XIII Congress of the 
International Society for Photogrammetry 
Helsinki, 1976 
Commission V 
Working Group Vll 
Invited Paper 
PH. HOTTIER 
Institut Geographique National 
Paris, France 
Accuracy of Close-Range 
Analytical Restitutions: Practical 
Experiments and Prediction 
The distinction between precision and accuracy; the 
prediction of accuracy; and the effects of measurement 
redundance, geometry, and the use of non-metric cameras 
are discussed. 
INTRODUCTION 
( A PHOTOGRAMMETRY does not consider large object distance such as in aerial 
photogrammetry, which involves the problems of refraction, but only the range 0 to 200 
meters. 
This report is limited to analytical restitutions, because analog restitutions are now being 
employed to a lesser degree in precision civil engineering applications due to the lower 
(likely 3 to 5 times) accuracy and also to the strict geometry conditions (only the normal case 
can be used on the modern analog stereoplotters). Nevertheless, in my opinion it also would 
be interesting to conduct similar studies for analog or semi-analytical restitutions. 
One may wonder why so general a problem has not been exhaustively treated in the past. 
The principal reason was probably the lack of civil engineering applications, the develop- 
ment of which is recent. There was no necessity to compare photogrammetric accuracy with 
the accuracy of other metric techniques, and to produce in this particular area efficient 
criteria and predictors of accuracy. Another reason is the multiplicity of parameters 
(geometry, physical characteristics of the photogrammetric system, redundance of the 
measurements) to be considered, and the necessity to conduct numerous and costly 
experiments. 
ACCURACY AND PRECISION 
The two concepts (accuracy and precision) should be carefully distinguished.* Let X be 
the true value of some physical quantity, and X an estimation of X based upon a particular 
measuring system S (X included in S). One always states a difference between the 
expectation of E,X of X within the measuring system and X: 
EX-TX 
Then we define the error of X as follows: 
em? anak mE RA ER wer 
where 
* ISP Commission VI 1964 Glossary of some terms and expressions in the theory of errors. 
PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING, 
Vol. 42, No. 3, March 1976, pp. 345-375.