3D Modeling of Rock-Cut Monuments with Astronomical Elements Using Aerial Photogrammetry

Abstract

This report presents the advantages of using drone-photographic scanning technology as a method for creating 3D documentation and 3D databases of rock-cut monuments with astronomical elements. Through this modern technology, together with specialized equipment and software, we have the advantage of obtaining a digital 3D model of the terrain and the existing archeological sites there. A procedure for digitizing the physical space of rock-cut monuments using integrated technology, in accordance with the standard for such sites, is shown. The data is stored in distributed databases. The digital space provides an opportunity to connect the monument with the celestial sphere, the main movements of the luminaries (Sun, Moon, and bright planets), and specialized astronomical software. Using the 3D modeling method, two Bulgarian rock-cut monuments were studied: the Belintash rock sanctuary near the village of Mostovo in the municipality of Asenovgrad and the cromlech near the village of Dolni Glavanak in the municipality of Madzharovo. It can be seen that the modeling of real archaeoastronomical concepts and the connections between the morphological elements of the monuments and the notable objects in the sky have been proven with a high degree of reliability. For example, rock outcrops and pillars are associated with sunrises and sunsets during the solstices and equinoxes.

1. Introduction

In the Neolithic and Bronze Ages, in a number of regions around the world, local inhabitants created a rock-cut culture. In its older layer, it was expressed in the generation of specific natural rock forms, and later it turned to the creation of processed monuments. First, they carved them into the rocks with the help of harder stone or bronze tools—these are the so-called rock-cut monuments. Subsequently, in many places, independent structures of huge and roughly split (hewn) rock blocks appeared in the form of pillars, slabs, and vertical, horizontal, linear, or circular combinations of these, which are the so-called megalithic sites [1,2].

On the ground, there are both pure megaliths (menhirs, dolmens, and their derivatives) and mixed or quasi-megalithic sites. The mixing can go in two directions:

-

Along with the typical rock-cut and megalithic elements, the site may contain sections executed in classical dry masonry of relatively small stone pieces;

-

Along with the typical megalithic elements, the site may contain sections formed by rock-cutting, incising, and splitting.

Some of the most impressive rock-cut cult complexes have been preserved on the territory of Bulgaria [3]. These are the places in whose sacred territory all possible elements are usually found—rock-cut altars, altars, purification pools, low-relief disks, caves (natural or rock-cut), stairs and platforms cut into the rock foundations of rooms, pole beds of wooden structures, and buildings. Often, but not necessarily, the entire space or its central part is protected by a wall [4]. The most striking examples of rock-cut monuments are “Belintash” near the village of Mostovo, Asenovgrad municipality; “Tangardak Kaya” near the village of Ilinitsa, Kardzhali region; “Harman Kaya” near the village of Dolna Chobanka and “Tatul” near the village of Tatul, Momchilgrad municipality; “Kovil” near the village of Kovil, Krumovgrad municipality; “Markov Kamak” in the Rila Mountains, Blagoevgrad municipality; “Buzovgrad” near the village of Buzovgrad, Kazanlak municipality; and “Zaychi Vrah” near the village of Kabile, Yambol municipality, Kromlech near the village of Dolni Glavanak, Madzharovo municipality [5] (Figure 1).

Rock-cut monuments and megaliths have been preserved with amazing consistency in the principles of construction. In this sense, it could be argued that the spread of the idea of them is the oldest globalization carried out in the world. The first constructive principle used is that megaliths are not created through classical masonry, but by grouping and assembling two main types of building elements—pillars and slabs. The second generally valid principle is that the building elements are so large that they often have the size of the building itself, i.e., their number is minimal [6,7].

From a physical point of view, rock-cut and megalithic sites are interesting in at least three aspects.

1. The first physical aspect is related to the stability of the structure from the point of view of statics—cuttings and tools, stability of the construction, joints between the few but very large building elements, the strengthening role of mounds and rock clusters around, etc.

