TW200939154A - An edge extraction and enhancement - Google Patents
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- TW200939154A TW200939154A TW097109015A TW97109015A TW200939154A TW 200939154 A TW200939154 A TW 200939154A TW 097109015 A TW097109015 A TW 097109015A TW 97109015 A TW97109015 A TW 97109015A TW 200939154 A TW200939154 A TW 200939154A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/13—Edge detection
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/181—Segmentation; Edge detection involving edge growing; involving edge linking
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20172—Image enhancement details
- G06T2207/20192—Edge enhancement; Edge preservation
Abstract
Description
200939154 九、發明說明: 【發明所屬之技術領域】 本發明係為一種邊緣萃取與強化方法,尤其是有關於 一種可使用硬體實現使用拉普拉斯運算及拉普拉斯切的 低雜訊邊緣萃取與強化方法。 【先前技術】 ® 在數位影像系統中,一項基本且重要影像處理技術, 就是先把影像邊緣萃取出來,進而用來強化影像邊緣的亮 度,把模糊影像強化改善為清晰影像。於習知技藝中,它 不論方向性對於影像邊緣作強化的效應。然而單以上述運 算方法去擷取影像中物體邊界仍有所缺點:此類方法雖使 物體邊緣鮮明化,但相對的亦對影像中的雜訊有同樣的效 果。而且以具方向性邊緣強化法處理後的邊緣資料大多支 離破碎,並無法提供完整的物體邊界資料。 〇 美國專利第6,463,175號揭露一項邊緣萃取與強化方 法,其可使用等冪(idempotent)處理及濾波器運算來降低 結構引導(structure-guided)影像失真,然則該案需使用電 腦實現,相較於本案以使用硬體實現,其處理速度慢且需 更大更多之軟硬體資源,方得以實現邊緣萃取與強化方 法。 緣此,本案之發明人係研究出一種簡易而有效的邊緣 萃取與強化方法,其可使用硬體實現,對於影像的高頻部 5 200939154 份會產生強化作用,而低頻部份則會衰減,係可改善習知 技術中之處理速度慢且需更大更多之軟硬體資源且雜訊 被放大之現狀。 【發明内容】 善習知技術中之雜訊被放大之目的。 依據本發明一範例(exemplary example),提供一種用以 調整一像素yij之亮度值之邊緣萃取與強化方法,係可使用 硬體實現包括以下步驟: 本發明係關於—種邊緣萃取與強化方法,其係利用拉 ❹普拉斯運算及拉普拉斯切,進而達成可使用硬體實現,改 於水平、垂直、200939154 IX. Description of the Invention: [Technical Field] The present invention relates to an edge extraction and strengthening method, and more particularly to a low noise which can be implemented using a Laplace operation and a Laplace cut using a hardware. Edge extraction and strengthening methods. [Prior Art] ® In digital imaging systems, a basic and important image processing technique is to extract the edges of the image to enhance the brightness of the edges of the image and enhance the blurred image to a clear image. In the conventional technique, it has the effect of strengthening the edge of the image regardless of the directionality. However, the above-mentioned operation method to capture the boundary of the object in the image has its shortcomings: although this method makes the edge of the object sharp, it also has the same effect on the noise in the image. Moreover, the edge data processed by the directional edge strengthening method is mostly fragmented and cannot provide complete object boundary data. U.S. Patent No. 6,463,175 discloses an edge extraction and enhancement method that uses idempotent processing and filter operations to reduce structure-guided image distortion, but the case needs to be implemented using a computer. Compared with the case, the hardware is implemented, the processing speed is slow, and more and more soft and hardware resources are needed to realize the edge extraction and strengthening method. Therefore, the inventor of the present invention has developed a simple and effective method of edge extraction and enhancement, which can be implemented by using a hard body, and the high-frequency part of the image 5 200939154 will be strengthened, and the low-frequency part will be attenuated. It can improve the current situation in the prior art that the processing speed is slow and more and more hardware and software resources are needed and the noise is amplified. [Summary of the Invention] The noise in the good knowledge technology is amplified. According to an exemplary example of the present invention, an edge extraction and enhancement method for adjusting the brightness value of a pixel yij is provided, which can be implemented by using a hardware. The present invention relates to an edge extraction and enhancement method. It uses Laplace Plass operation and Laplacian, which can be achieved by using hardware, horizontal, vertical,
第一邊緣值, 對角方向對一第一影像做拉普拉斯運 ,運算具有一水平 —邊緣值乘以一第一增益再與該第一 一第二影像。The first edge value, the diagonal direction of the first image is Laplace, the operation has a horizontal value - the edge value is multiplied by a first gain and then the first second image.
