Pixel matching technique used for restoration of Mediterranean historical buildings Open Access

Despite its relatively small three-dimensional (3D) pixel size, the pursuit for the accurate royal cubit of the Grand Pyramid, the Cheops Pyramid, reveals distinctive features of constructability. For instance, it possesses a north-south square base in its perpetual segments. The ‘Great Pyramid’ has become synonymous with paradoxes and attracts theorists (Petrie, 1883). Egyptologists concluded that the construction of the Cheops Pyramid took place during the twenty-sixth century BC and spanned approximately 27 years (Tallet, 2017).

Hence, it is pertinent to uncover the accurate royal cubit dimension to establish the minimal correct dimensional parameter for any form and graphical representation.

In Figure 1, the Pyramid’s volume is represented as 6 R_c³, with a base of 5D pixel R_c side and a height of 5D pixel R_c. Therefore, the volume can be calculated as follows:

R_c³ = 0.144, R_c = 0.5241482788 m

R_c = 52.41482788 cm (value 1)

Value 1 signifies the most accurate and precise dimension of the royal cubit that has not been discovered or identified by any researcher or explorer before.

Notably, value 1 corresponds to the dimension of the King’s Chamber (see Figure 2 for more clarification), which is 5.24 m, and this dimension is ten times the value of R_c extracted from our above equation.

In this context, the pixel’s dimension is defined as 524.1 mm. In the above exploration of the dimensional jewel and in hand with this research, the protection and regeneration of historical buildings can reduce the loss of people’s cultural places. This also promotes confidence and mutual protection of any sequence in the architectural constructability norms (Li and Han, 2021).

Hence, the quest for a metric jewel that interpolates across any of the unforeseen historical built environment has become possible given the below research approach.

The interplay between advanced construction algorithms, architectural pixel form and the sustainability of historic buildings is deeply intertwined with the Mediterranean historic buildings, particularly in the context of the constructability code for fully compressible structures.

Toward the end of the twentieth century, the debate surrounding equations and their application became a central topic in architectural practices as the latest wave of advanced technology, notably artificial intelligence, emerged. Thus, our focus lies in distinguishing between natural and artificial architecture.

Efforts to enhance building performance have led to investigations into incorporating natural materials (such as sandstone, limestone, natural lime, granite, timber and grave.) and energy sources with minimal environmental impact, particularly in historic structures. However, there remains a need to establish a precise methodology for achieving this goal.

Indeed, it is not a matter of chance that landmarks like the Grand Pyramid have endured – their continued existence results from carefully considering environmental factors and applying advanced techniques such as the exact plumbing tools, own type and form of dimensions, perfectly sealed joints using sharp chisels, most precise alignment towards the North using the magnetic compass, wooden posts for alignment, knowledge of sun path and its equinox and advanced astrology studies. As a result, these buildings reduce energy and time consumption, pollution and operational costs.

This implies that the master designer likely had methods for regulating the energy and effort required for such a building. Consequently, this would entail a more robust and demanding set of guidelines and objectives for designers.

The climate is a significant influencer in regional architecture, profoundly impacting customs, philosophical concepts and construction methods. Achieving a nearly thermally stable state in the Grand Pyramid should be regarded as an advanced stage in the evolution of local architecture. Thermal conditions, if not addressed, can lead to significant problems (Andersen et al., 1992). Most of the problems of thermal fluctuation can be encircled around the expansion and contraction of joints and materials, which will lead to the collapse of sealed joints and infiltration characteristics of buildings and, in the end, impose permeability of water and air, which will end in high humidity inside the buildings and fail in maintaining fixed temperature in the interiors.

The response, however, will be tailored to the specific site, primarily addressing the prevailing natural conditions.

The climatic elements that can be influenced by thoughtful material and built-form design encompass air temperature and humidity, radiant temperatures (surface temperatures exposed to visitors), opportunities for natural ventilation, shading and daylight, solar exposure and the potential for solar energy utilisation.

Designers control the town’s topographical features, building density, distances between pyramids, orientation, landscape design, building colours and material selection (choosing between heavyweight and lightweight materials).