2. The second physical aspect is related to archaeoastronomy—orientation of the sites in some specific directions that are astronomically significant and directed towards stars, constellations, the Sun, the Moon, sunrises, sunsets, culminations, etc. The orientation is probably related to early mythology or to attempts to create stable calendars [8].

3. The third physical aspect is related to the possibility of their direct dating. Conventional dating in archaeology is related to the found artifacts. However, it is indirect—it dates the last use of the object, but not the time of its creation. Physical dating methods—thermoluminescence (TL), photoluminescence (PL), or optically stimulated luminescence (OSL), and the uranium–thorium (U-Th) method—indicate the very moment of creation of the object [9].

The research, cultural–historical, and religious interest of wide public circles in rock-cut and megalithic monuments all over the world constantly gives rise to research, educational, restoration-conservation, and exhibition-tourist projects for individual objects or groups of them [10].

The beginning of these rock topoi of faith dates back to the end of the Chalcolithic era (around 5000 BC), and their formation as sanctuaries with religious, administrative, and economic functions, belonging to the population of entire regions, marks the ethnogenesis processes of the Thracian and other paleo peoples. Some of these sanctuaries became royal cities (Kabile, Yambol region; the archeological reserve near the village of Sveshtari, Razgrad region; the rock complex between the villages of Perperek and Gorna Krepost, Kardzhali region) or sacred territories with temples and necropolises (the village of Starosel, Hissar region). Such processes are observed in antiquity in other regions of Southeast Europe and Asia Minor.

Ancient Thrace is the contact zone, opened to the south to the Aegean world, to the southeast to Anatolia, to the northeast to the Black Sea steppes and the Caucasus, and to the northwest/west to Central Europe and Italy, due to the Thracian belief in immortality and their role as a “plaque tournante” (rotating disk) between East and West. One of the mysteries of the Thracian rock-cut and megalithic complexes, to which no answer has been given, is why such sanctuaries, described in ancient Greek and Latin sources and philosophical-Neoplatonic treatises and traditionally considered philosophical-religious speculative constructions, are found precisely on the territory of ancient Thrace. The rock sanctuaries and megalithic complexes on the territory of present-day Bulgaria are located mainly in the mountains (Rhodopi, Strandzha, Sakar, and Stara Planina). They show similarities with the rock sanctuaries in the ancient Anatolian cultures (Phrygian, Hittite, Urartian, and Lycian), as well as with the Hellenic, Paleo Balkan, and Italian. The specific thing is that in the Thracian rock complexes all possible elements are found, which are present individually or in combination in the other cultures mentioned above—rock-cut rooms, stairs, sacrificial platforms and sacrificial pits, altars, sacred caves, suns, votive niches, chutes for draining sacrificial liquids, etc. [11]. At the same time, the knowledge of rock cutting was used very rationally to drain the rocky terrains and form stone, wooden, and adobe rooms. It is traditionally assumed that the ancient Phrygians, who, according to Herodotus, migrated from Thrace to Asia Minor and established their kingdom there, brought their veneration of the Mountain Great Mother Goddess, glorified in rock-cut sanctuaries and megalithic complexes, precisely from the Thracian European southeast (the most famous rock-cut complex of the Phrygians is the “City of Midas”). On the territory of Southeast Europe and Asia Minor, rock-cut sacred sites can generally be typified as sanctuaries for the confession of mass mystery rites, sanctuaries for individual initiation rites, sanctuaries for the confession of doctrinal rites of closed societies, sanctuaries with necropolises, and sacred caves for initiation rites through katabasis (“descent into the Underworld”) [2]. Many of the rock-cut sacred sites of the Thracians and other paleo peoples have become hereditary topoi of faith and have been assimilated over the centuries by folk Christianity, and some have been transformed into Aliyan (Shiite) sanctuaries. Many of these topoi of faith are still revered by people of different ethnic consciousness and religious affiliation as holy places [12].

