以自然鄰點內插法與頻帶分段線性修正重建物體頻譜反射率之研究

Abstract

本研究重點在提出一個新的物體頻譜反射率重建方法，將真實量測的物體頻譜反射率資料與八條虛擬的反射頻譜，使用自然鄰點內插法(Natural Neighbor Interpolation，NNI)並藉由頻譜不同頻帶的線性修正方法來估計待測物體的頻譜反射率。這是一個標準從RGB值轉換到頻譜估計頻譜反射率的重建問題，已有許多研究提出各種解決的方法，並且各自有其重建優缺點。基於內插計算與線性修正的處理，新方法不僅提高重建頻譜的準確率，也避免超出色域範圍外會產生的外插情況。 本研究方法主要分為兩個步驟。首先，使用真實量測的色票資料以自然鄰點內插法重建出反射頻譜。額外增加八條預先估計的虛擬頻譜，當作是sRGB色域的最邊界處，確定所有在色域內的測試樣本都可以被計算出來，不會有外插的問題產生。內插重建後的反射頻譜在D65標準照明體打光下，與輸入的sRGB色域測試樣本比較，其色差結果是很精確的。接著，三個定義的波長S、M、L作為調整內插重建後的頻譜控制點，讓新調整的頻譜色差繼續降低。這個頻帶修正方法分別是由波長400 nm 到S波長、S波長到M波長、M波長到L波長、L波長到波長700nm四個分段的線性轉換所組成。 在色彩顯像模擬實驗方面，首先將馬克貝斯頻譜資料加上八條虛擬頻譜為訓練樣本，孟賽爾色票頻譜作為測試樣本這組實驗為例，在標準照明體D65下，用色差公式〖∆E〗_2000 計算其最大色差是1.6366，平均色差是0.0915。接著透過頻帶的修正，可得到最大色差1.4869，平均色差是0.0726。顏色的差異進一步得到改善。除此之外，同時也針對整個sRGB色域進行評估，計算由RGB色頻數值重建後的頻譜，其最大色差是1.6671，平均色差是0.0315。如果訓練樣本換成孟賽爾色票加上八條虛擬頻譜資料，則最大色差是1.4915，平均色差是0.0126。經由實驗數據證實本研究所提出的研究方法，估計的物體頻譜反射率相當準確。In this paper, we proposed an accurate recovery method of object spectral reflectance using the traditional natural neighbor interpolation, shortly named as NNI, with band-divided linear correction. Essentially, such a recovery problem was usually to transform the RGB channel values into a spectrum to simulate the reflectance of an object. There were many previous researches offering various solutions to this problem with more or less advantages and drawbacks. Our work improved the recovery result based on the interpolation approach with further correction of spectral reflectance. This new solution proposed not only gives more accurate results, but also avoids the extrapolation problem causing by the phenomena out of gamut. Our method consists of two stages of recovery procedures. First, the NNI interpolation was used to construct the spectral reflectance from the real samples of color checkers. Eight additional pre-determined spectra were imposed for the corners of the sRGB color space, named virtual extreme spectra, to guarantee all the test samples in the gamut spanned by the known samples; such that, the interpolating scheme worked well without the extrapolation problem. Secondly, the spectra resulting from NNI were further fine-tuned according to the difference between its sRGB color under illuminant of D65 and the original input one of ground true. Three pre-specified wave lengths, denoted S, M, and L, were selected as the control points to correct this NNI spectrum approaching to a new one with less color difference. This correction was composed of 4 piecewise linear transformations related to 4 bands from 400nm to S, from S to M, from M to L, and from L to 700nm respectively. Some experiments were performed to evaluate the performance of the new NNI with the virtual extreme spectra and the additional correction stage. At first, the 1269 checker spectra from Munsell book was used as the test samples under the training samples from Macbeth 24 color checkers. The largest color difference of 〖∆E〗_2000 was 1.6366 based on the illuminant of D65, and the average difference was 0.0915. And, the color differences were further improved, if the band-divided correction was adopted. Then, the largest 〖∆E〗_2000 was 1.4869, and the average difference was 0.0726. In addition, the entire gamut of sRGB was also evaluated. The spectra recovered from the specified RGB channel values lead to the largest color difference was 1.6671 and the average one was 0.0315 under the illuminant of D65, based on the training samples of Macbeth color checkers. The largest difference was 1.4915, and the average one was 0.0126, based on the training samples of Munsell book checkers. These experimental results showed that the proposed method was very accurate for the recovery of spectral reflectance.