This approach seeks to create a dynamic thermal, air quality, acoustic and lighting environment that acknowledges the need for varied landscapes.

As one of the critical factors, the choice of construction materials will play a pivotal role in developing new buildings. The primary objectives are that the selected materials should be suitable for the local climate and the desired climatic response, be locally sourced, have low embodied energy, leverage local construction skills, be recyclable and align with the chosen structural approach.

Advancements in construction technology have continually harnessed the advantages of using stone as a building material due to its durability, aligning well with contemporary needs for resilience against natural factors. In the case of stone structures, there are many examples of implementing additional back and reinforcement at the four corners in the case of cross-vaults or supporting both sides in barrel vaults, and in other areas, certain buttresses exist to act against lateral forces.

In terms of innovation, when compared with the historical development of stone as a construction material, the discovery of patterns and principles governing the placement of such stone blocks marked a significant leap forward.

Over time, the embedded information within these buildings has been collected and integrated. It is now feasible to transform this knowledge into a modular pixel arrangement, much like modern architecture, which can leverage these technologies and attain new sensory qualities.

Across several regions, pyramid-building techniques have enabled structures to prosper in challenging environments. Typically, these techniques adapt to seasonal variations and use locally available materials. Consequently, such buildings are inherently responsive to their environmental surroundings in design.

The closed square base housing development, constructed using accumulated dry-stone techniques, involves setting masonry without bonding agents, which reduces the likelihood of cracks.

This masonry seamlessly integrates with its environment, forming an organic unity. This concept applies to closed chambers in general. Construction materials are sourced from the site, and the simple, closed shape of the Pyramid effortlessly blends with the natural landscape.

By utilising pixelated modular elements, the Pyramid’s final pattern is effectively preserved, enhancing the visual appeal of this iconic structure. The substantial construction also provides excellent thermal insulation. A shaft opening ensures continuous ventilation, avoiding large wind drafts.

The fortunate alignment of the Pyramid in parallel to the north-south direction following the magnetic contours unfolds various possibilities. In summary, pyramid architecture demonstrates a profound understanding of climatic factors, resulting in practical solutions for building construction.

The quality of pyramidical architecture can be attributed to three key factors: scale, massing and spatial design.

The massing is particularly commendable and achieves a harmonious integration between the Pyramid and its surrounding landscape. This harmony is rooted in the straightforward prismatic design and the commitment to a consistent scale. This scale establishes a repetitive rhythm of mass and void, seamlessly covering the terrain without disrupting its natural relief.

This architectural monument underscores the self-sufficiency of local architecture, expressed through various convincing, regionally rooted construction traditions.

The balance of massing and the harmony of forms in such landmarks serve as exemplary models. The arrangement of the pyramids reflects a profound understanding of the environment and showcases a remarkable sense of balance.

The unity between construction and the natural landscape has persisted for centuries, even though the stonemason’s trade and the craftsmanship of working with stone are declining.

The Mediterranean historical architecture also reflects a sense of harmony and proportion, inspiring new building designs that manifest in diverse forms, all in harmony with their surroundings.

In ancient times, architects and engineers designed their projects with a deep understanding of local conditions, available resources and the fundamental principles guiding renewable energy and materials.

They considered multiple factors, including the choice of materials, construction techniques, production methods, transportation, assembly and disassembly of building components, all while evaluating the energy content and the materials’ life cycle.

Load-bearing structures and building exteriors are excellent examples of durability, ensuring efficient use of materials, labour and energy while minimising disposal costs.

Building elements served as a passive means to incorporate constructional, design, modular and dimensional requirements, all of which are subject to additional considerations related to durability.

In this manner, architects and engineers collaborated across various specialities to create a comprehensive plan and strategy based on well-informed decision making.

Traditional methodologies often examine problems from multiple dimensions, going beyond the conventional two or three dimensions.

Therefore, when it comes to designing the information for any building, it necessitates a profound understanding of its construction norms and material characteristics, as discussed earlier.

