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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Historical perspective images have been proved to be very useful to properly provide a dimensional analysis of buildings façades or even to generate a pseudo-3D reconstruction based on rectified images of the whole structure. In this paper, the case of Gobierna Tower (Zamora, Spain) is analyzed from a historical single image-based modeling approach. In particular, a bottom-up approach, which takes advantage from the perspective of the image, the existence of the three vanishing points and the usual geometric constraints (

Despite the high proliferation of three-dimensional scanning systems, which have revolutionized the data acquisition fashion, photogrammetry, and computer vision techniques, have evolved to offer powerful and friendly tools that can render virtual worlds that meet the most demanding expectations: high geometric accuracy on the points, high radiometric quality on the surfaces of the object, and an integrated environment where the user can interact and even play with the model or demand from its data base sophisticated information. In addition, historical buildings modeling through laser scanner become impossible when the structure does not exist or the whole building has been destroyed. In these cases, the problem increases since the building cannot be reconstructed from two or more images [

This contribution relies on software, sv3DVision, developed in 2005 [

Through the years, the software has been successfully tested on a variety of environments, such as architecture, forensic sciences, traffic scenes and engineering; it has been awarded by the ISPRS Organization and has been used in the teaching/learning of Cartographic Engineering. However, this is not the main motivation that has decided us to present this contribution, but rather the importance of using our work to preserve, enhance, and highlight the historical heritage of our community, Castilla-Leon.

This paper addresses the problem of single historical photography dimensional analysis and pseudo-3D modeling (see infra for an explanation of this term) of demolished buildings, focusing the case of study on the emblematic “Gobierna Tower” located in Zamora (Spain). The proposed method is suitable for those regular structures, which contain several geometric constraints, such as planarity, orthogonality, and parallelism, and hold the three orthogonal principal directions (

One of the most highlighted cases in lost buildings, that belonged to the architectural heritage of the city of Zamora (Spain) [

During its long-term presence, the Stone Bridge has undergone continuous transformations, transformations that have been necessary to reduce the devastating effects of the endemic swellings that knocked down the city slums.

At the end of the 19th century, its state was so worrisome that it was closed to the traffic and replaced upstream by another viaduct. Once the local authorities dealt with the construction of a new metallic bridge, also decided to recover the battered Stone Bridge. Between 1905 and 1908, Luis de Justo, Civil Engineer, designed and executed eleven projects that modified radically the appearance of the medieval bridge of Zamora, in addition to repairing it. Up to then, the Stone Bridge of Zamora displayed a similar configuration to the original one. Several documents show this fact, such as the View of Zamora by Anton van Wyngaerde (1570) (

Over the cutwater of the previous tympanum to the angle, rose the tower of La Gobierna, popularly known due the weather vane that topped it. Moreover, in Wyngaerde’s View or in Blas de Vega’s elevation, an initial door prevented parking on the deck during the night. In the other extreme, over the northern pier, an arc rose that opened the bridge by to the city.

Nothing remains today. After Luis de Justo rehabilitation, the slopes were modified and the spillways were extended, and even new ones were added. The works undertaken by the Department of Public Work between 1905 and 1907 [

The vanishing points, (

As can be seen from

It can be seen that the principal point,

In any case, it can be seen that the first step is always to determine the position of the three vanishing points related to a certain building and this relies heavily on both the robustness of the pose configuration and on the ability of extracting straight lines from the image that intersect on each of the vanishing points. The quality of the process, as will be discussed later, thus, depends on the definition of the image lines and on the angle that each bundle of vanishing lines spans. From this, it can be seen that when the perspective angles are poor, the vanishing point are far away from the center of the image, decreasing, therefore, the reliability of the process.

The “Gobierna Tower” together with its bridge was documented through several drawings, historical photographs and even with a topographical surveying performed by the engineer Luis de Justo in 1905. In particular, the most relevant documents correspond to Wygaerden [

The following figure (

There are two ways of retrieving the metric information of the object from a single image: automatic and manual. The first one is always preferable when the image exhibits high quality (high-resolution and definition of the vanishing lines), when the ratio between correct observations (automatically extracted line segments) and mistaken observations (blunders derived from shadows, scars on the image, reflections,

The automatic approach is structured in three steps:

Extracting edge pixels by means of the Canny filter [

Clustering pixels into raster segments according to neighboring criteria and with length restrictions in a fashion very similar to the Burns Method [

Determining vector lines (first and last points) from raster segments according to a plane collinearity condition.

The output from these processes is the input in the following one: the determination of the vanishing points. Several methods of approaching this have been implemented [

A whole set of possibilities have been applied to automatically process the target image but none of them has been successful due to the reasons outlined above. Thus, finally, the manual procedure was applied and even though there is really a very small set of lines, an acceptable result has been reached and this have been possible by the application of the modified Hough Transform Method, which is briefly described in the following lines:

As is well known, the Hough Transform [

This leads (at least) to the following series of consequences (

The Hough procedure works by quantizing the image space, then extracting all information for every discrete cell, translating this information to the equivalent parameter space, and, finally, proceeding to some voting scrutiny to find out the relevant feature that meets the target criteria (The drawback related to the singularity of the parameter a when lines are close to verticality is overcome by tuning from the Cartesian (

To determine a vanishing point the procedure is as follows:

For every start and end point of every line segment rendered by the automatic or manual extraction, the correspondent line in the parameter space is computed and represented. Every cell that lies on the line receives one vote.

A voting procedure is undertaken so that the most visited cells give the lines that form families of lines that pass through each of the vanishing points.

