Patent Publication Number: US-7714939-B2

Title: Reliability estimation of temporal noise estimation

Description:
FIELD OF THE INVENTION 
   The present invention relates generally to video processing, and more particularly to noise estimation in video signal processing. 
   BACKGROUND OF THE INVENTION 
   Noise estimation is required in many algorithms to process image or video optimally. For example, in TV system, noise reduction is often applied as the first step to obtain noise-free video sequences. An optimal algorithm of noise reduction first estimates the noise variance of input video sequences, and then performs noise reduction. Noise estimation is very important in this case, because overestimation leads to image blurring and underestimation leads to insufficient noise reduction. 
   In order to describe the problem of noise estimation, let g t  denote the incoming video frame at time instant t and g t (i,j) denote the corresponding pixel value at the coordinates (i,j) where i represents the ordinate and j represents the abscissa. Generally, we assume the input video sequence is corrupted by independent, identically distributed additive and stationary zero-mean Gaussian noise with variance σ 0   2 , that is, any pixel g t (i,j) can be denoted as:
 
 g   t ( i,j )= f   t ( i,j )+ n   t ( i,j ),  (1)
 
   where f t (i,j) denotes the true pixel value without noise corruption and n t (i,j) is the Gaussian distributed noise component satisfying
 
n t (i,j)˜N(0,σ 0   2 ).  (2)
 
