Using 3-D models, one archaeologist is recording the structures’ exact measurements.
We focused on the background regions of the image sequences that cover almost the entire surface of the cave, while shooting the guide from a variety of viewpoints and angles. Then we came up with the idea of employing a SfM technique to solve two problems at once: stitching the background images, and using them to reconstruct the 3D geometric information of the inner surface of the cave.
A.
3D Reconstruction by Photosynth
We employ Microsoft Photosynth [4] to reconstruct the 3D geometry of the cave. Photosynth is convenient and easy to use and allows us to take digital photos and upload them onto Photosynth website through the internet. Data of 3D point clouds can then be generated for users to download point clouds from the website. The core technique of this application is based on Snavely et al. [5], in which unorganized photo sets can be used for reconstructing 3D scenes from the intrinsic information of the photos and by visualizing the reconstructed scenes on a web browser. The process of scene reconstruction is accomplished by a SIFT (scale-invariant feature transform) keypoint detector [6] and SfM [7].
Kawae builds precise 3-D models of the pyramids using photographs and videos. Here, he stands on the top of a pyramid for the best view.
When Yukinori Kawae explores the Great Pyramids at Giza, he isn’t after treasure or lost chambers—he’s looking for dimensions. For all that the pyramids have been dug, scanned, and photographed, the exact measurements of many are still unknown.
Kawae first saw the pyramids in 1992 as a 19-year-old traveling from Japan to study them. He was disappointed: They were much smaller than he’d imagined. Today, as an archaeologist, he values every inch of the pyramids in his mission to preserve their unique stone construction.
For the past decade Kawae has been recording the sites in precise detail. He creates digital 3-D models of the pyramids using laser scanners and photogrammetry, a method that stitches together photographs and videos captured from different vantage points. He also mapped the unusual cave-like indentation on the side of Khufu, the largest pyramid, and made a model of the oldest pyramid before restoration work began.
With this information, he hopes to illuminate how the pyramids were built. Then he wants to enlist muography—an imaging technique that uses cosmic rays to scan a structure’s density and create a blueprint of its interior. Kawae compares his detailed examinations to a “crime scene investigation.”
Laser scans, cosmic ray detectors, and 3-D models have unearthed Indiana Jones-style mysteries and opened archaeological sites to researchers of all ages and nationalities across the world. Last year an archaeologist studying laser scans found hints of hidden chambers in King Tut’s tomb. In February a class at Harvard University “toured” a virtual reality version of Giza’s complexes built from scans and photographs. Crowdsourcing this information, Kawae says, “may solve the mysteries of the pyramids”—but walking the site “is equally important to sitting in front of the data.”
In high school Kawae became obsessed with the pyramids after watching a TV documentary. Now he’s quick to say that sweating under the Egyptian sun isn’t as glamorous as Hollywood portrays it.
His most exciting find so far? A pile of trash, unearthed a decade ago, which provided a glimpse into the daily lives of ancient people. The purpose of archaeology, Kawae says, is “to record everything about the past and to understand human beings. We are not treasure hunters. We need information rather than treasure.”
3D Reconstruction of the “Cave” of the Great Pyramid from Video Footage
Abstract
— Studies on the great pyramid of King Khufu (2509-2483 BCE ±25) in Egypt are numerous, but only a few surveys, which are the basis of any hypotheses on the construction of a pyramid, have been conducted. In particular, since no observation of the core of the pyramid has been made, theories about the structure are still hypothetical. In 2013, a Japanese TV production company had the opportunity to climb the northeast corner of the pyramid to shoot a crevice that led to an open space (named “cave”) inside the pyramid, located about 80m from the ground. The authors are fortunate to be allowed to use this video footage for academic research. We employed a “structure from motion” (SfM) technique using Microsoft Photosynth to reconstruct the 3D point cloud of the surface of the cave. Twenty minutes of footage was split into thirty thousand image frames, out of which we selected three hundred images shot using several smooth motions of the camera and used these for the SfM process. SfM tracks the “feature points” in the image sequence to estimate the camera motion and then triangulates these feature points to produce the point clouds. As a result, the static feature points from the overall surface of the cave were effectively collected and reconstructed as point clouds, whereas inconsistent points from a moving person are automatically eliminated through the SfM process. Thus we have produced, albeit in a small area, the first record of the actual structure of the great pyramid’s core. The production of a 3D model from existing video footage is a rather new methodology in the field of archaeology. This set of techniques can be applied to not only academic investigation but also to the restoration and conservation of damaged heritage and artifacts.
Keywords— Pyramid masonry; SfM (Structure from Motion); point clouds; Egyptology; Archaeology; 3D recording
I.
