隨著科技的日新月異，在生活中已隨處可見QR碼存在於我們的生活。QR碼內所藏的資訊，使用者只需透過行動裝置內的應用程式拍照或掃描即可得知訊息。因其便利性有些商家、廣告商會直接將商品資訊儲存於QR碼中，以便消費者更容易獲得詳細的商品資訊。隨著QR碼的應用越來越普及，將QR碼黏貼於柱面上並且能快速解碼已是不可忽視的一環。至今，對於QR碼黏貼於柱面的解碼往往會花費過多的時間，這不合乎QR碼(quick response code)「快速響應碼」的原意。
本論文我們將透過透視投影(perspective projection)的方法對於不論是正貼或斜貼之QR碼進行校正及解碼。首先我們取得黏貼於柱面而產生變形之QR碼的2D影像校正點，以及估計出QR碼斜貼的角度後；再透過交比(cross ratio)得知QR碼的版本大小；接著利用已知的版本資訊建構出每一個校正點的3D世界座標，最後使用我們所取得的2D影像校正點和建構出來的3D世界座標校正點計算出我們所需要的相機矩陣；接著再使用透視投影(perspective projection)將因黏貼於柱面而產生變形之QR碼導正為一個方正且標準的QR碼，並使用標準的QR解碼器進行解碼。
我們模擬了版本4到版本11，斜貼順時針30度至逆時針30度，每三度為一個單位，由實驗結果我們發現當版本數提高時，容許斜貼的角度越來越小。主要原因為當版本數提高時，QR碼的模點數亦會提高，而每一個模點所涵蓋的像素即會相對縮小，因此我們需要更多更為精準的校正點來計算出更為精確的相機矩陣對QR碼進行規正。在日常生活中，QR碼斜貼的機會不高，因此我們嘗試使用我們的方法對於QR碼正貼於圓柱進行解碼，發現我們所能正確導正並且解碼的QR版本為13，已大大提升了至今為止柱面QR碼所能解碼的版本數，因解碼流程相當精簡，相較於過去的解碼方法，本實驗所需花費的解碼時間大幅下降。

Nowadays, the QR (quick response) code can be seen everywhere in our daily lives. QR codes contain a wide variety of information which can be fetched easily through smart phones and tablets. With such convenience, the QR code is adopted by a great number of companies and advertisers in promoting their products. With the growing popularity of the QR code, it has become necessary that they can be decoded swiftly on curved surfaces in many applications. Up until now, the slow decoding speed of the QR code has not succeeded in living up to what its name suggests—a “quick response”.
In this essay we try to decode and correct the QR codes which are posted on cylinders, both upright and slanting. First of all, we find the 2D calibration points and the slanting degrees of the QR codes posted on curved surfaces. Next, we find what versions the QR codes belong to with the Cross-Ratio method, and gave each calibration point a world. Then, we calculated the camera matrixes with the 2D calibration points and their corresponding 3D world coordinates. Finally, we are able to correct the slanting QR codes posted on curved surfaces into upright and standard forms with the perspective-projection method. Having accomplished the above steps, we decode the QR codes with standard QR decoders.
Various versions of the QR codes were tested, ranging from 4.0 to 11.0, with the slanting degrees ranging from 30-degree clockwise to 30-degree counter-clockwise. The degrees were switched every 3 degrees. With this experiment we found that the higher the versions of the QR codes, the smaller the slanting degrees were allowed. The reason is that the higher the versions, the more the module number, and the smaller the pixels covered by each module. Therefore, in order to figure out even more accurate camera matrixes for the rectification of the QR codes, we needed calibration points which are more accurate. However, since the chance of seeing QR codes posted slanting in our daily lives was relatively low, we tried to decode upright QR codes posted on curved surfaces. As a result of our experiment, we were able to decode QR codes with versions as high as 13.0, meaning we have significantly promoted the decodable versions on curved surfaces. Due to the fact that our decoding process is rather simplified compared to conventional methods, much less time is needed for decoding the QR codes.

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