増益再與該第—影 較佳者, 該第一影像為3X3之矩陣, 、負方向之變數;以及 一影像相加 増益再與 厂一似冬从万程式表示如下; Y’ =第一影像Yin +第二邊緣值 該矩陣係可表示 6 200939154 * 為 yij。 較佳者,該拉普拉斯運算於水平、垂直、對角方向之 增益為可調。 較佳者,該拉普拉斯切於正方向之變數為可調。 較佳者,該拉普拉斯切於負方向之變數為可調。 較佳者,該第一增益為可調。 較佳者,該第一增益範圍為0到4。 ® 較佳者,該第一影像為10位元。 較佳者,該硬體為嵌入式系統或特定應用積體電路。 為使貴審查委員對於本發明之結構目的和功效有更 進一步之了解與認同,茲配合圖示範例詳細說明如後。 【實施方式】 圖一係為本發明之輸入影像矩陣示意圖,本發明邊緣 萃取之係把輸入影像依水平、垂直及對角三個方向進行拉 ® 普拉斯運算取出影像邊緣,並賦予相同或不同增益進而控 制三個方向邊緣強化程度。該影像中之一像素(如y22) 及其周圍像素以一 Y矩陣為例,如: yn yi2 yi3 y2i m y23 ysi ys2 y33 較佳的,Y矩陣為3乘3之矩陣103。 7 200939154 Y’為經本發明之運算處理後得到之矩陣。Preferably, the first image is a matrix of 3×3, a variable of a negative direction; and an image is added to the image and then expressed as follows: Y′ = first image Yin + second edge value The matrix can represent 6 200939154 * is yij. Preferably, the Laplace operation is adjustable in horizontal, vertical, and diagonal directions. Preferably, the Laplace cut in the positive direction is adjustable. Preferably, the Laplace cut in the negative direction is adjustable. Preferably, the first gain is adjustable. Preferably, the first gain range is from 0 to 4. ® Preferably, the first image is 10 bits. Preferably, the hardware is an embedded system or a specific application integrated circuit. In order to enable the reviewing committee to have a better understanding and recognition of the structural purpose and efficacy of the present invention, the following examples are described in detail with reference to the illustrated examples. [Embodiment] FIG. 1 is a schematic diagram of an input image matrix of the present invention. The edge extraction system of the present invention extracts the edge of an image by pulling the input image in three directions of horizontal, vertical, and diagonal directions, and assigns the same or The different gains in turn control the degree of edge enhancement in the three directions. One pixel (such as y22) and its surrounding pixels in the image are exemplified by a Y matrix, such as: yn yi2 yi3 y2i m y23 ysi ys2 y33 Preferably, the Y matrix is a matrix of 3 by 3. 7 200939154 Y' is a matrix obtained by the arithmetic processing of the present invention.
LoY,、 yn — _yj2 yis Yn ------ y23 yai ---- __X32 y33LoY,, yn — _yj2 yis Yn ------ y23 yai ---- __X32 y33
χν+ι^車項技Λ者可知,γ矩陣亦可表示為(2劇则 XJN + U之矩陣,其中Ν為自然數。 ,該W像巾之—像素yij (如Μ)及其周圍像素以一 5乘5之矩陣γ矩陣1〇5為例,Χν+ι^ car technology knows that the γ matrix can also be expressed as (2) the matrix of XJN + U, where Ν is a natural number. The W-like towel-pixel yij (such as Μ) and its surrounding pixels Take a 5 by 5 matrix γ matrix 1〇5 as an example.
