fig4 is a systematic composition diagram of the invention . the system is applicable to a grayscale - transformed image data for calculating the grayscale value p of a destination pixel p surrounded by four original pixels a , b , c and d . the four original pixels a , b , c and d form a rectangle including the destination pixel p . the composition of the interpolation system of the invention includes a receiving module 10 , a calculation module 20 for the transformation matrix of central pixels , a judging module 30 and an operator 40 . as shown in fig3 , the rectangle composed of the four original pixels a , b , c and d is divided into 16 sections a 11 ˜ a 44 . the sections a 11 ˜ a 44 include central reference pixels r 1 ˜ r 16 . the receiving module 10 receives grayscale values p 1 , p 2 , p 3 and p 4 of the four original pixels a , b , c and d ; and an interpolation transformation matrix m . the interpolation transformation matrix m is presented by : m = [ dxdy ( 1 - dx ) ⁢ dy dx ⁡ ( 1 - dy ) ( 1 - dx ) ⁢ ( 1 - dy ) ] = [ m 1 m 2 m 3 m 4 ] the above interpolation transformation matrix m is of linear interpolation . when the user applies a different interpolation algorithm , a different transformation matrix m is then used . the elements m 1 , m 2 , m 3 , m 4 of the interpolation transformation matrix m are calculated by the relative distances dx , dy from coordinates of the destination pixel p and the original pixels a , b , c , d . therefore , the calculation module 20 applies the interpolation transformation matrix m and the relative coordinates of the central reference pixel r to the four original pixels a , b , c , d to get the distances dx , dy and calculate the four elements m 1 , m 2 , m 3 , m 4 of the transformation matrix m for each central reference pixel r 1 ˜ r 16 . the calculations are complicated . therefore , they are processed by software . this can save the time of hardware operation . then , the judging module 30 determines the position of the destination pixel p and identifies the operational section it belongs to . for example , the destination pixel p is located in the section a 23 , which is the operational section for further operations . the central reference pixel r 7 of the section a 23 is used to apply the operation of four elements of the interpolation transformation matrix m . any destination pixel p located in a same section gets a same grayscale value . finally , the operator 40 applies the four elements of the interpolation transformation matrix m corresponding to the central reference pixel r 7 of the section a 23 , operates with the four grayscale values p 1 , p 2 , p 3 and p 4 of the original pixels a , b , c , d , and gets the grayscale value p of the destination pixel p . in the aforesaid inner product operation , the elements of the two matrixes are first multiplied ( m 1 × p 1 · m 2 × p 2 · m 3 × p 3 · m 4 × p 4 ) then added ( m 1 × p 1 + m 2 × p 2 + m 3 × p 3 + m 4 × p 4 ). therefore , the operator 40 requires a multiplier and an adder . also , as the multiplication and addition are simple , they reduce the hardware load and save the time of image process . fig6 is a flowchart of an interpolation method of the invention . the components described in the flowchart can be referred to fig4 . first , the receiving module receives the correspondent grayscale values of four original pixels and an interpolation transformation matrix ( step 51 ). the interpolation transformation matrix m is designated by user . therefore , when the user chooses a different transformation matrix for calculating the grayscale value p of the destination pixel p , the specific interpolation transformation matrix m is loaded . then , the calculation module for the transformation matrix of central pixels calculates the four elements of interpolation transformation matrix corresponding to each central reference pixel ( step 52 ) according to the interpolation transformation matrix and the relative coordinates of the central reference pixels and the original pixels . because the interpolation transformation matrix m corresponding to each central reference pixel is relative to the distances dx , dy , the calculation of four elements m 1 , m 2 , m 3 , m 4 of the transformation matrix m requires relative coordinates of the destination pixel p to the original pixels a , b , c , d . the calculation of the elements m 1 , m 2 , m 3 , m 4 is more complicated . therefore , this step is made by software . then , the judging module determines an operational section containing the destination pixel p according to coordinates of the destination pixel ( step 53 ). any destination pixel p located in a same operational section can apply a same interpolation transformation matrix m . finally , the operator makes an inner product of the four elements of interpolation transformation matrix in the operational section of the destination pixel to the grayscale values of the original pixels so as to get grayscale value of the destination pixel ( step 54 ). this step uses simple multiplication and addition operations . therefore , the operator 30 includes a multiplier and an adder for the inner product operation for getting the grayscale value p of the destination pixel p . the number of sections in the original pixels square depends on precision requirement . for example , as shown in fig7 , the square composed of the original pixels a , b , c and d is divided into 64 sections for calculating the grayscale value p of a destination pixel p . the more sections provide a more precise grayscale value p . however , it costs more time of process . on the contrary , as shown in fig8 , the square composed of the original pixels a , b , c and d is divided into four sections for calculating the grayscale value p of a destination pixel p . the less sections provide a less precise grayscale value p . however , it saves time of process . therefore , the section number is determined according to user &# 39 ; s requirement of precision . fig9 is an illustration of a cubic interpolation process applied to 16 original pixels a to p surrounding a destination pixel p for calculating the grayscale value p of the destination pixel p . the sixteen original pixels a to p are located in a 4 * 4 matrix and formed with nine sections 60 . each original pixel a to p has a correspondent grayscale value p 1 ˜ p 16 respectively . the destination pixel p is located in a central section 61 . the central section 61 is further divided into a plurality of sub - sections 611 each having a central reference pixel ( not shown in the drawing ). the greyscale value p of the destination pixel p is calculated by inner product of an interpolation transformation matrix m nm and grayscale values p 1 ˜ p 16 of original pixels a to p according to a cubic interpolation process applying the following equation : a n ⁢ ⁢ m = m n ⁢ ⁢ m ⁡ [ p1 p2 m p15 p16 ] , n = 1 ∼ 4 , m = 1 ∼ 4 m11 = [ m ⁢ ⁢ a 11 m ⁢ ⁢ b 11 m ⁢ ⁢ c 11 m ⁢ ⁢ d 11 ⁢ k m ⁢ ⁢ q 11 ] 1 × 16 m12 = [ m ⁢ ⁢ a 12 m ⁢ ⁢ b 12 m ⁢ ⁢ c 12 m ⁢ ⁢ d 12 ⁢ k m ⁢ ⁢ q 12 ] 1 × 16 ⁢ m m44 = [ m ⁢ ⁢ a 44 m ⁢ ⁢ b 44 m ⁢ ⁢ c 44 m ⁢ ⁢ d 44 ⁢ k m ⁢ ⁢ q 44 ] 1 × 16 in which ma 11 , mb 11 , mc 11 . . . mq 11 represents sixteen elements of a matrix m 11 ; ma 12 , mb 12 , mc 12 . . . mq 12 represents sixteen elements of a matrix m 12 , and so on . the calculation of greyscale value p of the destination pixel p is similar to aforesaid linear interpolation but the number of original pixels a to p is increased . therefore , a cubic interpolation is applied . the more original pixels provide a more precise grayscale value p . however , it cost more time of process . therefore , the pixel number is determined according to user &# 39 ; s requirement of precision . the invention being thus described , it will be obvious that the same may be varied in many ways . such variations are not to be regarded as a departure from the spirit and scope of the invention , and all such modifications as would be obvious to one skilled in the art are intended to be included within the scope of the following claims .