The vast amount of information that a historic landmark like the Cheops Pyramid represents conveys valuable lessons about structural innovation and the embedded mathematical codes, making it one of the most significant human-made structures symbolising the universe’s mysteries.

The Cheops Pyramid, along with many fully compressible buildings in the Mediterranean, may be one of the last of its kind, exemplifying the architecture of information or, more precisely, an information-rich structure.

The pixel code, referred to as the Modulor and established in this section, has been projected onto various architectural landmarks in Baakleen village, which date from the eighteenth and nineteenth centuries and even as far back as the seventeenth century.

Fortunately, the Modulor is evident in various buildings through architectural elements, structural components, floor-to-floor levels, functional layouts, wall-to-wall plans, façade typologies and ceiling heights.

In addition, it was found that building blocks constitute approximately 40% of the total built-up area, leaving 60% as void space in buildings. This finding aligns with the conclusion regarding the significance of void in the spatial constitution, marking a novel discovery in the author’s research.

The standards in this section, based on the Modulor, are consistent with building elements. This new finding has not been previously discussed or identified in earlier literature, denoting this paper as the first publication to determine such a code.

The methodology seeks to establish the ideal building code for Mediterranean villages and cities by examining the spatial regulations of local architectural styles. It aims to derive an optimal model that benefits the community and individuals, thereby advancing toward the most effective representation of residents’ interests by ensuring public health and safety.

In addition, this publication aims to identify the vital influential elements shaping the daily functional interactions of residents, merchants and institutional figures.

The methodology involves conducting a comprehensive 3D survey of Baakleen’s houses, landmarks and institutions, gathering relevant data from each structure. The data are then transformed into an engineering and architectural code aligning with local and international standards for future compliance.

The conclusion highlights the best spatial configuration and its impact on the local regulatory aspects of architectural practice. By extracting this ‘Modulor’ from various historical buildings in Baakleen, the study aims to restore the authenticity of architectural practice among local architects.

Over the past five centuries, Baakleen’s historical builders have dedicated themselves to mastering the construction of compressible structures and aligning with the regional structural vocabulary of the eighteenth and nineteenth centuries. This journey has necessitated the authors’ efforts to document these historical remnants through an initial 3D scan, digital analysis, visual assessment and further extrapolation to guide future developments.

The substantiated Building Code addresses a comprehensive range of elements, including structural strength, life safety, energy conservation, accessibility, ventilation, adequate lighting, sanitation and means of egress.

The above applies to all types of occupancies, whether single-family or multi-family and includes studies of townhouses that may be attached to single- or multi-story buildings.

In every building, the occupant load for any building design, as per the International Building Codes (IBC), should not exceed one person per 0.47 m² of usable floor space, which, when converted into the Modulor system, equals ((13 × 0.5241)/10)².

The Lebanese habitats and dwellings, especially those dating back to the early nineteenth century, serve as preserved sociological artefacts of their time.

We have substantiated a prototypical residential unit that adheres to the modular grid type based on the royal cubit value detailed in the author’s previous publication on the golden royal cubit, which measures 0.5241 m (Ghoussayni et al., 2021). For visual representation, refer to Figure 3.

The figures below illustrate the Modulor Lebanese residence, designated as Prototype 1, built in Mount Lebanon during the nineteenth and twentieth centuries.

Therefore, this prototype adheres closely to essential standards regarding floor area and occupancy requirements stipulated by the IBC. It also outlines the suitable number of occupants for a family dwelling.

These Lebanese habitat prototypes, particularly those from the early nineteenth century, serve as authentic sociological records frozen in time.

The residence features four primary rooms, each designed to be modular and uniform, with a central hall running longitudinally through the entire building.

The number of residents/occupants is determined based on the following calculation, which is aligned with the IBC. Refer to Figure 4 for details. The maximum modular floor area allowance per occupant (residential) is 17.58 m² gross, whereas the maximum floor area allowance in IBC per occupant (residential) is 18.6 m² gross (refer to Figure 5 for more clarification). The gross area is calculated by multiplying 64 by the area of each module (0.5241 × 0.5241 m). With 27 by 20 grids, the total area equals 148.3276 m², accommodating 540 area modules.

