**1. Introduction**

Photogrammetry (the art and science of determining the position and shape of objects from photographs [1]) has been used since the early 20th century as an efficient method of generating mapping of large areas of the territory, from images obtained with cameras on board an aircraft.

The "General Method of Photogrammetry" describes the stereoscopic processing of images: acquisition of a pair of images that verify artificial stereoscopy conditions; orientation of the images to each other; and virtual three-dimensional exploration of the stereoscopic space generated and cartographic capture of points:


• Virtual three-dimensional exploration of the stereoscopic space generated and cartographic capture of points. In 1892 Stolze invented the floating mark, which allows metric three-dimensional exploration. Two marks located in photography paths are perceived as a single point located in space. If the observer can move the marks on the images while receiving a stereoscopic perception of them, they can "pose the floating mark" on the surface of the object. This way of obtaining 3D coordinates is known as photogrammetric restitution or stereo compilation (**Figure 1**).

The *XY* precision is directly proportional to the scale of the image, *mb*, and the measurement precision of the image, *σi*:

$$
\sigma\_{\mathbf{x}\mathbf{y}} = \sigma\_{\mathbf{i}} \ast m\_{\mathbf{b}} \tag{1}
$$

The precision of the measure on the image plane, *σ<sup>i</sup>* usually �6 μm [1] can be expressed in terms of pixel size, *px*, as a fraction (*1/k*). This value *k* can be considered as an indicator of measurement precision in the image.

$$
\sigma\_i = \frac{\mathbf{p}\mathbf{x}}{k} \Rightarrow \sigma\_{\mathbf{xy}} = \frac{\mathbf{p}\mathbf{x}}{k} \ast m\_b \tag{2}
$$

Moreover, the product of pixel size for image scale provides the pixel size in the ground, *GSD (Ground Sample Distance)*:

$$\text{GSD} = \text{px} \ast m\_b \Rightarrow \sigma\_{\text{xy}} = \frac{\text{GSD}}{k} \tag{3}$$

Thus, the precision observed in *XY* can be expressed as a fraction of the *GSD*. Once the empirical planimetric standard deviation, *SXY*, is obtained, the empirical measurement precision of the image, *Si* is get. From *Si* the value of *k* can be computed which is a good value of comparison between cameras.

**Figure 1.** *Floating mark principle.*

*Stereoscopic Precision of the Large Format Digital Cameras DOI: http://dx.doi.org/10.5772/intechopen.97125*

$$\begin{aligned} \mathbf{S\_{xy}} &= \mathbf{S\_i} \ast m\_b \Rightarrow \mathbf{S\_i} = \frac{\mathbf{S\_{xy}}}{m\_b} \\ \mathbf{S\_i} &= \frac{\mathbf{p} \mathbf{x}}{k} \Rightarrow k = \frac{\mathbf{p} \mathbf{x}}{\mathbf{S\_i}} \end{aligned} \tag{4}$$

From this expression it follows that the higher *k*, the better precision.

It is important to note that *σ* expresses the theoretical precision while *S* expresses the empirical standard deviation which is determined from measurements.

The precision in *Z*, *σZ*, depends on the precision of measurement of the horizontal parallax, *σPx*, the image scale, *mb*, and the ratio height/base, *H/B* [1]:

$$
\sigma\_x = \sigma\_{\rm Px} \* \sigma\_b \* \frac{H}{B} \tag{5}
$$

The measurement precision of the horizontal parallax can be replaced by the measurement precision in the image plane, *σi*. The ratio height/base can be replaced by the ratio focal/photobase (*c/b*), then:

$$
\sigma\_x = \sigma\_i \ast m\_b \ast \frac{c}{b} \tag{6}
$$

The precision of the measure in the image plane, *σi*, can be expressed in terms of pixel size as a fraction of it. In this case, it is assigned a value of *1/k*:

$$\begin{aligned} \sigma\_i &= \frac{\mathbf{p}\mathbf{x}}{k} \\ \sigma\_x &= \frac{\mathbf{p}\mathbf{x}}{k} \ast m\_b \ast \frac{c}{b} \end{aligned} \tag{7}$$

Moreover, the product of pixel size for image scale provides the pixel size in the ground, *GSD*:

$$\begin{aligned} \text{GSD} &= \text{px} \ast m\_b\\ \sigma\_{\overline{x}} &= \frac{\text{GSD}}{k} \ast \frac{c}{b} \end{aligned} \tag{8}$$

As can be seen, precision in *Z* can also be expressed in terms of the *GSD*, the focal length and photobase. This is a function of longitudinal overlap, *RL*, together with the image width:

$$b = (\mathbf{1} - R\_L) \* \text{width} \tag{9}$$


**Table 1.**

*Ratios* c/b *or various photogrammetric aerial cameras, calculated for a longitudinal overlap of 60%.*

The value *c/b* affects proportionally the *Z* precision, so that the higher the value of this ratio less precision in *Z* (**Table 1**).