For the most part, the rock-cut and megalithic monuments are registered but have not been documented with modern methods [11]. The difficult accessibility and their remoteness from populated areas further increase the cost of the activities of discovering, documenting, preserving, and socializing the individual monuments. For this reason, the rock-cut and megalithic monuments are not known to the general public but only to a very narrow circle of specialists. The lack of professional documentation for the sites makes it difficult to preserve them, introduce them into a scientific approach, and interpret them in the Eurasian cultural and historical context. This context concerns the overall problem of the Southeast European–Asia Minor–Black Sea–Aegean rock topographies of faith and the formation of the oral “faith-ritualism”, which developed in parallel with the classical literary Olympian religion.

Astronomical study of rock-cut monuments shows that visual observations of the celestial bodies are one of the most ancient technological practices of mankind. The movement of celestial objects determined the living conditions of people. Knowing the basic laws of the movements of the Sun, Moon, planets, and stars in the sky, ancient populations were able to navigate in space and time. This knowledge was also used for their practical needs in compiling calendars, determining the deadlines for various agricultural works, predicting the flood of rivers, rainy periods, the onset of droughts, seasonal winds, etc. In addition, people often identified the celestial bodies with the gods and, due to the nature of the cults to them, they conducted observations on them in particular detail.

In the process of developing observational methods, people learned to create devices for observing celestial bodies. For this purpose, they created stone landmarks in the area, which in later prehistoric eras evolved into complex megalithic and rock-cut monuments (horizon and meridian prehistoric observatories). Long-term observations of celestial bodies were associated with angular sightings of their sunrises, sunsets, and culminations along the line of the only two large circles of the celestial sphere visible to the naked eye—the horizon and the prime meridian. To increase the accuracy of observations, people created conditions for observing the sunrise (sunset) point by building long sighting lines, reducing the aperture of the viewing holes, using the plumb line and the horizontal plane, etc.

The annual celestial cycle is mainly associated with the natural movement of the Earth around the Sun. Visually, it was perceived by man as the movement of the solar disk relative to the fixed stars along a large circle of the celestial sphere (in later times it was called the ecliptic). During its movement, the Sun stops at several special points on the horizon line during the solar year: summer and winter solstices and spring and autumn equinoxes. Along the meridian line, the Sun occupies the highest position relative to the horizon at noon during the summer solstice and the lowest during the winter solstice.

One of the striking technological achievements of prehistoric civilizations is the sighting of sunrises, sunsets, and culminations with the help of megalithic structures and rock-cut structures. Sighting is associated with visually finding the exact direction to a celestial object by an observer standing at a certain place in a specific area. For the accurate determination of the position of the Sun relative to the horizon by the visual method, specific rock structures are required, connected to the line “observer-celestial object”.

To build a sighting line, three classic elements are needed: the observer’s location, a near and a far sight. Usually, the observation site is chosen at a high position, with a good circular view of the visible horizon. To avoid positional inaccuracies, a near sighting was built. It allowed the observer to visually find the point on the visible horizon connected to the specific sunrise. The situational analysis of rock landmarks shows that in order to increase the accuracy of observation, a landscape detail located on the visible horizon line was used: a peak, hill, large stone block, saddle, etc. If natural landmarks were not found in the desired direction, the ancient observer built artificial markers: menhirs and mound embankments, wooden or rock pillars. One of the most important characteristics of long-range sights is their angular size, which determines the accuracy of aiming. Therefore, long-range sights were chosen to be as far away from the observer as possible but still within the limits of clear visibility. The presence of two fixed markers set an axis of aiming that was independent of the observer and repeatedly reproducible in subsequent observations. When reducing the distance from the observation point to the nearby vizier, the latter was often neglected by ancient observers, at the expense of more accurate fixation of the observer (located on a rock throne, on a narrow rock platform, enclosed between two rock blocks, etc.).