   Thus, the problem of noise estimation is to estimate the noise variance σ 0   2  of the contaminated image g t  without the priori information of the original image f t . 
   A straightforward method of noise estimation is to compute the expectation of the local variance of image g t . This method suffers from the image structure, causing overestimation. To overcome this problem, several methods have been proposed. One method excludes the local variance if the gradient magnitude of the corresponding pixel is greater than a preset threshold. However, the gradient magnitude is also related with the noise variance, so it is difficult to find an appropriate threshold. Other conventional methods first extract the noise component with little structure by applying high-pass filters on the contaminated image g t , and then perform noise estimation on the noise component. One example decomposes the image into a pyramid structure of different block sizes, wherein the noise variance is estimated from a sequence of four smallest block-based local variances at each level. Another example, a Rayleigh distribution is fitted to the magnitude of the intensity gradient, wherein noise variance is estimated based on the attribute that the Rayleigh probability density function reaches maximum at value σ 0 . Other methods estimate multiplicative as well as additive noise. 
   All of the above methods utilize the spatial local statistics to estimate noise variance. The estimation accuracy depends on the separation of the noise component and the real image signal. The robustness degrades greatly if most of image contains complicated structure. 
   BRIEF SUMMARY OF THE INVENTION 
   The present invention addresses the above shortcomings. In one embodiment, the present invention provides a method for reliable noise estimation in a set of video frames. If there is no motion between two consecutive frames, the temporal local difference between two small blocks at the same spatial position in the two consecutive frames satisfies a certain distribution whose statistical characteristics are already known (the shape of the distribution curve is already known). The estimated noise variance derived from such distribution is very reliable. If motion exists between two consecutive frames, the distribution of the temporal local difference is affected by the motion information, may lead to unpredictable statistical characteristics. The estimated noise variance derived from such distribution is not reliable. 
   To improve the performance of the noise estimation method, the reliability of the estimated noise variance can be estimated. If the estimated noise variance is not reliable, it is discarded and the previous estimated reliable noise variance is used instead. To estimate the reliability, the ideal distribution curve of the temporal local difference is obtained by assuming the estimated noise variance is reliable. Then, the real distribution curve of the temporal local difference is compared with the ideal one. If they are very similar, the obtained noise variance is truly reliable. Otherwise, it is not reliable. The reliability thus can be calculated from the similarity of those two distributions. Since it may be difficult to measure the similarity of two distribution curves, instead of doing so, some characteristic values describing the shape of the distribution curves can be calculated. The obtained noise variance is reliable only if the characteristic values of the distribution of the temporal local difference are close to those of the ideal distribution. 
   In one implementation, the present invention provides a method for reliability estimation of temporal noise estimation in a sequence of video frames, comprising the steps of: obtaining temporal local difference signals from the difference between a previous frame and a next frame in the sequence of frames; determining a distribution of the temporal local difference; determining the characteristic values of the distribution; and comparing the characteristic values to expected values to obtain an indication of the reliability of the temporal noise estimation. 
   Other embodiments, features and advantages of the present invention will be apparent from the following specification taken in conjunction with the following drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a block diagram of an embodiment of a reliability estimator according for temporal noise estimation according to the present invention; 
       FIG. 2  shows examples of the distribution of MAE between two small blocks at the same spatial position of two consecutive frames without motion; 
       FIG. 3  shows an example implementation of characteristic value calculator of  FIG. 1 ; 
       FIG. 4  shows an example implementation of reliability detector of  FIG. 1 ; 
       FIG. 5  shows another example implementation of characteristic value calculator of  FIG. 1 ; 
       FIG. 6  shows another example implementation of reliability detector of  FIG. 1 ; 
       FIG. 7  shows another example implementation of characteristic value calculator of  FIG. 1 ; 
       FIG. 8  shows another example implementation of reliability detector of  FIG. 1 ; 
       FIG. 9  shows a block diagram of an embodiment of a combination reliability estimator according to the present invention; 
       FIG. 10  shows an example implementation of the final decision unit of  FIG. 9 . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring to the drawings, embodiment of the present invention is described below. In one embodiment, the present invention provides a method for reliable noise estimation in a sequence of video frames. If there is no motion between two frames, estimation of noise variance based on a temporal local difference between two small blocks at the same spatial position in the two consecutive frames satisfies a certain distribution whose statistical characteristics are already known (the shape of the distribution curve is already know). The estimated noise variance derived from such distribution is very reliable. If motion exists between two consecutive frames, the distribution of the temporal local difference is affected by the motion information, may lead to unpredictable statistical characteristics. The estimated noise variance derived from such distribution is not reliable. 
   To improve the performance of the noise estimation method, the reliability of the estimated noise variance can be estimated. If the estimated noise variance is not reliable, it is discarded and the previous estimated reliable noise variance is used instead. To estimate the reliability, the ideal distribution curve of the temporal local difference is obtained by assuming the estimated noise variance is reliable. Then the real distribution curve of the temporal local difference is compared with the ideal one. If they are very similar, the obtained noise variance is truly reliable. Otherwise, it is not reliable. The reliability thus can be calculated from the similarity of those two distributions. Since it may be difficult to measure the similarity of two distribution curves, instead of doing so, some characteristic values describing the shape of the distribution curves can be calculated. The obtained noise variance is reliable only if the characteristic values of the distribution of the temporal local difference are close to those of the ideal distribution. 
   In the commonly assigned patent application Ser. No. 10/991,265, “methods to estimate noise variance from a video sequence,” (incorporated herein by reference), the noise variance (standard deviation) is estimated based on the distribution of the temporal local difference, such as mean absolute error (MAE) between two small blocks at the same spatial position of two consecutive frames. 
   In one aspect the present invention provides an extension of said commonly assigned patent application, wherein according to an embodiment of the present invention it is assumed that the temporal local difference of each pixel is already known (e.g., obtained by the method described in said commonly assigned patent application). It is assumed that the estimated noise variance is reliable to obtain the ideal distribution curve of the temporal local difference. On the other hand, the real distribution curve can be obtained from the histogram of the temporal local difference. By comparing the real curve with the ideal one, it can be determined that the estimated noise variance is truly reliable or not. For convenience, some characteristic values are computed which indicate the shape of the real distribution curve which are independent of the noise variance. The characteristic values obtained from the ideal distribution are used as thresholds (described in more detail further below). Therefore, the reliability of the estimated noise variance can be determined by comparing the characteristic values of the real distribution with some thresholds. 
   The framework of reliability estimation of temporal noise estimation is shown by an example block diagram of a system  100  in  FIG. 1  according to an embodiment of the present invention. The system  100  includes a histogram calculator  102 , a characteristic value calculator  104 , and a reliability detector  106 . The inputs to the system  100  are temporal local difference signals and thresholds, and the output of the system  100  is a reliability estimation. The histogram calculator  102  determines the histogram (distribution) of the temporal local difference, and the characteristic value calculator  104  calculates the characteristic values from the histogram (distribution). Comparing the characteristic values of the temporal local difference and the thresholds, the reliability detector  106  outputs said reliability estimation, according to the present invention. 
   An example operation of the system  100  is described in more detail below. To estimate the reliability, the temporal local difference input is provided to the histogram calculator  102  to obtain the histogram/distribution. The characteristic value calculator  104  computes some characteristic values, wherein the reliability detector  106  compares the characteristic value to the threshold(s) to determine whether the estimated noise variance is reliable or not. Only reliable estimated noise variance (standard deviation) is used, and unreliable ones are discarded. 
   In the following, three examples of reliability estimation according to the present invention, which can be implemented in variations of the system  100  of  FIG. 1 , are described. For these examples, assume that MAE is the temporal local difference, and that the ideal distribution of the MAE (if no motion exists between two consecutive frames) is as shown by example  200  in  FIG. 2  as curves  202 ,  204 ,  206  and  208 , where k=H×W is the block size to compute MAE. The example curves  202 ,  204 ,  206  and  208  in  FIG. 2  correspond to the cases where the value k=H×W is 1, 2, 4, 8, respectively. (x-axis denotes ŷ and the y-axis denotes p(ŷ) described below). 
   Let ŷ be the MAE, and p(ŷ) be the probability density function (p.d.f.) of the distribution from the histogram calculator  102  ( FIG. 1 ). The same histogram calculator is used to obtain the normalized histogram h(ŷ) of the MAE that is the input in the three examples below. 
   Example 1 
   The first example implementation of the characteristic value calculator  104  and the reliability detector  106  are now described. The first example of the characteristic value calculator  104  is shown by the example block diagram of a unit  300  of  FIG. 3 . In the unit  300 , a maximum histogram value position calculator  302  determines ŷ p  as the MAE value corresponding to the maximum histogram value according to relation (3) below: 
   
