Reconstruction from a Single Meydenbauer Image

Objective:

Three-dimensional reconstruction of (the visible part of) a demolished building (Kommandantur unter den Linden, Berlin) photographed by

Albrecht Meydenbauer (1834-1921) with an uncalibrated camera.

Step 1: Scanning

Scanning the original photograph.

The image (865 x 1200 pixels) was supplied by

Matthias Hemmleb:

Orignal image (low resolution).

Step 2: Line Feature Extraction

Straight line features of the building are automatically extracted using a line-growing algorithm.

The result contains 223 lines with a minimum line length set to 40 pixels:

Automatically extracted lines.

Step 3: Vanishing Point Detection

Three vanishing points are automatically detected with a method based on a combination of clustering and statistical testing. Apart from parallelism, no assumptions about the geometry of the building are used in this step. Precision of end point co-ordinates of the lines was set to 1 pixel.

Here each image shows the lines that intersect in one of the vanishing points. No lines remained unclustered.

Lines of first vanishing point.

Lines of second vanishing point.

Lines of third vanishing point.

Step 4: Camera Calibration

The lines of the three vanishing points are used as the observations (sigma: 1 pixel) in a least-squares adjustment in which the intrinsic camera parameters are estimated. Parallelism and perpendicularity of the edges of the building are assumed, as well as perfectly square pixels.

Results (estimated standard deviation between brackets):

Focal distance : 1131 (11) pixels
Principle point x : Due to the so-called two-point perspective of the image, the x-component (horizontal position) of the principle point can not be estimated and was fixed in the middle of the image.
Principle point y : 586 (12) pixels (Note the excentricity of the principle point, resulting in parallel vertical building edges in the image.)
Radial lens distortion : Statistically insignificant.
Estimated standard deviation : 0.77 pixel (Precision of the co-ordinates of the line end points)

Step 5: Image Measurement and Specification of Additional Scene Knowledge

This is a manual step in which the building edges needed for reconstruction are measured and a point-line-face topology is established. Furthermore, additional geometric object constraints are specified, such as coplanarity of several faces and symmetry in the "oblique" ornaments at the top of the building.

Manually measured points, lines, and faces

Step 6: Single Image Bundle Adjustment Incorporating Scene Knowledge

In this step all gathered information is combined in a least-squares adjustment for the estimation of the co-ordinates of the corner points of the building and the parameters of its planes.

Some facts:

283 parameters (points, planes, image orientation)
100 individual image lines
32 shape constraints (parallelism, perpendicularity, symmetry)
86 degrees of freedom
A priori precision of end point co-ordinates: 1 pixel
Estimated variance factor: 0.535
Largest residual: 2.0 pixel
Formal standard deviations of most building points are below 10 cm (a few reach 40 cm).
6 co-ordinates (sigma set to 1 mm) and the length of the building (41.39 m derived from a cadastral map, sigma set to 10 cm) were fixed and define the co-ordinate system.

Step 7: Conversion to Texture-mapped VRML-representation

This is a fully automated step that requires the image, the measurements, and the object model. For each face the 8 parameters of the rectification used for texture mapping are computed by a least-squares adjustment. The red error ellipsoids visualize the covariance matrices of the point co-ordinates enlarged with a factor 10.

Screenshots of the