All this allowed the ancient observer to see with the naked eye the angular position of the Sun relative to the horizon while standing facing it. The system of near and far markers facilitated observation and increased its accuracy. This method of observation is often called the method of direct sighting of the Sun (the luminary). There is also a method of reverse sighting, in which the observer has his back to the Sun and observes the Sun’s rays passing through an opening of different size and shape. These rays, formed into a beam, are projected onto a rock surface on which signs are cut to determine the exact moments of angular coincidence of the sun’s projections. In addition, two types of sighting are fixed on the ground: linear and multiazimuthal. Linear sighting schemes allow one to three significant astronomical directions to be fixed. Multiazimuth sighting schemes allow for the fixation of four to 20 significant astronomical azimuths related to the positions of the Sun, Moon, and bright stars relative to the local horizon line or the prime meridian at the observational site.

In the last few years, the open source planetarium program Stellarium has gained great popularity in research and hypothesis testing in archaeoastronomy [13]. The program has significant application possibilities in the virtual 3D study of the specific architecture and landscape of archaeoastronomical monuments from any prehistoric period. Virtual archaeoastronomy with Stellarium allows 3D visualization of reconstructed megalithic and rock-cut structures in paleo-landscape reconstruction using computer graphics. The astronomical software is able to merge such 3D models together with the celestial sphere and objects on it at astronomically simulated positions in a specific historical era. Such a system is used for accurate visual simulation of astronomical situations potentially related to the orientation and structure of these monuments. This allows researchers to discover and/or better understand astronomical patterns of orientation and the astronomical objects that were observed from the monument. The software also allows for the study of light and shadow projections caused by sunlight or moonlight and related to the specific relief and architectural elements of the monuments [13].

The aim of our work is to create 3D models of two megalithic monuments of archaeoastronomical interest using unmanned aerial systems (UASs), photogrammetric methods for mapping, and the Structure from Motion (SfM) image processing method. First, in the Materials and Methods section, we consider drone technology with the use of digital cameras and appropriate software and methodology, which allows obtaining accurate digital spatial products for rock-cut monuments. In the Case Study section, we consider obtaining 3D models of two rock-cut monuments with astronomical elements—Belintash rock sanctuary and the cromlech near the village of Dolni Glavanak.

2. Materials and Methods

As one of the best representatives of two types of rock-cut monuments in Bulgaria and Europe, associated with astronomical practices for observations of the Sun in its extreme positions relative to the celestial equator. In prehistory, the Belintash rock sanctuary near the Municipality of Asenovgrad (horizon observations) and the cromlech near the village of Dolni Glavanak, Municipality of Madzharovo (meridian observations) have been studied using several methods of investigation.

2.1. Use of Unmanned Aerial Systems (UAS)

In this sense, the filming, documentation, and visualization of objects of the cultural and historical rock-cut heritage in Bulgaria has an expanding field of application. Modern unmanned aerial systems (UAS) offer a technology for obtaining geometric information about archeological sites, rock-cut monuments, and megaliths from images using various types of sensors. The use of digital cameras built into mid-range UAS, together with appropriate software and methodology, allows obtaining accurate digital spatial products for rock-cut monuments.

The objects selected by us by type and current condition do not imply the possibility of reconstructing their geometric structure only from metric data (geodetic measurements or data from map sources). For this reason, it is better to apply a technology for three-dimensional reconstruction based on data from remote sensing—photogrammetric shooting with an unmanned aerial system (UAS) or the so-called aerial photogrammetry.

Remote data collection methods of this type allow the creation of detailed three-dimensional models of historical monuments or archeological sites, showing their condition over time. This allows not only to record each stage of their study but also to analyze changes over time [14]. Remote sensing methods and three-dimensional modeling of objects using this data can be called three-dimensional, precise digitization of the relevant monuments, which constitutes an important digital archive. This archive serves to preserve historical data about the object but can also be the basis for its restoration in the event of events leading to damage, destruction, or subsequent socialization.

2.2. Photogrammetric Methods for Mapping Rock-Cut and Megalithic Monuments

Automated aerial and close-range digital photogrammetry have become powerful and widely used tools for three-dimensional topographic modeling. The development of algorithms for modeling the surface of the monument and its adjacent terrain, through digital image processing, radically improves the quality of data about the monument and the terrain [15]. Also, the decline in the price and improvement in the quality of compact cameras (SLR—Single-Lens Reflex Camera), as well as the methods for calibrating such non-metric cameras, leads to a wider use of photogrammetric modeling and the development of a wide range of software applications used to process the data.