yn yi2 yis y.. y.. yzi y23 y.. v.. y3i _ys2 ysa y.. y.. y. · y.. y.. y.. y.. y.. y.. y.. y.. y.. 本發明之邊緣萃取,係依水平、垂直及對角三個方 進行拉普拉斯運算萃取出影像邊緣該影像中之一~像素向 (如yu)及其周圍像素以一 3乘3之Y矩陣為例,第、—y 緣值201可被表示方程式為: —邊Yn yi2 y.. y.. yzi y23 y.. v.. y3i _ys2 ysa y.. y.. y. · y.. y.. y.. y.. y.. y.. y.. Y.. y.. The edge extraction of the present invention extracts the image edge according to the horizontal, vertical and diagonal three sides of the image. Taking a 3 by 3 Y matrix as an example, the -y-edge value 201 can be expressed as: - edge
LoY - 水平增益 X (y22x2-y2i-y23) + 垂直增益 X (y22x2-yi2-y32) + 對角增益 X (y22x4-yn-yi3-y3i-y33); 200939154 • 熟於該項技藝者可知,該影像中之一像素yi j (如y22) 及其周圍像素以一 N乘N之Y矩陣為例,第一邊緣值201 之通式亦可表示:LoY - horizontal gain X (y22x2-y2i-y23) + vertical gain X (y22x2-yi2-y32) + diagonal gain X (y22x4-yn-yi3-y3i-y33); 200939154 • Those skilled in the art know, One pixel yi j (such as y22) and its surrounding pixels in the image are exemplified by a Y-by-N matrix, and the first edge value 201 can also be expressed as:
LoY =水平增益 X (yN+i,tmx(2xN-l)-Eyi,j j=N+l) + 垂直增益 x (yN+i,N+ix(2xN-l)-Eyi,j i=N+l) + 對角增益 x (yN+i,N+ix(2xN-l)-Eyi,jj=+/-i); 將輸入影像做拉普拉斯運算得出影像的高頻項LoY, ® 即影像邊緣的資訊。在此使用者可藉由設定水平增益、垂 直增益及對角增益來給予水平,垂直,及對角線方向不同 增益,以控制三個方向邊緣強化程度之差異。 圖二係為本發明之邊緣強化示意圖,本發明則是針對 得出的影像的高頻項LoY,即影像邊緣的資訊數值進行拉 普拉斯切運算,得到針對個別影像邊緣所要調整的數值大 小LoY’ 即第二邊緣值301,並將第二邊緣值加回原始影 像相同的位置,便可達到邊緣強化的效果。拉普拉斯切運 Ο 算之方程式可表示如圖二。 使用者可藉由設定: 正、負向高/低級(high/low_level,H / L ) 調整邊緣部份和所要強化的程度。正、負向高/低級參數 設定的用意在限制真正需要強化的影像邊緣,避免雜訊強 化。 當 L<LoY<H, LoY’ =LoY-L; 當-H<LoY<-L,LoY’ =L〇Y+L; 9 200939154 當〜L<l〇Y<L, LoY,=〇; 當 LoY,=h-L;以及 當 l〇Y$L, LoY,=-(h-L);其中 H以及L為拉切中高低級之參數。 圖二設計上’根據原始輸入影影像的亮度(luminance) 數值的大小’哉們對會給予不同的邊緣強化增益 EE_gain’為了設計方便,可假設Y為1〇位元的輸入訊號, ® 邊緣強化增益301 (EE_gain)的值介於0到4之間。 而強化後的影像與原始影像的關係則為: 該第二邊緣值乘以一第一增益再與該第一影像相加後 輸出一第二影像。 強化後的影像與原始影像的關係之方程式可表示如 下: Y’ = Y + LoY’ X EE gain。 必須注意的是,本發明雖然以上述具體實施例作為說 〇 明,但並不以此為限。具有本領域之一般技術的人士當可 提出其他變化,而不脫離本發明之範圍。 以本發明之方法所形成之邊緣萃取與強化方法,尤其 是有關於一種使用拉普拉斯運算及拉普拉斯切的低雜訊 的邊緣萃取與強化方法,除了可以為一硬體實現之外,亦 可以為一被入式系統(Embedded system)或一特定應用積 體電路(ASIC)實現。同樣地,本發明之邊緣萃取與強化方 法之應用領域亦不以此為限。具有本領域之一般技術的人 200939154 士當可提出其他變化,如輸入Y為9位元的輸入訊號,而 不脫離本發明之範圍。 再請參照圖四,圖四係為依據本發明之一之邊緣萃取 與強化方法範例流程圖。第一影像中之一像素y i j (如y 2 2) 及其周圍像素以一 N乘N之Y矩陣401所表示,矩陣401 經拉普拉斯運算402後得到一第一邊緣值LoY,該第一邊 緣值LoY經拉普拉斯切403後得到一第二邊緣值LoY’ , ❹ 第二邊緣值LoY’經方程式404運算後得一輸出為第二影 像,方程式404可表示如下: 該第二邊緣值乘以一第一增益再與該第一影像相加後 輸出一第二影像。 Y,= Y + LoY,X EE_gain。 《實施範例》 為使貴委員進一步了解本發明於實際運用上之優越 性,發明人將以十一個矩陣為例依前述内容進行運算,其 ❿中: EE gain = 3.5 ; 而 水平、垂直及對角三個方向增益分別為:4、2及0; 而在實際運算中拉普拉斯切亦被可定義為以下的方程 式: 當 EE_th < LOY < 127+EE_th LoY’ =L0Y - EE—th; 當-128-EE_th < LOY < -EE_th LoY’ =L0Y+EE_th; 當-EE_th <= LOY <= EE—th LoY’ =0; 11 200939154 當 LOY >= 127+EE_th LoY’ =127;以及 當 LOY <= -128-EE—th LoY’ =-128;其中 EE_th為拉普拉斯切中高低級之參數。 當輸入矩陣為501A所表示(如圖五A) 影像中之一像素yij (如y22)經本發明之運算如下: LoY=4x(20-10-10)+2*(20-10-10)+0*(40-10-10-10-10)=0; LoY’ =0; y22’ =^22=10。 ❹ 當輸入矩陣為501B所表示(如圖五B) 影像中之一像素yu (如y22)經本發明之運算如下: L〇Y=0;L〇Y’ =0; y22’ =y22=12。 