限制和錯誤：結構分形分析之圖形前置處理標準優化

Limits and Errors: Optimising Image Pre-Processing Standards for Architectural Fractal Analysis

「分形分析」（fractal analyusis）的「盒計數變化」（box-counting variation）最常被用來計算視覺複雜的建築物、城市和景觀。這個方法係源自建築物或空間的海拔高度或平面數值，其中反映了圖像跨越多個觀察尺度所呈現的細節資料。在過去18年來，學者和設計師們大都採用「盒計數法」（box-counting method）來分析城市的規劃和建築。然而，儘管已有諸多有關此方面的研究，但此方法的限制－－包括所使用圖像之變化所造成的潛在錯誤率幅度－－則尚未被量化。其結果是，即使是對相同的圖像使用相同的數學方法，也經常得出廣泛的不同結果。針對這種現象，本研究對已被推理出會對結果產生影響、並與圖像預處理標準之盒子計數方法有關的四個因素進行測試。本文對上述各因素的7種不同測試圖像進行多重排列（multiple permutations）分析，以確定與各因素相關的限制或敏感性。此一分析的結果是用來理解變化對各「數據準備因素」（data preparation factors）的影響。此後，它們將可被通用於初始結構圖像數據最優化範圍標準的確定。

The box-counting variation of fractal analysis is the most common approach to calculating the visual complexity of buildings, cities and landscapes. This method derives a numerical value from an elevation or plan of a building or space, which reflects the amount of detail present in that image across multiple scales of observation. As a way of analysing urban plans and buildings, a range of scholars and designers have employed the box-counting method over the last eighteen years. However, despite the volume of this past research, the methodological limits-including the magnitude of potential error rates that are caused by variations in the images used-are yet to be quantified. As a consequence, often widely varying results have been produced using the same mathematical method and, ostensibly at least, the same image. In response to this situation, the present paper tests four factors that are associated with image pre-processing standards for the box-counting method and which, it has been theorised, have an impact on the results. For these four factors, multiple permutations of each of seven different test images are analysed in this paper in order to determine the limits or sensitivities associated with each factor. The results of this analysis are used to understand the impact of variations in each of these data preparation factors. Thereafter, they are used collectively to identify an optimal range of standards for the initial architectural image data.