3D object. In this process, we need the value of translation and rotation parameter which will be used to transform the coordinate of object to coordinate of camera (Schneider & Schwalbe, 2005). Figure 1 is the illustration of the step of transformation which occur in this research. Figure 1. Geometry of model for transformation process 1

2 Transformation between coordinate of object (X,Y,Z) and coordinate of camera (x,y,z) is written in equation (1). x = X 0 + X (1) which X 0 is translation parameter between coordinate of object and coordinate of camera. Equation (1) can also be used for Y and Z. The next step is process of transformation from 3D coordinate system (x,y,z) to spherical coordinate system (θ,ζ,r). The equation of the transformation is written in equation (2) and (3). θ = arctan y x (2) z ζ = arctan (3) x 2 +y 2 which R = radius of the spherical, θ dan ζ = direction of spherical. At the end, spherical coordinate (θ,ζ,r) will be transformed to image coordinate (x,y ) to get the visualization from the panoramic image of 3D model. The equation used for this transformation process is written in equation (4) and (5). x = R. θ (4) y = R. ζ (5) which θ, ζ, dan R is gotten in equation (2) and (3). The second step of this process is projecting the 3D model onto panoramic image which can be done using a combination of collinearity equation with equation (4) and (5) (Schneider & Schwalbe, 2005). The collinearity equation can be write in equation (6) and (7) (Atkinston, 1996). x a = c[r 11 (X o X A )+r 12 (Y o Y A )+r 13 (Z o Z A )] [r 21 (X o X A )+r 22 (Y o Y A )+r 23 (Z o Z A )] y a = c[r 21 (X o X A )+r 22 (Y o Y A )+r 23 (Z o Z A )] [r 31 (X o X A )+r 32 (Y o Y A )+r 33 (Z o Z A )] (6) (7) with r ij is the element of matrix rotation R which is impacted from ω, φ, and χ of outer orientation. X o, Y o, Z o, is the parameter translation from camera coordinate despite of coordinate object. The result of the combination equation is written in equation (8) dan (9) (Schneider & Schwalbe, 2005). x = R arctan (we) (8) y = R. arctan wo wa+wi (9) with, are we = [r 12 (X X 0 )+r 22 (Y Y 0 )+r 32 (Z Z 0 )] [r 11 (X X 0 )+r 21 (Y Y 0 )+r 31 (Z Z 0 )] wo = [r 13 (X X 0 ) + r 23 (Y Y 0 ) + r 33 (Z Z 0 )] wa = [r 11 (X X 0 ) + r 21 (Y Y 0 ) + r 31 (Z Z 0 )] 2 2

3 wi = [r 12 (X X 0 ) + r 22 (Y Y 0 ) + r 32 (Z Z 0 )] 2 The next step is transformation of panoramic coordinate to 3D coordinate. This process is evaluating the calculation of distance, direction, and area of the object. The equation used in this process is written in equation (2.19), (2.20) and (2.21) (Weisstein, 2015). X = r cos ( y ) sin (x ) (2.19) R R Y = r cos ( y ) x cos (x ) (2.20) R R Z = r sin ( y R ) (2.21) With r is the distance from the center of coordinate, y and x is the panoramic 360ᵒ coordinate R is the radius of the spherical, X, Y, and Z is 3D object coordinate. The process to define distance, direction, and area of the object can be done by using equation (10), (11), and (12). d = (X 2 X 1 ) 2 + (Y 2 Y 1 ) 2 + (Z 2 Z 1 ) 2 (10) θ = cos 1 c2 a 2 b 2 2ab (11) L= s(s a)(s b)(s c) (12) With d = distance, θ = direction, L = area. X,Y,Z = is coordinate object from the center of camera, a and b = is the line which construct direction, c = is the line in front of direction θ. 3.RESULT AND DISCUSSION Evaluation of panoramic image in this research is divided into two kind of evaluations. The first evaluation is about visualisation from the panoramic image 360ᵒ. The second evaluation is about the metric calculation of the object in the room. Data used in this research is sparse cloud and dense cloud. Figure 2 and 3 are visualisation of sparse cloud and dense cloud. Figure 1. Sparse cloud 3

4 3.1.Visual Evaluation Of Panoramic Image Figure 3. Dense cloud Figure 4 and 5 are the panoramic images which are the result of the projection process. Figure 6 is the panoramic image which is the result of stithching process. Figure 4. Visualisation of panoramic image from sparse cloud projection 4

