人類視覺在影像處理扮演重要關鍵。然而，依據幾何光學，我們發現眼睛並不是一個完美的光學系統，它的清晰區域非常小。所以，設計完美的影像產生系統，如果超出眼睛所能感知的能力，將會造成浪費。

基於此一結果，我們提出3個應用領域。第1，「尖銳區域著色法」，用於加速3D場景之產生。第2，「多重解析度影像壓縮法」，可以提高影像壓縮率。第3，「快速影像縮放法」。雖然此法所縮放過的影像產生鋸齒狀，然而其速度比其它方法快達22到40倍，因此相當適合用於虛擬實境，光學字元、符號與車牌辨識。此一演算法沒有用到浮點數運算，所以也相當適合應用於嵌入式系統，如個人數位助理。

Human Visual System plays an important factor in image processing.
However, based on geometric optics, we found the eye is not a
perfect optical system; its “Region of Sharp Area” is very small.
Therefore, it would be wasteful to design a system with perfect image render of which the eye could not utilize.

Based on this result, we introduce three kinds of applications.
First, we investigated a “Region Of Sharp Area” render, with this scheme,
we have successfully speeded up the 3D scenes generation. Secondly, we
proposed a “Multiple Resolution Image Compression” algorithm,
with this method, we have successfully improved the image compression ratio.
Thirdly, we develop a fast image resizing scheme that produces
significantly improved quality over the pixel replication method.
This algorithm is suitable for real-time image resizing applications
including: Virtual Reality, Optical Character Recognition, Symbol Recognition, and Car License Plate Recognition. Although this method produced “jaggies” at the edges in the resized image, the execution time is about 22 to 40 times fast than the Windows and the Weiman scheme, respectively. This scheme doesn't use floating-point operations and buffer area, so, it is suitable for image viewer based on embedded system, such as Portable Digital Assistant.

CHAPTER 1 Introductions - 1 -
1.1 Resizing Digital Image  - 1 -
1.2 Organization of the Dissertation - 4 -

CHAPTER 2 The Optical Model of Human Visual System - 5 -
2.1 Background - 5 -
2.2 Construction of the Eye - 6 -
2.3 Simplified Model of the Eye - 8 -
2.4 Image Formation in the Eye - 9 -
2.4.1 Image Location and Image Height of thin lens - 9 -
2.4.2 Image Location and Image Size in the Eye - 14 -
2.5 Region Of Sharp Area - 15 -
2.6 Image Confusion of the Eye - 17 -
2.7 Application to Virtual Reality – ROSA render - 21 -
2.8 Application to Image Compression – Multiple Resolutions Image Compression  - 26 -
2.9 Summary - 29 -

CHAPTER 3 Methods to Resize Digital Image - 36 -
3.1 Basic Definitions  - 36 -
3.2 Digital Image Resizing  - 37 -
3.2.1 Interpolation and Spline-based Method  - 38 -
3.2.2 Fourier Transform and Cosine Transform(FT/CT)  - 41 -
3.2.3 Pixel Replication - 43 -
3.2.4 Area re-sampling - 47 -
3.3 Summary  - 47 -

CHAPTER 4 Image Resizing by Random Sampling  - 49 -
4.1 Introduction  - 49 -
4.2 Proposed Fast Image Resizing Algorithm  - 51 -
4.3 Experimental Results  - 53 -

CHAPTER 5 Conclusions  - 63 -

APPENDIX A Weiman Algorithm in C language  - 65 -

Bibliography  - 72 -

List of Figures
2.1 The Human Visual System - 6 -
2.2 The Human Eye - 7 -
2.3 Simplified Model of the Eye - 9 -
2.4 Object and Image relationships for a thin lens - 10 -
2.5 Circles of Confusion.(Not to scale.)  - 14 -
2.6 Photos with camera focused on middle object, the far and near objects will be blurred - 15 -
2.7 Image Formation in the Eye - 16 -
2.8 (a)Mapping an point from the object plane to the image plane, (b) Circle of Confusion of the eye - 19 -
2.9 Three masks for average filter - 22 -
2.10 Source picture to test the Region of Sharp Area and Confusion of the eye   - 23 -
2.11 Partition an image to sharp area and blurry area - 24 -
2.12 Human Visual Effect of Fig 2.10, by using three average filters - 25 -
2.13 Model object as triangles - 26 -
2.14 Area of triangle and Polygon - 26 -
2.15 Generate 3D scenes by small polygon, then enlarge to its original size - 27 -
2.16 Region of Sharp Area render - 31 -
2.17 Polygon render - 32 -
2.18 Block diagram of a Transform Encoder - 32 -
2.19 Zigzag scan - 33 -
2.20 Divided the image into three non-equal area as 1/4, 1/2 and 1/4 in its   width and height - 33 -
2.21 An image to test Multiple Resolution Compression scheme - 34 -
2.22 Result generated by the Single Resolution Compression scheme - 34 -
2.23 Result generated by the Multiple Resolution Compression scheme - 35 -

3.1 Matrix representation of a digital image - 37 -
3.2 Enlarge 4 pixels to 5 pixels by Piecewise Polynomial Interpolation - 41 -
3.3 Lena  - 43 -
3.4 Zoom Lena by 2  - 44 -
3.5 Rothstein’s code for a line of slope 5/7 - 45 -
4.1 Zoom by Pixel Replication - 50 -
4.2 Sample of Zoom by Pixel Replication - 51 -
4.3 Sample of Zoom by Random Pixel Replication - 53 -
4.4 PSNR and Speedup times of Barbara - 58 -
4.5 Zoom of Baboon - 59 -
4.6 Zoom of Barbara - 60 -
4.7 Zoom of Cman - 61 -
4.8 Zoom of Lena - 62 -

List of Tables
2.1 Some important characteristic of Eye - 8 -
2.2 Render Speed up(Pentium 133MHz, f=2)  -  28 -
2.3 Render Speed up(Pentium II 233MHz, f=2)  - 28 -
2.4 Improved Multiple Resolutions Image Compression Rate, each picture had 512 × 384 pixels, file size qual to 196608 bytes  - 29 -
3.1 Operations require to compute Pl(xi) - 39 -
3.2 Operations require to scale a scan line from w pixels to W pixels - 39 -
3.3 Floating-point Operations require to scale an image from w×h to W×H - 39 -
4.1 PSNR(Enlarge to 320 × 320 then reduce to 256 × 256) - 56 -
4.2 Speedup times(relative to Random pixel replication), enlarge to 320×
320 then reduce to 256 × 256 - 56 -
4.3 PSNR(Reduce to 192 × 192 then enlarge to 256 × 256) - 57 -
4.4 Speedup times(relative to Random pixel replication), reduce to 192 × 192 then enlarge to 256 × 256 - 57 -

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