The distance between the distant rooms measures 15 m, while the closer rooms are approximately 9 m away. Consequently, the distant rooms serve as a seating area and kitchen. The seating room can accommodate up to 15 occupants. However, the rooms near the entrance function as bedrooms with a capacity of six occupants, prioritising their evacuation in case of a fire scenario before the seating rooms, where the traffic flow is optimised for net-zero congestion. Refer to Figure 3, where the 15 m travel distance is highlighted in red and the 9 m travel distance in green.

Regarding the built-up area of this prototype, it totals 161.5123 m², comprising 41.2021 m² for walls and 23.40282 m² for the area occupied by columns, leaving a void area of 96.90738 m². Thus, the void area constitutes approximately 60% of the total built-up area. Refer to Figures 4 and 5 for more clarification.

On the other hand, the stair clearance beyond the handrail measures 1.2054 m, as depicted in Figure 8. This value aligns closely with the IBC standard of 1.2 m. The stair dimensions in this book adhere to the Modulor of 0.5241 m, highlighting the slight deviation from the IBC standard.

The Modulor human is calculated to have dimensions of approximately 1.7 m in height and 0.5241 m in width, as illustrated in Figure 6. In a standing position, the hands can extend up to 2.0 m.

Furthermore, the ceiling height in Prototype 1 measures 4.7169 m from the floor finish to the ceiling level. This ceiling height aligns with the 15-m path and the 9-m path.

The Modulor slope is designed to be 1:20 for ramps, meaning the ramp’s length is 10.482 m with a vertical rise of 0.5241 m, as depicted in Figure 7.

The handrail height is 1.048 m, twice the Modulor module height of 0.5241 m.

The ‘Modulor’ continues to establish a universal standard for human dimensions, providing a consistent scale for residents.

The 1:20 slope is exceptionally accommodating for disabled individuals and wheelchairs, calculated based on the modular length relative to the modular height difference.

Similarly, the staircase dimensions, including the tread and riser, adhere to the modular dimensions of royal cubits. Refer to Figure 8 for more clarification.

The egress path measures 1.0482 m, compared with the IBC standard of 0.912 m. Refer to Figure 9.

Similar considerations apply to wheelchair dimensions, as illustrated in Figure 10.

The pedestrian behaviour within the residence varies in open-air spaces, where the corridors’ shading coefficient can influence public actions, particularly in high-temperature conditions. In such cases, most pedestrians prefer shaded pathways, and this factor needs to be considered.

Multi-level corridors and residences should account for the distribution of pedestrian traffic based on age, gender and travel distance, incorporating vertical conveyance options such as elevators, escalators and staircases.

Similarly, on a single level, the design platform should consider age, gender and travel distance as crucial factors in connecting rooms and other areas.

Considering age differences, it is important to recognise that people at different life stages exhibit varied acceleration factors, such as walking speed and interests. This variation leads to distinct movement patterns, with children often walking in circles and adults having more linear paths.

In addition, gender is a factor that cannot be overlooked, especially in residential facilities that may be oriented toward men, women, or children. Women often tend to move in multiple directions, seeking various movement options, whereas men typically follow straighter, more defined paths. Therefore, it is essential to consider these differing trajectory patterns in the design and planning of residential spaces.

When considering travel distance and level changes, the choice of ramps, stairs, escalators or elevators can significantly impact transitions. Accessibility for disabled individuals must be prioritised, as their transition speed differs from younger generations. Refer to Figure 11.

Cultural differences can also influence group behaviour, necessitating careful consideration in the design process.

In addition, the author should examine emergency scenarios, such as earthquakes or fires, to ensure that corridors can function as effective refuges, surpassing the standard residential or pedestrian requirements in normal conditions.

This prototype is a stepped Lebanese habitat designed to accommodate site steepness constraints.

