Quantifying alignment among architectural objects using white-box neural computing

Abstract

A method for measuring the degree of alignment among architectural objects, such as a set of windows, is described; the machinery is fuzzy neural tree based on likelihood, which has been implemented in a computer program using the C# language in this work. The validity of the computational alignment assessment is verified by experiment. Alignment in the context of architectural objects characterizes the relative positioning among at least two objects, such that an edge defining the first object together with an edge defining the second object lie on a fictive line. Alignment can apply to diverse types of architectural elements, such as walls, windows, doors, and columns. The alignment concept is important in architecture and architectural design. This is because several attributes that are commonly articulated to characterize an architectural edifice, for instance order, balance, vividness and harmony, refer to geometric relations among objects, so that it is common sense to expect a basic relationship attribute, like alignment, to have named architectural attributes. However, up till now alignment has remained a verbal concept without counterpart as quantifiable expression. Thus, up till now, the precision of the descriptions concerning alignment itself, as well as the relevance of the concept in other qualitative architectural attributes, is bound to be low, hampering effectiveness of architectural design and evaluation processes. The contribution of this research is to make a step in the direction of overcoming this deficiency. In this work, uniquely the degree of alignment among openings of façades of building is computed in the form of likelihood. Although the alignment concept for two edges can be roughly considered to be a Boolean attribute, one notes that the alignment becomes weaker, namely less conspicuous, when the distance between edges increases, or when other objects happen to lie in between the edges. Moreover, alignment in architecture generally refers to multiple relations among multiple objects, where more than one edge of an object can be in graded alignment with edges of other objects, while some objects may not be in alignment at all. To cope with the issue, the computational representation of the alignment concept in this work is accomplished using a neural computing method known as fuzzy neural tree. The method is based on the likelihood concept. It is to deem suitable for the task at hand because it emulates the aggregation of information in a way that resembles to that accomplished by human reasoning. Namely, the computations taking place at each neuron of the model have an interpretation as a fuzzy logic operation, while at the same time they have a dual interpretation in terms of likelihood. In this way, the multi-facetted alignment conditions are dealt with, while the interpretability of the operations is not sacrificed. This is in contrast with artificial neural network computing, which is a black-box approach and thus does not allow interpreting the information processing operations. The validity of the computational alignment measurement put forward in this study is verified by experiment. The alignment score for a number of facades obtained by computation is compared with assessments given by a number of people, and the correlation among the two information sets is analyzed. The participants are presented 12 facades in the form of images printed on a foam board material that have the identical overall dimensions, but differ as to their window patterns. Three groups of four facades are presented together. Initially the participants rank the four facades of a group by pairwise comparisons. Thereafter they assign an alignment score to each façade in the group. The same grading procedure - ranking with ensuing grading - is carried out for the architectural attributes we hypothesize to be influenced by the alignment attribute. Based on the neural representation of alignment, it was possible to carry out the correlation and dependence analyses by means of both, parametric and non-parametric statistical methods, for depth of the pursued insight. Future work includes identifying, whether the strength of the influence the alignment concept has on architectural attributes is dependent on design properties like horizontal or vertical orientation of the aligned objects, or whether the strength differs from architectural style to style, say modern versus post-modern architecture.