INTRODUCTION
In March 2013 a Japanese TV production company, TV Man Union, had the opportunity to climb the northeast corner of the great pyramid of King Khufu (2509-2483 BCE ±25) [1] at Giza plateau, Egypt. The purpose of the program made by the company is to introduce Jean-Pierre Houdin’s internal ramp theory [2]. The TV crew successfully filmed two open spaces, “notch” and “cave”, that are, according to Houdin, a possible remnant of space for the internal ramp. The notch of the northeast corner of the pyramid is located on the 104
th
course, which is about 80m from the ground (Figs. 1 and 2). This half-open space has a crevice in the north that led to another open space (“cave”) inside the pyramid.
Fig. 1.
The location of the “notch” of the northeast corner of the pyramid. Fig. 2.
Closeup shot of the “notch” facing the southwest.
One of the authors, climbing with the crew, did not ascertain any evidence supporting Houdin’s theory but rather found interesting archaeological features showing the masonry at the core of the pyramid. Previous archaeological surveys of the great pyramid have only focused on the external part of the monument and inner spaces such as chambers and passages [3], but no observation of the core of the pyramid has been made. Therefore, this is
the first data produced of the actual state of the core of the great pyramid. II.
OBJECTIVES OF THE PROJECT
The aim of this project was to apply and test a structure from motion (SfM) technique for video footage for non-archaeological purposes in order to reconstruct a 3D model of the study area. The authors are fortunate to be allowed exclusive usage of the video footage of “Discovery of the World's Mysteries” (a cultural quiz TV program) from TV Man Union for academic research. The three main objectives of the project are: 1. Generation of a 3D point-cloud model of Khufu’s “cave” from video footage. 2. Production of line drawings of the study area for archaeological research. 3. Presentation of archaeological interpretations of this study area. III.
METHOD
Due to the limited conditions permitted by the local authorities, for example the number of people allowed to climb the pyramid and time limitations to stay in the area, only the shooting of material for an introductive TV program was allowed. Almost every frame of the footage targets the guide who keeps explaining and moving around the cave. This footage is of particular value, especially considering that this was only the second opportunity in the world to shoot the cave using a digital VCR in HD quality (the first document was made by the National Geographic Society). Therefore, we attempt to extract additional geometrical information from the cave to assist further archaeological interpretations by using the post- process data of the video footage. The following table shows the specifications of the original data:
Camera equipment Panasonic AG-HMC155 Lens LEICA DICOMAR lens with optical image stabilizer, motorized/manual mode switching, F1.6-3.0 f=3.9mm to 51mm/35mm equivalent: 28mm to 368mm Format of video footage Apple ProRes 422, 1920x1080, linerPCM, 24bit little-endian, 48000Hz Bit rate 21
Mbps (average), 24
Mbps (maximum) FPS 29.97 Volume of data 24.74 GB Data rate 144.43 Megabit/sec
We focused on the background regions of the image sequences that cover almost the entire surface of the cave, while shooting the guide from a variety of viewpoints and angles. Then we came up with the idea of employing a SfM technique to solve two problems at once: stitching the background images, and using them to reconstruct the 3D geometric information of the inner surface of the cave.
A.
3D Reconstruction by Photosynth
We employ Microsoft Photosynth [4] to reconstruct the 3D geometry of the cave. Photosynth is convenient and easy to use and allows us to take digital photos and upload them onto Photosynth website through the internet. Data of 3D point clouds can then be generated for users to download point clouds from the website. The core technique of this application is based on Snavely et al. [5], in which unorganized photo sets can be used for reconstructing 3D scenes from the intrinsic information of the photos and by visualizing the reconstructed scenes on a web browser. The process of scene reconstruction is accomplished by a SIFT (scale-invariant feature transform) keypoint detector [6] and SfM [7].
Fig. 3.Stitched images and 3D scenes by Photosynth that allow for browsing and exploring on a website.
The SIFT algorithm is used for feature extraction from the images and for finding matching images. The SIFT keypoint detector is invariant to image transformations such as scales, rotations, and translations, and thus capable of robustly finding feature points from images shot by different camera positions and angles. SfM aims to recover camera parameters, pose estimates, and provide 3D scene geometry from image sequences. SfM calculates the correlation between feature points in an image pair and estimates the camera transformation during the shooting of the two images [7]. The number of feature points matched by the transformation of the same camera motion is checked by the RANSAC algorithm [8]. The RANSAC algorithm then adopts the majority of the feature points that adhere to the same transformation. When many of the same feature points can be tracked across an image sequence, geometrically consistent matches can be found. Such image sets and feature point sets are registered as a “track” in [5]. To deal with the large number of photos to apply SfM stably, selecting a good image pair to produce tracks
is important. Finding a good image pair is achieved by checking whether many of the feature points can be matched by a transformation that includes a large amount of camera translation, that is, a long baseline for triangulation. In cases where image features that match well are shared by multiple tracks, the coverage of the reconstructed surfaces grows appropriately in the resultant 3D scene.
B.