We have substantiated a prototypical residential unit that adheres to the modular grid type based on the royal cubit value detailed in the author’s previous publication on the golden royal cubit, which measures 0.5241 m (Ghoussayni et al., 2021). Refer to Figures 12 to 16 for visual representation.

The findings are encouraging as they substantiate the historical records and prove that 3D scans have paved the way for a new dimension of the historical establishment.

Indeed, it is the most accurate and precise depiction of the actual geometric composition of such historic buildings, which made it possible to reach inaccessible locations using computer software and facilitated the illustration of the fourth dimension in discovering the building’s timely erection of its blocks.

The other finding represents the actual symbolic integrity, reflected in how the building blocks are arranged and can be easily captured, counted and analysed using software such as Recap and AutoCAD. Furthermore, the model in 3D space can be browsed in all directions and zoomed up to a millimetre scale.

Building information modeling models could be drawn with the help of a point cloud originating from the laser device. Energy models are now available to study the energy efficiency factors facilitating the design of a physical 3D model using the latest technology of 3D printing.

The 3D print can be fabricated on any scale, even up to 1/1 scale, and used to fill in the void in the facade of the historical building after carefully studying the most suitable architectural element that can fit in.

Therefore, interpolating over the missing grid was another way to rediscover the phasing by which this building was constructed over time and distinguish the old from the newly imposed renovations.

The most authenticating element was the scientific digital constituent of laser scan technology that originated as a digital twin to the existing historic building, making it easy to conclude valid dimensions for the various architectural ornamentations.

In addition, the locals and official keepers of such historical edifices provided positive feedback on the importance of the implemented digital scanning technology. Some feedback came in writing from formal entities, such as municipalities, Hariri Foundation and Institute Francais, while others came as oral feedback.

We were encouraged to repeat the same methodology on similar local buildings using the same 3D laser technology, which paved the way to producing virtual dimensions for heritage sites in the local region and Baakline specifically.

Baakline sits on top of an ancient urban fabric (refer to Figure 17 for more clarification), which facilitates identifying the various local historical typologies. When digging into the arrangement of the old city’s buildings, the modular typology was found at a dimensional depth of around 5.241 m in three directions. The village is in Mount Lebanon on the west (Haddad et al., 2014).

Several historical Baakline houses and properties along the mountaintop were left to decay, specifically, the House of the first Maani Family (Emir Fakhreddine), and the current road was constructed in their vicinity. Refer to Figure 18 for more clarification.

Extending the historical grid to a condition of proximity to the village historical centre improves the pedestrian and touristic experience.

The main finding that stands out through our short experience on-site and as encountered in the methodological process and established within the field of digital survey and replicating buildings using 3D laser scan is determined by our ability to propagate accurate scientific records and progress through our findings into the realm of theory.

Similarly, we have obtained results on the non-physical aspects, such as the architectural narration and social field, by identifying patterns and repetitions throughout the various historical landmarks. The sociological norms expressed herein reflect the scientific patterns, which mandated a progressive attempt to digitise the historical landmarks to preserve the last remains of architectural imprints dating back to before the nineteenth century. The habitats and dwellings have frozen the records of time; thus, the risk lies in forgetting the precise records.

Hence, our task was to mitigate the subjective portrayals of historical facts by illuminating the actual objective trace from the local communities with at least one primary architectural evidence of singularity and actual arbitration for old technological norms by validating against the most recent encounters in structure and pattern design. The new findings demonstrated in such remarkable buildings reflect how solidly the local communities of Baakline have maintained and preserved their social habits, moral standards and values over time.

The architecture herein exemplifies a sense of enclosure for everyday day’s patterns and reincarnates the old routes of living into the future of communications, thus displaying on its screen the priceless value of nature that sets humans as evident observers of time and space and offers a sustainable future for the Lebanese ecology.

The pixel code, in other terms, the modular extracted and established in the previous section, is projected over the various architectural landmarks in Mediterranean villages and cities that date back from the eighteenth and nineteenth centuries and even much more historic daring back to the seventeenth century.