2.3. Image Processing Method–SfM

The Structure from Motion (SfM) method is based on matching features (points) in multiple overlapping images to simultaneously and automatically solve for the three-dimensional camera position and image geometry [16]. The SfM method is based on the principles of photogrammetry, in which a significant number of photographs taken from different overlapping viewpoints are combined to recreate the studied rock object—i.e., a 3D structure is obtained from a series of overlapping images.

However, the SfM method differs significantly from traditional photogrammetry. While classical photogrammetry relies on overlapping image strips obtained from parallel flight lines, SfM reconstructs the three-dimensional geometry of rock features from random (unordered) images. An important condition is that a physical point of a rock feature is present in multiple images. The principle of using randomly positioned images is possible thanks to advances in automatic image matching. For example, the scale-invariant feature transformation SIFT [17] is one such approach, where the key approach is the ability to recognize a specific physical feature present in multiple images regardless of the scale (i.e., resolution) of the images and the viewpoint of the image. Classical photogrammetry relies on images with the same resolution due to the image correlation-based processing approach. These approaches rely on cross-correlation, calculated with a simple image convolution operator, between pixel samples from two images. As a result, these cross-correlation methods are very sensitive to changes in image resolution. Furthermore, the use of image brightness and color gradients in algorithms such as SIFT, rather than absolute pixel values, means that an object can be identified by being registered from many viewpoints [16].

Another fundamental difference between classical digital photogrammetry and SfM methods is the need for ground control points with known coordinates. In classical photogrammetry, the coordinates of the control points are needed to solve the collinearity equations that define the relationship between the camera, the image, and the ground surface. The external orientation elements determine the spatial position and angular orientation of the camera at the time of creation of a given image.

In the SfM method, camera positions and orientations are automatically solved without the need to first have a grid of control points with known 3D coordinates [18]. Instead, they are solved simultaneously using many repeated iterative batch alignment procedures that are based on a database automatically extracted from the overlapping images [19].

2.4. Workflow for Applying the SfM Method

The ease of use of the SfM method, its accessibility, and the automated algorithm it provides make it convenient for a large group of users. With a simple digital camera and processing software, 3D point clouds and orthophotomosaics of the studied rock objects can be created. There are several photogrammetric programs using the SfM method. The most popular commercial solutions include Agisoft Photo Scan and Pix4D, which have become popular due to their user-friendly interface and support. There are also open source SfM solutions, which include Visual SfM, OSM-Bundler (software for reconstructing a 3D geometry from a set of photos, OpenStreetMap, for example), Photosynth Toolkit, OpenDroneMap, etc. While SfM programs differ from each other, they all follow a common workflow. The following workflow was developed by Rossi et al. [20]. Open source software varies depending on the program. Some allow several steps to be performed, while others have only one step and must be combined with additional modules and software products.

3. Case Study

Here we present the obtaining of 3D models of two rock-cut monuments with astronomical elements—Belintash rock sanctuary and the cromlech near the village of Dolni Glavanak, refs. [21,22,23]—using drone-photographic scanning technology (Figure 2a,b).

The drone we used, the DJI Inspire 1 Pro, was equipped with a Micro Four Thirds CMOS sensor, and a Micro Four Thirds lens mount, and a 3-axis stabilization system. The Inspire 1 Pro is equipped with a GPS-based stabilization system that is able to maintain the position of the aircraft even in particularly difficult flight conditions (wind speeds up to 45 km/h).

The camera of the Inspire 1 Pro–Zenmuse X5 records DCI 4k-4096x2160/23.98 p. It allows the capture of 16 MP images, with a resolution (spatial resolution) of 10 cm/pixel. In total, about 24,000 images were taken for the entire process of capturing each individual object (about 12,000 for each).

