Abstract:
The invention relates to an image resolution interpolation method utilizing two reference pixels, two equations and a compensation equation to determine an interpolation pixel. The two equations respectively determine two right weight values for the two reference pixels, and the invention more uses a product of the two right weight values, the compensation equation, and a difference which is between two reference pixels to adjust the image. The invention can be applied to an image of any size and maintains the sharpness of the image, wherein the image will not become blurred due to the interpolation.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     The invention relates to an image interpolation method and device, and more particularly to an image resolution interpolation method and device utilizing cubic equations and reference points reducing slope to increase image quality and reduce required hardware resources.  
         [0003]     2. Description of the Related Art  
         [0004]     In present display devices, the electronic screen system has been popularly applied in a plurality product, such as digital cameras, LCD TVs, LCD displays and the like. However, when the resolution of an image source differs from the resolution of the image display, an image resolution adjustment device is desirable to change the resolution of the image source to meet the resolution of the image display.  
         [0005]     If the resolution of the input image is 640×480 (VGA) and the output resolution requirement is 1024×768 (XGA mode), the resolution of the image must be increased. If the resolution of the input image is 1280×1024 (SXGA) and the output resolution requirement is 1024×768 (XGA mode), the resolution of the image must be decreased. To strike a balance between quality and cost, resolution processing is critical. Common used image resolution interpolation processing methods, include Bilinear, Cubic, Besier, Natural, Catmull-Rom, Hermite and similar.  
       BRIEF SUMMARY OF THE INVENTION  
       [0006]     The invention provides an image interpolation converting device to meet the function of the system client.  
         [0007]     The invention further provides an image resolution interpolation method and device utilizing cubic equations and a slope between two reference points to reduce required hardware resources.  
         [0008]     To achieve the described goal, the invention utilizes two reference points p( 1 ) and p( 2 ) and provides cubic equations: v 1 (t)= 2 tˆ3−3tˆ2+1; v 2 (t)=− 2 tˆ3+ 3 tˆ2; v 3 (t)=tˆ3− 2 tˆ2+t; v 4 (t)=tˆ3−tˆ2. The slope factor T is equal to [p( 1 )−p( 2 )]. The interpolation point pi(t) is equal to v 1 (t)*p( 1 )+v 2 (t)*p( 2 )+T*(v 3 (t)+v 4 (t)) and pi(t) is limited within a valid range, for example, pi(t) is limited within the range between  0  and 255 as the interpolation point pi(t) is an 8-bit value. The interval gain factor, t, is evaluated based on the input image resolution and the output display resolution, for example, t is equal to 0.625 when the resolution is changed from 640 points to 1024 points. The image resolution interpolation method of the invention can scale the image at will preserve the sharpness of the image, and the image will not become blurred due to the interpolation. The invention provides better performance and requires fewer hardware resources than the conventional interpolation method, such as Bilinear, Cubic, Besier, Natural, Catmull-Rom, Hermite and the like.  
         [0009]     A detailed description is given in the following embodiments with reference to the accompanying drawings. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]     The present invention can be more fully understood by reading the subsequent detailed description and examples with references made to the accompanying drawings, wherein:  
         [0011]      FIG. 1  is a schematic diagram of an embodiment of the interpolation method of the invention.  
         [0012]      FIG. 2  is a curve diagram of the equations defined by the invention.  
         [0013]      FIG. 3  is a block diagram of an embodiment of the invention.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0014]     The following description is of the best-contemplated mode of carrying out the invention. This description is made for the purpose of illustrating the general principles of the invention and should not be taken in a limiting sense. The scope of the invention is best determined by reference to the appended claims.  
         [0015]      FIG. 1  is a schematic diagram of an embodiment of the interpolation of the invention. P 1  and P 2  are pixels of the input image. T is a vector generated by P 1  and P 2 . Pi is the image interpolation point evaluated by the method of the invention and t is the interval gain factor of the interpolation point.  
         [0016]     Three cubic equations in one unknown are defined as following: 
 
 E 1( t )=2 t ˆ3−3 t ˆ2+1  eq.1 
 
 E 2( t )=−2 t ˆ3+3 t ˆ2  eq.2 
 
 E 3( t )=2 t ˆ3−3 t ˆ2+ t   eq.3 
 
         [0017]     The slope factor is defined as following: 
 
 T=V (P1)− V (P2),  eq.4 
 
 wherein V(P 1 ) is the image value of the pixel P 1  and V(P 2 ) is the image value of the pixel P 2 . 
 