Luckily, the modular is embedded in various buildings, from architectural elements, architectural vocabulary, structural elements, floor-to-floor levels, functional settings, wall-to-wall plans, façade typology and ceiling heights.

On the other side, the area of building blocks, when compared with the total built-up area, was found to constitute around 40%, which leaves 60% to the value of void in buildings, which aligns with the findings regarding the constitutional value of void in space (Ghoussayni et al., 2021). Hence, this is the novel finding of the author’s research.

The newly introduced standards in this paper were based on such modular and found to work along with building elements. This new finding has not been discussed or found in any earlier literature, which denotes this paper as the first publication identifying such code. The formulation of the new standard is identified in the Introduction and Research Approach sections, substantiated along with the ‘Results’ section and discussed in the ‘Discussion and Analysis’ section.

The golden building pixel code of Mediterranean villages and cities was investigated and defined by addressing the spatial controls of local architectural modules, extracting the optimal model that affects both the local collective and individuals and progressing in its turn toward the finest representation of residents’ best interest by safeguarding public health and life safety.

The adequate influential element that shapes the daily functional flow of residents, merchants and institutional figures were extracted.

The methodology starts with an entire site 3D survey of Mediterranean houses, landmarks and institutions, with relevant data acquired from each building and the output transformation into an engineering and architectural pixel code to comply with in the future, in liaison with local and international standards. Refer to Figure 19 for Modular pixel extraction.

The conclusion encircles the best spatial configuration and its impact on the local regulatory aspects of architectural apprenticeship, touching both the social and the individual by extracting such ‘modular’ from various Mediterranean historical buildings. Doing this will bring back the authenticity of architectural apprenticeship among the local architects. The figure below is considered a large body of literature devoted to the study of seating comfort (Reed, 2000).

This Lebanese residential Prototype can be called a ‘Bayt’, a dwelling room, or a House (Corpus, 2004). It was built around 1880. The prototype building was scanned using a 3D laser scanner in 2024.

We have portrayed a pixelated modular grid throughout the Prototype’s plan, section and elevation, which has been found to match 80–90. The matching was found in the plan, section and elevation.

This validates that the extracted modular from our end has substantiated an alignment that adheres to the modular grid type following the royal cubit extracted from the author’s previous publication on the golden royal cubit value, equal to 0.5241 m. See Figures 20, 21, 22, 23 and 24.

Figure 20 shows that the building depicts a rectangular plan as a single-floor structure with a side stone stair leading to the roof. The roof was used in the old days to dry figs, grapes and tomatoes.

Figure 21 depicts the simplicity of the building elements, from arcs to porches, sills, windows and doors.

Figure 22 superimposes the modular grid type onto the plan, which looks to fit precisely within the building’s external wall limits.

Figure 23 superimposes the modular grid type onto the elevation, which looks to fit precisely within the building’s floor levels.

• The main conclusion that stands out through our short experience on-site and as encountered in the methodological process and established within the field of digital survey and replicating buildings using 3D laser scan is determined by our ability to propagate accurate scientific records and progress through our findings into the realm of theory.

• Similarly, we have obtained results on the non-physical aspects: architectural narration and social field. The sociological norms expressed herein reflect the scientific patterns, which mandated a progressive attempt to digitise the historical landmarks to preserve the last remains of architectural imprints dating back to before the nineteenth century. The habitats and dwellings have frozen the records of time; thus, the risk lies in forgetting the precise records.

• Hence, our task was to mitigate the subjective portrayals of historical facts by illuminating the actual objective trace from the local communities with at least one primary architectural evidence of singularity and actual arbitration for old technological norms by validating against the most recent encounters in structure and pattern design. The new findings demonstrated in such remarkable buildings reflect how solidly the local communities of the Mediterranean have maintained and preserved their social habits, moral standards and values over time.

• The architecture herein exemplifies a sense of enclosure for everyday day’s patterns and reincarnates the old routes of living into the future of communications, thus displaying on its screen the priceless value of nature that sets humans as evident observers of time and space and offers a sustainable future for the Lebanese ecology.

All data, models and code generated or used during the study appear in the submitted article.