The drone’s flight mode was chosen to be linear-progressive, flying at a height of 30–50 m above each site. Given the characteristics of the adjacent terrain, the horizon, and the objects to be photographed (hilly terrain with mixed forest and low-stemmed vegetation in combination with a relatively high object), it was necessary to conduct two different types of photography flights. The first flight was a “double photogrammetric network” type to cover and model the entire territory. In the presence of vertical and hidden surfaces (such as the walls of the Belintash rock plateau and the individual upright stones of the cromlech), additional photography of the vertical elements was necessary. For this purpose, an additional free flight was carried out around the monuments, as well as photography of specific structural elements of them. The photos from both flights were reviewed and combined into one package for post-processing. Six ground reference points from the terrain were used.

3.1. General Stages of Work

The activities carried out include the following steps in the workflow for three-dimensional modeling:

(a)

Preliminary preparation:

-

Localization of the study areas, selection of specific rock-cut and megalithic sites, stabilization, and measurement of ground control points (GCP).

(b)

Photogrammetric shooting:

-

Selection of UAS;

-

Preparation of a flight plan with UAS;

-

Performance of flights and shooting of the rock-cut site and cromlech (Figure 2a,b).

(c)

Data processing:

-

Generation of digital products from the processed data;

-

Creation of vector metric data for the sites;

-

Three-dimensional modeling and visualization of the sites;

-

Development of a simplified three-dimensional model of the rock-cut monument “Belintash” near the village of Mostovo and cromlech near the village of Dolni Glavanak (Figure 3a,b);

-

Integration of the three-dimensional models into the specialized astronomical software Stellarium 25.3, obtaining the possibility of virtual astronomical observations in the supposed era of creation and functioning of the monument, as well as during various prehistoric periods of interest to the archaeoastronomer–researcher.

3.2. Image Processing and Creation of 3D Models

Step 1: The first step after shooting the sites is the selection of the desired images to be processed. We must have consecutive images that cover the rock-cut object. When using images captured with a UAS, an important condition is that there is such an overlap of the images that the selected object is present in multiple images. Algorithms for matching characteristic points rely on this principle, and therefore, the greater the overlap of the images, the more matches will be obtained during processing.

Step 2: Feature extraction procedure—after the images are imported into the processing system, an algorithm for extracting basic features must be executed for each image. This step generates a set of descriptors (control blocks) for each image. A descriptor is an identifier of a key point that distinguishes it from the rest of the mass of single points. In turn, descriptors must provide the invariance to find a correspondence between single points with respect to image transformations. There are numerous feature extraction algorithms, the most common of which is SIFT (Scale Invariant Feature Transform), developed by Lowe [17]. SIFT provides robust descriptors under various image conditions and is an algorithm that transforms an image into a large collection of local fundamental vectors, through which invariance (an unchanging feature of a single unit that unifies its variants) is obtained. Invariance is with respect to translation, rotation, scale, and partly for the illumination of the objects [24].

Step 3: Feature matching procedure—the next step in the SfM workflow is to create a feature matching table that connects all combinations of descriptors between the images. The goal is to calculate the connection points or correspondence between the images. The process of comparing two images can be described by the following sequence:

-

The main points and their descriptors are selected from the images;

-

By matching the descriptors, the corresponding key points are allocated;

-

Based on the set of matching key points, an image transformation model is built, through which one image can be obtained from the other.

This step can be computationally heavy due to the number of required comparisons of a large amount of data. The process can be run in parallel and divided into separate tasks. Multi-core or clustered computing environments can be used to reduce the required computation time [20].

Step 4: Group alignment procedure—group alignment is a solution for refining the visual reconstruction to create a mutually optimal 3D structure and camera parameters (http://www.theia-sfm.org/sfm.html (accessed on 5 September 2020), modified procedure). As a result of the large number of identical points identified during the automated image matching phase, SfM can solve the collinearity equations in an arbitrarily scaled coordinate system. In addition, the processing process also calculates the elements of the camera’s internal orientation (focal length, principal point coordinates, radial and tangential lens distortion, and other characteristics) (Figure 4a,b).

