# Least squares

The backbone of analytical methods consists of various mathematical and procedural concepts to represent relations between points in the object, their corresponding images and operational procedures to solve specific problems. Analytical photogrammetric procedures may be considered along three operational stages, each invol ving specific instruments (Fig. 6. 1), viz. , those used for acquisition of image data (mensural), those used for data-processing and analyses (computational) and those used for display or presentation of the results.
In view of the above, we would study the historical developments firstly with regard to the concepts and next with regard to the instruments and their potentials for the future. A mathematical model, in expressing the relevant concept, provides insight into the underlying chain of events. There is no mystery about the way in which this insight is achieved. The mathematical models have no scientific value unless they have been validated adequately through experience and research. Scientific validation is an openended process. As a mathematical model is successfully tested and used, it becomes established.
Otherwise it stands to be changed, modified or simply dropped. We have witnessed this through the historical development of analytical photogrammetry. Furthermore, photogrammetry being an applied science, it is the content and not the form of the mathematical statement (language) that matters most. Thus we have noticed that mathematical and operational concepts have been adapted to circumstances without really changing the basic contents. The following sections would highlight the conceptual developments without going into personal . details.

Hauck (1883) established the relationship between projective geometry and photogrammetry_ This should be considered to be the most fundamental geometric concept and the basis of most classic analytical photogrammetric developments. Ernst Abbe, the cofounder of the German Zeiss Works in 1871 started intense studies and tests for optical elements on the basis of rigorous mathematical analyses. F. Stolze discovered the principle of the floating mark in 1892 while Carl Pulfrich also of the Zeiss group developed a practicable method of measuring and deriving spatial dimensions from stereo-pholographic images with floating marks.
He presented in 1901 the ZeissPulfrich Stereocomparator by supplementing Eduard von Orel’s (1877-1941) first prototype Stereoautograph at the 73 rd Conference of Natural Scientists and Physicians held at Hamburg. Separately, a ssimilar stereocomparator was invented in 1901 by Henry G. Fourcade (1865-1948) of South Africa. He presented this at the Philosophical Society of Cape Town. Sebastian Finsterwalder (1862-1951) in a series of publications during 1899 to 1937 established a very sthrong foundation for analytical photogrammetry.
In these he brought about the geometric relations which govern resection and intersection as well as relative and absolute orientations. He predicted the future possibility of nadir point triangulation 311 and the applicatian af phatagrammetry to. astrageadetic measurements. He also. farmulated the basic laws af errar prapagatian in lang strip triangulatians. He was prabably the first persan to. use vectar terminalagy in phatagrammetry literature (Finsterwalder 1899, 1932). Eduard Dalezal 1862-1955) af Vienna, Austria pravided great internatianal driving spirit as he became the faunding President af the Internatianal Saciety far Phatagrammetry in 1909. He also. created the Internatianal Archives af phatagrammetry. viz. , the usefulness af auxiliary data and instruments in order to. avoid propagation of systematic errors in strip triangulation and the practical advantage of using wide-angle cameras. Heinrich Wild (1877-1951) presented in 1926 at the Second International Congress at Berlin his modified plotter prototype known as Police Autograph.

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