Errors cannot be controlled, they are usually uncertain in nature and cannot be completely eliminated. Due to these intrinsic characteristics, errors have always fascinated philosophers, writers, psychologists, scientists and mathematicians who have developed theories, studies and research on this topic despite the complexity of its nature. The errors considered in this paper were taken from an architectural survey and concern in particular, the implementation of image-based techniques. The experimentation with these techniques was carried out in collaboration with Prof. Antonio Almagro Gorbea’s Laboratorio de Arqueología y Arquitectura de la Ciudad in Granada (Spain). The case study was the Holy Chapel of the Saviour in Úbeda (Spain), a superb example of urban renaissance architecture, which was declared World Heritage by UNESCO in 2003. It was in the context of these activities that the idea of developing of an algorithm for the evaluation of error propagation generated in image-based and range-based survey techniques was conceived. In the topographic field there is an established and consolidated treatise on the theory of errors (or measurements) closely related to probabilistic and statistical studies; but for image-based and range-based survey, there are few references in the literature about this topic. In particular, it is interesting to note how errors are generated during the survey process and how and to what extent they influence the measurements. It is banal to observe empirically that with the use of advanced photogrammetric paradigms there is a greater nominal control of these errors. However, the use of pipelines that provide for the implementation of several software environments in series or in parallel, if not controlled, can lead to the generation of serious uncertainties. In this proposal, the evaluation and interpretation of data by the operator - in a subjective but not arbitrary way – is considered particularly important. The mathematical approach adopted incorporates the uncertainty in the description of the information, by defining, through Fuzzy logic, a degree of reliability and belonging for the photogrammetric techniques (in the case study, compared to laser scanners). According to this hypothesis, and after examining the phases of the process, a report on the hardware tools used in the survey case was compiled, , then, w the analysis of software, was classified according to whether it was intended for indirect data processing or graphic restitution. Subsequently, after a study of the types of errors that can be generated in each single step and from each individual instrument, the relative weights were outlined and assigned (according to what was previously highlighted), for a final estimate of the error. Thus, after determination of the propagation, a test of the algorithm by a three-dimensional comparison was performed with the aim of analytically validating the proposed approach according to the convergence of the first results returned.
L’errore è qualcosa di non controllabile ‘a prescindere’, quasi sempre di natura incerta e che non può essere mai del tutto eliminato; eppure, proprio per queste sue caratteristiche intrinseche ha da sempre affascinato filosofi, scrittori, psicologi, scienziati e matematici che hanno elaborato teorie, studi e ricerche su questo tema, con un atteggiamento quasi di sfida per la sua complessa natura. Gli errori oggetto di questo lavoro riguardano il rilievo architettonico, in particolare, l’implementazione di tecniche image-based svolte con la collaborazione del Laboratorio de Arqueología y Arquitectura de la Ciudad di Granada del Prof. Antonio Almagro Gorbea. Il caso di studio è stata la Sacra Capilla del Salvador di Úbeda, manufatto dichiarato patrimonio mondiale dell’umanità dall’UNESCO nel lontano 2003, magnifico esempio di architettura e urbanistica rinascimentale. È nata così l’idea di sviluppare una sperimentazione per la codifica di un algoritmo per la valutazione della propagazione degli errori che si generano con le tecniche fotogrammetriche; infatti, se in ambito topografico esiste una affermata e consolidata trattatistica sulla teoria degli errori (o delle misurazioni), strettamente correlata a studi probabilistici e statistici, per i rilievi image-based sono pochi i riferimenti in letteratura circa queste problematiche e su come gli errori si generano durante il processo e su quanto influiscono sulle misure e con che peso. È banale osservare empiricamente come con l’uso di paradigmi fotogrammetrici avanzati vi sia un maggior controllo nominale di questi errori; tuttavia il ricorso a pipeline che prevedono l’implementazione in serie o parallelo di più ambienti software può condurre, se non controllato, alla generazione di gravi incertezze. Nella proposta avanzata ha assunto particolare importanza la valutazione e l’interpretazione dei dati da parte dell’operatore – in maniera soggettiva ma non arbitraria –, con un approccio matematico che incorpora nella descrizione dell’informazione l’incertezza, definendo, tramite la logica Fuzzy, un grado di appartenenza e affidabilità alle tecniche fotogrammetriche (nel caso di studio, rispetto a quelle range-based). Secondo questa ipotesi e dopo aver passato in rassegna le fasi che compongono il processo, è stato affrontato un resoconto sugli strumenti hardware utilizzati per il rilievo di fattispecie, proseguendo, poi, con l’analisi degli applicativi software, classificati a seconda se destinati all’elaborazione indiretta dei dati o alla restituzione grafica. Successivamente, dopo uno studio della tipologia degli errori generabili in ogni singolo step e da ogni singolo strumento, sono stati delineati e assegnati i pesi, per una stima finale dell’errore. Infine, dopo averne determinato la propagazione si è proceduto a testare l’algoritmo mediante un confronto tridimensionale, con l’intento di validare analiticamente l’approccio proposto in base alla convergenza dei primi risultati restituiti.
Una prima proposta per un algoritmo per la valutazione degli errori delle restituzioni fotogrammetriche (A first proposal of an algorithm for the evaluation of the error in the photogrammetric restitution)
BARBA, Salvatore
;CONDORELLI, FRANCESCA
2018
Abstract
Errors cannot be controlled, they are usually uncertain in nature and cannot be completely eliminated. Due to these intrinsic characteristics, errors have always fascinated philosophers, writers, psychologists, scientists and mathematicians who have developed theories, studies and research on this topic despite the complexity of its nature. The errors considered in this paper were taken from an architectural survey and concern in particular, the implementation of image-based techniques. The experimentation with these techniques was carried out in collaboration with Prof. Antonio Almagro Gorbea’s Laboratorio de Arqueología y Arquitectura de la Ciudad in Granada (Spain). The case study was the Holy Chapel of the Saviour in Úbeda (Spain), a superb example of urban renaissance architecture, which was declared World Heritage by UNESCO in 2003. It was in the context of these activities that the idea of developing of an algorithm for the evaluation of error propagation generated in image-based and range-based survey techniques was conceived. In the topographic field there is an established and consolidated treatise on the theory of errors (or measurements) closely related to probabilistic and statistical studies; but for image-based and range-based survey, there are few references in the literature about this topic. In particular, it is interesting to note how errors are generated during the survey process and how and to what extent they influence the measurements. It is banal to observe empirically that with the use of advanced photogrammetric paradigms there is a greater nominal control of these errors. However, the use of pipelines that provide for the implementation of several software environments in series or in parallel, if not controlled, can lead to the generation of serious uncertainties. In this proposal, the evaluation and interpretation of data by the operator - in a subjective but not arbitrary way – is considered particularly important. The mathematical approach adopted incorporates the uncertainty in the description of the information, by defining, through Fuzzy logic, a degree of reliability and belonging for the photogrammetric techniques (in the case study, compared to laser scanners). According to this hypothesis, and after examining the phases of the process, a report on the hardware tools used in the survey case was compiled, , then, w the analysis of software, was classified according to whether it was intended for indirect data processing or graphic restitution. Subsequently, after a study of the types of errors that can be generated in each single step and from each individual instrument, the relative weights were outlined and assigned (according to what was previously highlighted), for a final estimate of the error. Thus, after determination of the propagation, a test of the algorithm by a three-dimensional comparison was performed with the aim of analytically validating the proposed approach according to the convergence of the first results returned.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