The intermediate stage in the SfM workflow is to obtain a point cloud (initial sparse cloud) with local X, Y, and Z coordinates that are not in the real coordinate system. At this point, GCP coordinates (ground control points) and/or camera position GPS coordinates are entered to transform and register this SfM point cloud to an established coordinate system (World Geodetic System WGS, International Terrestrial Reference System ITRS, or European Terrestrial Reference System ETRS). This transformation is linear and rigid and produces a point cloud suitable for mapping applications.

Step 5: Procedure for generating a dense 3D point cloud—as a result of the batch alignment, the camera parameters for each image are obtained, and a sparse three-dimensional point cloud is generated for the studied rock object. With these parameters, the 3D cloud is densified. The cloud compaction process uses the parameters (elements of internal and external orientation) of the camera, the correspondence between the 2D images, the features around the 2D correspondences, and the triangulation algorithm to extract 3D points for the rock object [20]. Such a frequently used system is PMVS an algorithm for reconstructing 3D scenes from multiple 2D images by analyzing patches of pixels proposed from Furukawa and Ponce [24].

Step 6: Surface reconstruction procedure—for the reconstruction of the object surface of the rock monument, the “Poisson Surface Reconstruction” algorithm can be used, through which we obtain a textured surface from the generated 3D point cloud (with oriented normals). This is an approach that expresses the surface reconstruction as a solution to the spatial Poisson problem [25]. This step results in products such as orthorectified images (orthophotomosaics) and three-dimensional textured surfaces [26].

Step 7: Visualization procedure—after obtaining the digital products in the previous stages of the SfM workflow, the last step is their visualization. Commercial software packages, such as Agisoft PhotoScan and Pix4D (https://gmv.cast.uark.edu/photogrammetry/photogrammetry-software/agisoft-photoscan/ (accessed on 5 September 2020), https://www.pix4d.com/product/pix4dmapper-photogrammetry-software/ (accessed on 5 September 2020)) have built-in visualizers of 3D clouds and textured surfaces. The open source program Blender has been used for additional processing of 3D point clouds and surfaces, as well as for their visualization (https://www.blender.org/ (accessed on 5 September 2020)). In our case, the SfM image processing method was applied to model the structue of the terrain surface of the rock-cut monument “Belintash” near the village of Mostovo and the cromlech near the village of Dolni Glavanak, Madzharovo Municipality [27,28].

3.3. Results

In this study, the created 3D models of the rock-cut monument “Belintash” near the village of Mostovo and the cromlech near the village of Dolni Glavanak, Madzharovo Municipality, are presented as separate visualizations. In order to reach the final product of our work—3D models of archaeoastronomical monuments—an orthophoto mosaic for the area with a spatial resolution of 5 cm/pixel is built as an intermediate product in the computer’s memory as the basis for obtaining a Digital Surface Model (DSM) shown on Figure 3a,b and a Digital Terrain Model (DTM) shown in Figure 4a,b.

This is followed by a procedure for embedding the 3D model in the specialized astronomical software Stellarium, which provides virtual access for astronomical observations from specific points on the territory of the studied monuments during their existence (Figure 5a,b).

Screen visualization is important for the presentation, research, and detailed restoration of the monuments. It can be a static rendering (photorealistic visualization), a dynamic animation (made from multiple sequentially arranged photorealistic images), or an interactive viewing of the object using the VRML (Virtual Reality Modeling Language) format.

4. Discussion

In this study, remote sensing with a DJI Inspire 1 Pro drone equipped with a Micro Four Thirds CMOS sensor and a Micro Four Thirds lens mount and a 3-axis plus GPS-based stabilization system has been successfully applied to obtain high-precision spatial data of the rock-cut monument “Belintash” near the village of Mostovo and the cromlech near the village of Dolni Glavanak. These are typical archaeoastronomical monuments from the territory of Europe, related to horizon and meridian observations of the Sun in its extreme positions relative to the celestial equator.