         [0018]     The interpolation point Pi is defined as followings: 
 
 Pi ( t )= E 1( t )* V ( P 1)+ E 2( t )* V ( P 2)+( V ( P 1) V ( P 2))* E 3( t )  eq.5 
 
         [0019]     The interval gain factor, t, is evaluated based on the input image resolution and the output resolution of the display, for example, t is equal to 0.625 when the resolution is changed from 640 points to 1024 points. According to the described equations, the interpolation point Pi can be represented by the following equation: 
 
 Pi ( t )= V ( P 1)*(2 t ˆ3−3 t ˆ2+1)+ V ( P 2)*(−2 t ˆ3+3 t ˆ2)+ T (2 t ˆ3−3 t ˆ2+ t )  eq.6 
 
         [0020]     The interpolation point Pi(t) is limited within the range between 0 and 255 as the interpolation point Pi(t) is an 8-bit value. Thus, the input image can be scaled in any resolution by adjusting the interval gain factor, t, and the reference points, such as P 1  and P 2 . In  FIG. 1 , the interval gain factor, t, is equal to 0.5.  
         [0021]     Please refer to  FIG. 2 .  FIG. 2  is a curve diagram of the equations defined by the invention. The vertical axis y represents the variable  200 . The horizontal axis represents the variable t  200 . Curve  202  represents a set of the domain and range of the equation E 1 (t). Curve  203  represents a set of the domain and range of the equation E 2 (t). Curve  203  represents a set of the domain and range of the equation E 3 (t). Curve  204  represents a set of the domain and range of the equation E 4 (t).  
         [0022]     According to the described, it is clear that the spirit of the invention is that when the interpolation point Pi is closer to the pixel P 1  than the pixel P 2 , the weighted value of the pixel P 1  generated by the equation E 1 (t) is greater than the weighted value of the pixel P 2  generated by the equation E 2 (t). On the other hand, when the interpolation point Pi is closer to the pixel P 2  than the pixel P 1 , the weighted value of the pixel P 2  generated by the equation E 2 (t) is greater than the weighted value of the pixel P 1  generated by the equation E 1 (t). In other words, when t is more than 0 and less than 0.5, E 1 (t) is more than 0.5 and E 2 (t) is less than 0.5, and when t is more than 0.5 and less than 1, E 2 (t) is more than 0.5 and E 1 (t) is less than 0.5. Furthermore, the sum of E 1 (t) and E 2 (t) is equal to 1. Definitely, the equations E 1 (t) and E 2 (t) are cubic equations in one unknown and they are only examples of the invention, and the invention is not limited thereto. For example, the equations E 1 (t) and E 2 (t) could be quadratic equations in one unknown or biquadratic equations in one unknown, wherein the equation E 1 (t) and the equation E 2 (t) only correspond with the described limitations.  
         [0023]     Furthermore, the compensation equation E 3 (t) has to conform with that the equation E 3 (t) equals 0 at t=0 and t=1. Thus, it can conform with that the bounded condition when t is equal to 0, Pi(t) is equal to V(P 1 ) and when t is equal to 1, Pi(t) is equal to V(P 2 ). And the constant value of the equation E 3 (t) is equal to 0 because E 3 ( 0 ) is equal to 0. Besides, the function value of the compensation equation is bilateral symmetry of a line t=0.5. The domain of equation E 3 (t) is between 0 and 1 and the range of equation E 3 (t) is between −1 and 1. Thus, an average value of the values of the interpolation points is located between the pixels P 1  and P 2  and each value of interpolation point is located between V(P 1 ) and V(P 2 ). Moreover, one feature of the compensation equation E 3 (t) is that at least one solution is at the interval between 0 and 1 when the compensation equation E 3 (t) is equal to 0.  
         [0024]     The method of the invention can be implemented by hardware, software, firmware or the combination thereof. Please refer to  FIG. 3 .  FIG. 3  is a block diagram of an embodiment of an image resolution interpolation device of the invention. The image resolution interpolation device comprises an input unit  301  and a computing unit  302  for transforming the resolution of the image from a first resolution to a second resolution. The input unit  301  receives a first image value V(P 1 ) of pixel P 1  and a second image value V(P 2 ) of pixel P 2 . The computing unit  302  evaluates interpolation values Pi (t) based on a first equation in one unknown, a second equation in one unknown, a third equation in one unknown and a ratio of the second resolution to the first resolution and generates an image with the second resolution based on the interpolation values Pi(t).  
         [0025]     While the invention has been described by way of example and in terms of preferred embodiment, it is to be understood that the invention is not limited thereto. To the contrary, it is intended to cover various modifications and similar arrangements (as would be apparent to those skilled in the art). Therefore, the scope of the appended claims should be accorded the broadest interpretation so as to encompass all such modifications and similar arrangements.