當輸入矩陣為501C所表示(如圖五C) 影像中之一像素yu (如y22)經本發明之運算如下: LoY=4;LoY’ =0; y22,=y22=12。 當輸入矩陣為501D所表示(如圖五D) 影像中之一像素yu (如y22)經本發明之運算如下: ❹ LoY=8;LoY’ =4; y22=14; y22’ =28。 當輸入矩陣為501E所表示(如圖五E) 影像中之一像素yu (如y22)經本發明之運算如下: 1^(^=164(^:125 722=14: y22’ =56 〇 當輸入矩陣為501F所表示(如圖五F) 影像中之一像素yu (如y22)經本發明之運算如下: LoY=8;LoY’ =4; y22=14; y22’ =28。 當輸入矩陣為501G所表示(如圖五G) 12 200939154 影像中之一像素yij (如y22)經本發明之運算如下·LoY = horizontal gain X (yN+i, tmx(2xN-l)-Eyi, jj=N+l) + vertical gain x (yN+i, N+ix(2xN-l)-Eyi, ji=N+l ) + diagonal gain x (yN+i, N+ix(2xN-l)-Eyi, jj=+/-i); Do the Laplacian operation of the input image to obtain the high-frequency term LoY, ® Information on the edge of the image. Here, the user can give horizontal, vertical, and diagonal gains by setting the horizontal gain, vertical gain, and diagonal gain to control the difference in edge enhancement between the three directions. 2 is a schematic diagram of edge enhancement according to the present invention. The present invention performs a Laplacian operation on the high-frequency term LoY of the obtained image, that is, the information value of the image edge, and obtains a numerical value to be adjusted for the edge of the individual image. LoY' is the second edge value 301, and the second edge value is added back to the same position as the original image to achieve the edge enhancement effect. The Laplace cut Ο equation can be represented as shown in Figure 2. The user can adjust the edge portion and the degree of enhancement to be achieved by setting: positive/negative high/low level (H / L). The positive and negative high/low parameters are designed to limit the edges of the image that really need to be enhanced to avoid noise enhancement. When L<LoY<H, LoY' =LoY-L; when -H<LoY<-L, LoY' = L〇Y+L; 9 200939154 when ~L<l〇Y<L, LoY,=〇; LoY, =hL; and when l〇Y$L, LoY, =-(hL); where H and L are the parameters of the middle and low level of the cleavage. Figure 2 is designed to 'based on the brightness of the original input image's luminance value'. We will give different edge enhancement gains EE_gain' for design convenience. It can be assumed that Y is a 1-bit input signal, ® edge enhancement The value of gain 301 (EE_gain) is between 0 and 4. The relationship between the enhanced image and the original image is: the second edge value is multiplied by a first gain and then added to the first image to output a second image. The equation for the relationship between the enhanced image and the original image can be expressed as follows: Y' = Y + LoY' X EE gain. It should be noted that the present invention has been described in the above specific embodiments, but is not limited thereto. Other variations can be made by those skilled in the art without departing from the scope of the invention. The edge extraction and strengthening method formed by the method of the invention, in particular, a method for edge extraction and strengthening