The first of them—“Belintash”—demonstrates a developed technique for linear sighting, with very good positioning of the near and far sights. The orientation of the sighting lines coincides with sunrises of the Sun during the solstices, and for a far sighting at the summer solstice, a special stone mound was built, in the upper part of which a large amount of wood ash was discovered (probably the remains of a ritual fire). On the rock plateau “Belintash”, where the prehistoric observatory was developed, one can see the observer’s place, the foundations of sighting pillars, and various ritual rock elements such as altars, ritual pits, cylindrical wells, chutes, etc.

The rock-cut structures of “Belintash” give the possibility of relatively high accuracy in observing the sun throughout the year. Determining the moments of the solstices and equinoxes allows for the division of the tropical year into four parts (almost coinciding with the seasons). The use of relatively small angular peaks and saddles along the line of the local eastern horizon allowed ancient observers to achieve an accuracy of about 5ʹ. Sighting was performed using closely spaced benchmarks, located linearly at different distances from the observer. Increasing azimuthal accuracy was achieved by placing two benchmarks close to each other so as to obtain a narrow strip to limit the observer’s visual angle to the line of the visible horizon [29].

The other rock-cut monument studied in this work is a cromlech near the village of Dolni Glavanak, Madzharovo Municipality. It is located on a relatively high peak, with an excellent circular view of the local horizon [22]. The local horizon for an observer standing in the center of the cromlech or next to some of the standing stones provides numerous landscape landmarks, coinciding with characteristic sunrises of the Sun. Thus, the sectoral arrangement of the stone circle connects the standing structures of the cromlech in a system for horizon astronomical observations. Accuracy of the observations also increases to about 2ʹ, due to the formation of narrow observation windows for an observer standing at certain positions outside the stone circle. In addition, the cromlech expands the possibilities for observing sunrises and culminations of the Moon and heliacal sunrises of bright stars at any time of the solar year [28].

This allowed for the sighting of 18 to 32 significant sunrises and sunsets with great angular accuracy. Such a two-sight scheme for direct and reverse observation of sunrises was also universal as an instrumental basis, which enabled observers to measure time intervals in the range of a solar year, month, day, and within short time intervals of up to 5 min. This achievement remained unsurpassed until the invention of the gnomon, which allowed the direct and reverse sighting methods to estimate time intervals with an accuracy of up to 1 min.

Much of archaeoastronomical research is concerned with the assessment of the azimuthal orientations of artificial or sometimes natural structures in order to find correlations with potential astronomical targets, such as the rising/setting of luminaries or the interaction of light and shadow on certain dates, such as the solstices and equinoxes. Given the difficulties of observing such structures over months or even years, it is necessary to record or reconstruct the structure in question and introduce a virtual 3D model into the Stellarium computer system, capable of accurately depicting the sky, the pattern of the observing site, and the effects of light and shadow depending on the chosen astronomical simulation, including the situation at other time intervals.

The ability to load a properly georeferenced and accurate 3D model into a virtual space and identify and observe lines of sight, combined with the reconstruction of past sky panoramas, or to observe light and shadow effects that would have changed over weeks and months in just minutes after simulation, can clearly illustrate and demonstrate these phenomena to a wider audience. Similarly, archeologically sound virtual reconstruction beyond today’s often deteriorated condition can be used to recreate the likely appearance of the site in the past.

For processing the results of photogrammetric shooting, special attention has been paid to the application of methods for obtaining three-dimensional models from non-metric cameras, using international experience in this area.

The results of processing using the SfM method and three-dimensional modeling software show that the technology used is applicable to a significant extent for digitization, three-dimensional modeling, and visualization with high accuracy of rock-cut monuments and megalithic structures with a complex design. Digitization is important, on the one hand, for the preservation of cultural and historical sites with archaeoastronomical content, and on the other hand, for the creation of a spatial database that allows for analysis and development of three-dimensional visualizations and applications. Once we have an archive of precisely digitized 3D models of the monuments, we can always compare them with their current state and analyze the changes that have occurred over time—information needed for their restoration.

Aerial photogrammetry with UAS in combination with appropriate software applications has been shown to be a successful tool for documenting and analyzing difficult-to-access rock-cut and megalithic monuments of archaeoastronomical interest.