原子力顯微鏡(Atomic Force Microscope, AFM)能夠捕捉奈米解析度下的生物高
分子畫面，並且經常被用在長條狀高分子生物(Long Chain Biopolymer)樣本的成
像，例如:去氧核醣核酸(deoxyribonucleic acid, DNA)。有許多研究致力於使DNA於AFM 的成像更加清楚，以及為了更加了解DNA 長鏈高分子模型，所以國
際上很多團隊發展了分子鏈的幾何特徵運算，常見的幾何特徵、例如：輪廓長
度(Countour Length)和持久長度(Persistence Length)。輪廓長度指的是DNA 輪廓外型的總長，在不同的影像解析度下計算輪擴長度會有誤差。因此在之前的研究中
有很多學者提出了不同的演算法來進行估測，而不同演算法亦有不同修正精的度
方式。本論文之前的研究是分析八連通費里曼鏈碼來設計出針對不同解析度下輪
廓長度的計算，我們將DNA 影像經過一系列的影像處理後將二值影像細線化至
單一像素寬，並針對單一像素寬的DNA 影像分析並整理出形狀數來對輪廓長度
的估測結果進行修正。持久長度代表DNA 分子鏈的剛性，能夠預估DNA 的彎
曲情形。然而在計算DNA 的持久長度時，需要精準的曲線輪廓長度以及精準的
輪廓切向量，才能有準確的估測結果。因此本論文將研究DNA 切向量的估測方
式。

Atomic Force Microscopy (AFM) captures nano-scale resolution biopolymers with
relative ease, and has been applied to image string-like biopolymer samples , such as
deoxyribonucleic acid (DNA). In order to make the calculation of DNA Geometric characteristics
such as contour length and Persistence Length , there are many researches
devoted to acquiring clearer AFM image of DNA. Contour length refers to the length of
the DNA shape , and there are some error when calculating in different image resolutions.
In the previous study, there are many researcher have proposed different algorithms to
estimate , and different algorithms have different ways to revise the accuracy. The previous
study of this paper was analyze the 8-connected Freeman chain codes, to design a
estimater for estimating contours length in different pixel resolutions. We do a series of
image processing for the DNA image after that we thining binary image into single pixel
width , and analysing the single width images pixel , then sort out the shape numbers and
use the shape numbers to revise the estimating result.The persistence length represents the
rigidity of the DNA molecular chain and can predict the bending of the DNA. in order to
have accurate estimattion in persistence length , we need the accurate contour length and
the contour tangent . Therefore, we will study the DNA contour tangent estimation
method.

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