For all these lines the correspondent parameters (_{i}

The best coordinates of each of the vanishing points are computed by applying a least squares criteria to the equation: _{0} = _{i}x_{0} + _{i}_{0},_{0}) are the coordinates of a vanishing point.

In order to avoid residual outliers, a weighting procedure is applied to the above task, so that a robust M-estimator, modified Danish estimator [

Once the coordinates of the three vanishing points are computed the interior and exterior orientation parameters are addressed from the perspective pyramid, built from these points plus the point of view (

The orthocenter of the triangle formed by the three vanishing points (

The rotation angles (

On the horizontal triangle (^{2} =

On the vertical triangle (^{2} =

Finally, the swing angle (

Once these parameters are known, the coordinates of the point of view, _{S}_{a}_{a}_{b}_{b}_{AB}_{p}_{p}_{aA}_{bB}

Finally, once the interior and the exterior orientations are solved, the dimensional analysis process and the pseudo-3D modeling process are available (

For any object point _{T}

In addition, dividing the first and third equations by the second one and rearranging we get

After analyzing more than ten images, the only historical photograph that properly worked presents a size of 7.7 × 12.18 cm and is scanned with a pixel resolution of 150 dpi providing an image of 455 × 719 pixels (

According to the proposed approach, the photograph is manually vectorized with lines clustered along the three main object directions (

Computed the main structural components of the process, the geometric internal camera parameters, _{S}, the user must introduce some known measurement of the building together with some geometric constraint in order to overcome the indetermination problem

The following table (

It should be noted, the more weakness along the

Again, from

Fixed the camera pose, a dimensional analysis was performed based on distances. This process was performed using the collinearity condition constrained with some geometric clues, such as coplanarity, parallelism, or perpendicularity

Finally, a pseudo-3D model was generated based on the rectified facades computed geometrically from vanishing points, that is, using the collinearity equations supported by a geometric constraint (

When the lack of information is clearly due to the non-existence of the object of interest, such as historical demolished buildings, classical but solid perspective geometry statements can be of great utility, instead of advanced image processing techniques, especially in those cases in which only individual or single images exist. The main goal of this study was to provide a dimensional analysis and even a pseudo-3D reconstruction of the demolished historical building “Gobierna Tower” using single historical photographs. To this end, a single image-based modeling method has been developed and adapted to this specific case. The accuracy assessment results come to confirm that from a single view we can measure distances and areas and even to provide a simple 3D model with enough quality. The results obtained could be useful for the authorities of Zamora’s Council as they have been considering reconstructing the “Gobierna Tower”. The monument would play an important touristic role but specially would meet a popular demand supported by social and cultural reasons which would be directly connected with the identity of Zamora’s society.

With relation to the workflow developed and the results obtained the main conclusions are the following:

Manual processing permits achieve better results than automatic processing. This is due to the weakness related to low number of vanishing lines, poor quality image, high number of blunders and poor perspective geometry.

Although robust estimators (especially RANSAC) have proven largely its efficiency in filtering gross errors, this is not the case. As just stated, when the image is poor both in geometry and radiometry, the automatic approach leads to an excessive number of blunders and so, the manual identification of vanishing lines is better.

An original vanishing point method based on the Hough Transform, which guarantees efficiency and quality in the results, even with unfavorable cases (a three-point perspective getting close to two-point perspective), has been successfully applied. Other methods to compute the vanishing points, such as the triangle area minimization or the Gaussian sphere, have not provided good results.

A relative error of 1% has been obtained for the accuracy assessment of the results. This value can be considered very good since the single image-based modeling approach developed involves many steps and thus the corresponding error propagation.

Finally, it should be remarked that the method is only applicable in scenes with strong geometric contents (

All authors contributed extensively to the work presented in this paper.

The authors declare no conflict of interest.

Detail of the Stone Bridge of the Zamora city drawn by Antón van den Wyngaerden, in 1570.

Bridge over the Duero river in Zamora, photograph acquired by J. Laurent, in 1870. Photograph of the southern half (arcs 7–3).

Vanishing point geometry:

Workflow developed for the historical single image-based modeling applied to the case study of the “Gobierna Tower”.

Interpretation of several cases of the Hough Transform applied to straight lines. For each of the four cases, the Image Space is represented at the left and the Parameter Space is represented at the right. In the Image space, there can be seen: (

(

The coordinates of the point of view, _{AB}

Dimensional analysis on a plane (in this case _{T}

Historical photograph (1900) used for the single image-based modeling approach.

Perspective pyramid computed for the single image-based modeling approach. The vanishing points (

(

Different cases between image and parameter spaces for the Hough transform.

1 | A straight line | A point |

2 | A point (family of straight lines that intersect on a point) | A straight line (family of points that belong to a line) |

3 | A set of collinear points (that belong to the same line) | A set of lines that intersect on the same point |

4 | A vanishing point (set of lines that intersect on a point) | A set of collinear points (the straight line to which they belong represents the vanishing point) |

Vanishing points coordinates and its errors.

2,253.8 | −587.42 | 283.55 | |

504.79 | 582.40 | −7,425.58 | |

0.057 | 0.046 | 0.318 |

Internal and external parameters of the unknown camera.

25.29 | _{S} | ||

65.40 | _{S} | ||

44.86 | _{S} |

Accuracy assessment: dimensional analysis of distances.

1.84 | _{L1} |
4.66 | _{L6} | ||

4.08 | _{L2} |
10.05 | _{L7} | ||

4.40 | _{L3} |
5.18 | _{L8} | ||

4.45 | _{L4} |
0.87 | _{L9} | ||

14.38 | _{L5} |
8.70 | _{KD} |