基於(k,n)門檻技術影像分享的實作有很多，而最常被使用的有1979年Shamir的多項式內插法以及1983年Asmuth和Bloom的中國餘式定理的方法，這兩種方法的重構都需要繁瑣複雜的計算，為了避免訊息還原所需的複雜運算，在1995年Naor和Shamir提出了一種將(k,n)門檻技術用在視覺分享上的技術，在此之後就有廣泛的研究關於視覺分享的實作。

(k,n)視覺影像分享也是一個加密的技術，而它是將視覺訊息去產生n個陰影稱為分享的影像，然後還原的執行是藉由透明度的重疊，不需要採用任何運算的工作，然而為了實現完美的還原，導致分享的影像總是比原本的影像大，本論文研究了圖像尺寸不變的方法，雖然不能完美的還原，但在視覺上還可以接受。

There are lots of implementations for image sharing based on (k,n) threshold techniques. The most frequently used ones are based on Shamir’s polynomial interpolation in 1979 and Asmuth and Bloom’s Chinese remainder theorem approach in 1983. The reconstruction of these two methods requires tedious complex computations. To avoid the complex computations for information recovery, Naor and Shamir proposed a (k,n) threshold technique for visual sharing in 1995, which have been widely studied in the implementations for visual image sharing afterwards.

The (k,n) visual image sharing is also a cryptographic technique where visual information is used to generate n shadows called shared images and the reconstruction can be performed by transparency overlapping without adopting any computing effort. However, to achieve a perfect reconstruction, the size of shared images is usually much larger than the original ones. This thesis studies the image size invariant approaches with a visually acceptable recovery subject to an imperfect reconstruction.

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