5 Figure 5. Visualisation of panoramic image from dense cloud projection Figure 6. Visualisation of panoramic image from stithching Based on Figure 4, 5 and 6, we can discuss the evaluation of the visualisation from the result of 360ᵒ panoramic image. Interior room in Figure 4 can not be ilustrated, but it can be ilustrated in Figure 6. It can be happen because when we use sparse cloud, the density of the point cloud is limited. On the other hand, panoramic image which is the result of dense cloud projection can give good ilustration for interior room and this result is a good as panoramic image which is the stitching result shown in Figure 6. Input process of panoramic image into virtual reality software can be another way to do visual evaluation. This process can give us the visualization of the panoramic image when this image is used to be virtual reality. The suitable of this panoramic image and the virtual reality software is another point of visual evaluation. Figure 7 and 8 are illustrations of panoramic images in virtual reality software. 5

6 Figure 7. Ilustration of panoramic image 360ᵒ in virtual reality software Figure 8. Ilustration of virtual reality from projected panoramic image 360ᵒ 6

7 The afflication in virtual reality software give the good result when using projected panoramic image 360. Object in interior of the room can be illustrated and the zoom in-out action can be done in that result. This discussion indicate that the projected panoramic image 360ᵒ has good quality as stithching panoramic image Metric Evaluation Metric evaluation is began with transformation process from 2D panoramic coordinate into 3D object coordinate. Metric evaluation can be done with equation (10), (11), and (12). The distribution of point for metric evaluation is shown in Figure 9 and 10. Figure 9. Sampel point distribution of 3D reference Figure 10. Sampel point distribution of 3D from the transformation RMSE of distance calculated is 1.51E-07 m, RMSE of direction calculated 4.55E-07 ᵒ, and RMSE of area which calculated is 5.95E-07 cm 2. The result of RMSE from the calculation give is very small. It indicate that the metric calculation at the 3D result from transformation of panoramic image is proper to use. 7

8 The calculation of distance, direction, and area using conventional way will give the bigger RMSE than the calculation using this method. This can occur because of the error or accuration of the tools used for measuring the metric information. As a sampel, when we use a ruller to measure the distance of the object which has m for the accuration, the result of this measurement have stochastic error which is 0.05 mm. The sthocastic error will not be found when we use panoramic image which has 3D coordinate. 3.3.Discussion Application of panoramic image is developed in many field of studies. One of them is marketing. The marketing process of a building or imterior desain of room will be easier when we use panoramic image which has been based on 3D coordinate. The virtual reality is the one way to marketing the interior room or a building, when the metric information can be informed, the buyer can get the valid information of the object without any ground check. Panoramic image based on 3D coordinate can be used in conservation building. Conservation building in this term is about cleaning, adding an interior object and painting. That activity will be more efisien in case of planning. For example, in painting process, the amount of paint provided for a room can be calculated by knowing the area that is calculated directly in 360ᵒ panoramic image based on 3D coordinate system. Two kind which discuss in the text above only can be do in panoramic image which based on 3D coordinate. It would be the point plus than panoramic image in usual. 4.CONCLUSION Conclusion which result of this research is : a. Panoramic image based on 3D coordinate or texture range image can be constructed with 3D coordinate transformation into 2D coordinate. b. The calculated RMSE of distance result which is 1.51E-07 m, RMSE of direction which is 4.55E-07 ᵒ, and RMSE of area which is 5.95E-07 cm 2. The RMSE value of the calculation result is very small. It indicates that the metric calculation can be done in this model. References Atkinston, K. B. (1996). Close Range Photogrametry And Machine Vision. whittles Publishing, pp Dwi N, R., Suryatin, B., P, S., & Setyawan, A. (2006). Matematika : untuk SMP dan MTs kelas VII. Bandung: Grasindo. Kanginan, M. (2007). Matematika. Bandung: Grafindo Media Pratama. Krismanto, A. (2008). Pembelajaran Sudut Dan Jarak Dalam Ruang Dimensi Tiga. Jogjakarta: Pusat Pengembangan Dan Pemberdayaan Pendidik Dan Tenaga Kependidikan Matematika. Maas, H. G., & Schneider, D. (2004). Photogrammetric Processing of Digital 360 Panoramic Camera Image Data. GIM, 1-6. Pramulyo, H. (2014). Transformasi Data Point Cloud Pada Citra Panoramik Proyeksi Silinder Dan Bola Untuk Estimasi Perhitungan Posisi Dan Jarak (Studi Kasus Candi Borobudur). Bandung. Purworahardjo, U. (2000). Sistem Dan Transformasi Koordinat. Bandung: Penerbit ITB, pp 2-3 Schneider, D., & Schwalbe, E. (2005). Design And Testing Of Mathematical Model For A Full-Spherical Camera On The Basis Of A Rotating Linear Array Sensor And A Fisheye Lens. 8

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