Application to the cave photos
Twenty minutes of footage was split into thirty thousand image frames out of which we selected three hundred images shot using several smooth motions of the camera, and we used these for the SfM process. Image sequences shot using the same smooth motion of the camera are expected to be used for producing a track in the SfM. Within the track, some clear feature points are consistently included in the images shot by comparatively distant viewpoints so that the many SIFT keypoints are steadily reconstructed as point clouds, and this allows for a higher potential to be connected with that of other tracks. Examples of the image sequences are shown in Fig. 4.
The 3D point clouds produced from the photo set are shown in Fig. 3. We found that the consistent feature points from the static surface of the cave are effectively collected for producing point clouds, whereas most of the inconsistent feature points from the guide are automatically eliminated through the SfM process. Once the point clouds are acquired, we can take advantage of the 3D coordinates in a way that arbitrary portions of the wall surface can be extracted and projected onto a picture plane to produce elevation and ground plans as needed for expressing archaeological interpretations (Fig. 5).
C.
Visualization for Archaeological plans
We also employed a visualization technique called PEAKIT (LANG CO., LTD.). PEAKIT has several features that are capable of enhancing the visibility of the point clouds by (1) auto noise reduction, (2) 3D to 2D orthogonal projection, (3) feature shape detecting and especially, (4) coloring point cloud by using predefined lookup table so as to support archaeological interpretations. Here we applied features (2) and (4) to create 2D images, called Colored Distance Maps (CDMs). For example, Fig. 6 illustrates the CDMs of a plan and sections of the west and south of the target point clouds. The color of the points in CDMs expresses the quantized distance between a point and an arbitrary plane. A warmer color means a shorter distance from a reader’s viewpoint, and a cooler color means a longer distance. The plan is a projection to the X-Y plane, the northern and southern sections are projections to the Z-X plane, and the eastern and western sections are projections to the Y-Z plane
IV.
I
NTERPRETATION
The point cloud data of the cave produced by SfM allows us to trace its shape. However, it should also be noted that this shows points of not only the lowest blocks but also those of higher blocks. Therefore, we used CDM point cloud images generated by PEAKIT that show the depth or height of the area for the production of line drawings of a plan and elevation (Fig. 7). The following points were ascertained:
1. The cave does not show any indication of a breaking down of the structure like “Al-Mamun's breach” located 7m above the northern face of the pyramid's base. In addition, the point cloud image clearly shows that the ceiling stones fit together tightly. Therefore, it seems reasonable to suppose that the cave is an artificial structure. 2. The masonry of this area is not perfectly aligned in orientations like that of the outside; ceiling stones in particular were placed on an irregular base. Interestingly, the sizes of the stones of the cave are quite different from those of the outside. The height of the cave, consisting of two masonry courses, is approximately 2m. The two courses are almost the equivalent of the total height of the three course of the outside: 106th course (63.5-64cm), 107th (63-63.5cm), and 108th (74.4-75.5cm) . The function of the cave has not yet been fully ascertained at this time and to discuss this in details is beyond the scope of this short paper, but this area may have contained fine-grained sand as a packing material, which has already been found inside the great pyramid by a French mission [9]. The structures of the cave and the notch indicate that the pyramid of Khufu seemingly has a core of steps (that is, the “notch”) in horizontal courses of rough masonry like that of the construction of the pyramid of Menkaure (the 3rd pyramid of Giza).
V.
CONCLUSION In the course of this project, we showed that a 3D reconstruction from normal video footage is feasible with SfM. Although the image data produced has no certain scale, orientation, and level as it stands now, it was to a certain extent beneficial for academic research in understanding the masonry of the core of the pyramid. A future challenge will be to identify archaeologically important elements such as a scale, an orientation, and a level in the target. The production of a 3D model with SfM, particularly from existing “video footage” is a rather new methodology in the field of archaeology [10]. One of the unique characteristics of this technique is to produce a point cloud of a structure without a human in the video as his image was eliminated in the SfM process. Moreover, archaeological interpretations of scarce point cloud data can be satisfactorily made with the application of the visualization technique PEAKIT (Fig. 7). We expect that this set of techniques can be applied to not only academic investigation but also to the restoration and conservation of damaged heritage and artifacts. A
CKNOWLEDGMENTS
The authors would like to give special thanks to Mr. Tamotsu Iwagaki, a director of TV Man Union Inc. for providing the valuable video data. We wish to thank Mr. Shin Yokoyama, the president of LANG Co., Ltd., for his generous collaboration in the PEAKIT analysis. We are also grateful to Mr. Takeo Narita, a designer of Narita Seisakushitsu, for his help with design issues. We especially want to express special thanks to Ali El-Asfar, the general director of Giza Pyramids. This work was also partially supported by JSPS, Grant-in-Aid for Scientific Research (24510239).
Rererences/Sources/Photos/Bibliography
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