using low noise of Laplace operation and Laplace cut, except that it can be realized by a hardware In addition, it can also be implemented as an embedded system or an application-specific integrated circuit (ASIC). Similarly, the field of application of the edge extraction and strengthening method of the present invention is not limited thereto. Persons having ordinary skill in the art 200939154 Other changes may be proposed by the priest, such as inputting Y as a 9-bit input signal without departing from the scope of the present invention. Referring again to Figure 4, Figure 4 is a flow chart of an example of an edge extraction and enhancement method in accordance with one of the present inventions. One pixel yij (such as y 2 2) and its surrounding pixels in the first image are represented by an N-by-N Y matrix 401, and the matrix 401 is subjected to a Laplace operation 402 to obtain a first edge value LoY. An edge value LoY is obtained by Laplacian 403 to obtain a second edge value LoY', and a second edge value LoY' is obtained by the equation 404 to obtain an output as a second image. Equation 404 can be expressed as follows: The edge value is multiplied by a first gain and then added to the first image to output a second image. Y, = Y + LoY, X EE_gain. "Examples of Implementation" In order to give your members a better understanding of the superiority of the present invention in practical use, the inventors will use eleven matrices as an example to perform operations according to the above, in which: EE gain = 3.5; and horizontal and vertical The diagonal gains in the three directions are: 4, 2, and 0; and in actual operation, Laplace cut can also be defined as the following equation: When EE_th < LOY < 127 + EE_th LoY ' = L0Y - EE —th; when -128-EE_th < LOY < -EE_th LoY' =L0Y+EE_th; when -EE_th <= LOY <= EE-th LoY' =0; 11 200939154 when LOY >= 127+EE_th LoY' = 127; and when LOY <= -128-EE-th LoY' = -128; where EE_th is the parameter of the high and low level of Laplacian. When the input matrix is represented by 501A (as shown in Figure 5A), one of the pixels yij (such as y22) in the image is operated as follows: LoY=4x(20-10-10)+2*(20-10-10)+ 0*(40-10-10-10-10)=0; LoY' =0; y22' =^22=10. ❹ When the input matrix is represented by 501B (as shown in Figure 5B), one of the pixels yu (such as y22) in the image is operated as follows: L〇Y=0; L〇Y’ =0; y22’ =y22=12. When the input matrix is represented by 501C (as shown in Figure 5C), one of the pixels yu (such as y22) in the image is operated as follows: LoY = 4; LoY' = 0; y22, = y22 = 12. When the input matrix is represented by 501D (as shown in Figure 5D), one of the pixels yu (e.g., y22) in the image is operated as follows: ❹ LoY = 8; LoY' = 4; y22 = 14; y22' = 28. When the input matrix is represented by 501E (as shown in Figure 5E), one of the pixels yu (such as y22) in the image is operated as follows: 1^(^=164(^:125 722=14: y22' =56 〇当输入The matrix is represented by 501F (Fig. 5F). One pixel yu (such as y22) in the image is operated as follows: LoY=8; LoY' = 4; y22=14; y22' = 28. When the input matrix is 501G Represented (Figure 5G) 12 200939154 One of the pixels yij (such as y22) in the image is operated as follows:
LoY=24;LoY’ =20; y22=14; y"22 =84。 當輸入矩陣為501H所表示(如圖五Η) 影像中之一像素yi j (如y22)經本發明之運算如下·LoY=24; LoY’ = 20; y22=14; y"22 =84. When the input matrix is represented by 501H (as shown in Figure 5), one of the pixels yi j (such as y22) in the image is operated as follows:
LoY=16;LoY’ =12; y22=14; y〗2,=56。 當輸入矩陣為5011所表示(如圖五I)LoY=16; LoY’ =12; y22=14; y〗 2,=56. When the input matrix is represented by 5011 (Figure 5 I)
Ο 影像中之一像素yu (如yu)經本發明之運算如下:之一 One pixel yu (such as yu) in the image is operated as follows:
LoY=32;LoY’ =28; y22=14; y22’ =112。 當輸入矩陣為501J所表示(如圖五J) 影像中之一像素yi j (如y22)經本發明之運算如下·LoY=32; LoY’ =28; y22=14; y22’ =112. When the input matrix is represented by 501J (as shown in Figure 5J), one of the pixels yi j (such as y22) in the image is operated as follows:
LoY=48;LoY’ =44; y22=14; y22’ =168。 當輸入矩陣為501K所表示(如圖五K) 影像中之一像素yi j (如yu )經本發明之運算如下. LoY=8;LoY, =4; y22=896 ; y22’ =903。 唯以上所述者,僅為本發明之範例實施態樣爾,當不 月包以之限定本發明所實施之範圍。即大凡依本發明申往 利範圍所作之均等變化與修飾,皆應仍屬於本 蓋之範圍内’故本發明實為—富有新穎性、進^性^函 供產業湘树者,賴合專㈣請要件妓 及可 所至禱審查委員明鑑’並折惠准,是 【圖式簡單說明】 13 200939154 圖一係依據本發明之一之輸入矩陣示意圖; 圖二係拉普拉斯切用於本發明邊緣強化方法之示意 圖; 圖三係依據本發明之一邊緣強化方法之增益之示意 圖; 圖四係依據本發明之一邊緣萃取與強化方法範例示 意圖;及 ❹ 圖五A〜五K係依據本發明輸入矩陣示意圖。 【主要元件符號說明】 103-矩陣 105-矩陣 201-第二邊緣值 301-邊緣強化增益 401-矩陣 G 402-拉普拉斯運算 403- 拉普拉斯切 404- 方程式 501A〜K-矩陣 14LoY=48; LoY’ =44; y22=14; y22’ =168. When the input matrix is represented by 501K (as shown in Figure 5K), one of the pixels yi j (such as yu) in the image is operated as follows: LoY = 8; LoY, = 4; y22 = 896; y22' = 903. The above is only the embodiment of the present invention, and the scope of the invention is not limited by the present invention. That is to say, the average change and modification of the scope of the invention according to the scope of the invention should still fall within the scope of the cover. Therefore, the present invention is actually a novelty, a goodness, and a letter to the industrial Xiangshu. (4) Please ask for the 妓 妓 可 审查 审查 审查 审查 ' 并 并 并 并 并 并 并 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 BRIEF DESCRIPTION OF THE DRAWINGS FIG. 3 is a schematic diagram showing the gain of an edge enhancement method according to the present invention; FIG. 4 is a schematic diagram showing an example of an edge extraction and strengthening method according to the present invention; and FIG. 5A to 5K. The input matrix diagram of the present invention. [Major component symbol description] 103-matrix 105-matrix 201-second edge value 301-edge enhancement gain 401-matrix G 402-lapar operation 403-lapras 404- equation 501A~K-matrix 14
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