     
       
         
           
             
               
                 
                   
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                 ( 
                 3 
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   In this implementation, the first characteristic value m 1  is obtained by summing unit  304  according to relation (4) below: 
   
     
       
         
           
             
               
                 
                   m 
                   1 
                 
                 = 
                 
                   
                     ∑ 
                     
                       
                         y 
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   Relation (4) above is equivalent to integration of the p.d.f. p(ŷ) over the interval [0,2ŷ p ], as shown in relation (5) below: 
   
     
       
         
           
             
               
                 
                   m 
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   In the ideal case (no motion between the two consecutive frames), it can be obtained that m 1 ≈1 If motion exists, m 1  decreases. Therefore, given a threshold t 1 (t 1 ≦1) if m 1 ≧t 1 , we say that there is no motion and the estimated noise is reliable. 
   According to the above analysis, the first example of the reliability detector  106  ( FIG. 1 ) can implemented as shown by the example in  FIG. 4  as the unit  400 , which inputs the first characteristic value m 1  and the threshold value t 1  to provide a reliability indication. The function of unit  400  comprises determining: if m 1 ≧t 1 , then reliability=1 (i.e., “true”); otherwise, reliability=0 (i.e., “false”). The output “true” indicates reliable while the output “false” indicates not reliable. 
   In application, the integration or summation range is not limited to [0,2ŷ p ]. If another range is used, the threshold value t 1  should be adjusted correspondingly. 
   Example 2 
   The second example implementation of the characteristic value calculator  104  and the reliability detector  106  are now described. The second example implementation of the characteristic calculator  104  ( FIG. 1 ) is shown by the block diagram of a unit  500  in the example of  FIG. 5 . A maximum histogram value position calculator  502  determines ŷ p  according to relation (3) above. Then, the first summation unit  504  determines the sum: 
             ∑       y   ^     =   0       2   ⁢       y   ^     p         ⁢       h   ⁡     (     y   ^     )       .           
Further, the second summation unit  506  determines the sum:
 
             ∑       y   ^     =       3   4     ⁢       y   ^     p             5   4     ⁢       y   ^     p         ⁢       h   ⁡     (     y   ^     )       .           
Then, a divider  508  divides said two sums, such that unit  500  generates the characteristic value m 2  according to relation (6) below:
 
   
     
       
         
           
             
               
                 
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   The characteristic value m 2  is equivalent to the normalized integration of the p.d.f. p(ŷ) in the central area 
             [         3   4     ⁢       y   ^     p       ,       5   4     ⁢       y   ^     p         ]     ,         
according to relation (7) below:
 
   
     
       
         
           
             
               
                 
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   In the ideal case (i.e., no motion between the two consecutive frames), it can be derived that m 2  is close to a constant value, denoted as C m     2   . This constant value is related to the block size k=H×W. If motion exists, it often leads to a flatter distribution of ŷ and a smaller m 2 . Therefore, given a threshold t 2 (t 2 ≦C m     2   ), if m 2 ≧t 2 , we say that there is no motion and the estimated noise variance is reliable. According to the above analysis, the second example of the reliability detector  106  ( FIG. 1 ) implements the function  600  in the example  FIG. 6 , which inputs the second characteristic value M 2  and the threshold value t 2  to provide a reliability indication wherein according to unit  600 , if m 2 ≧t 2 , it is assumed that there is no motion and the estimated noise variance is reliable. 
   In application, the integration or summation range is not limited to 
           [         3   4     ⁢       y   ^     p       ,       5   4     ⁢       y   ^     p         ]         
and [0,2ŷ p ]. If other values are used, the threshold value t 2  should be adjusted correspondingly.
 
   Example 3 
   The third example implementation of the characteristic calculator  104  and the reliability detector  106  are now described. The third example implementation of the characteristic value calculator  104  ( FIG. 1 ) is shown by the block diagram of a unit  700  in the example of  FIG. 7 . A maximum histogram value position calculator  702  determines ŷ p  according to relation (3) above. Then, a summation unit  704  determines a characteristic value m 3  according to relation (8) below: 
   
     
       
         
           
             
               
                 
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   The characteristic value m 3  is equivalent to a normalized shape parameter over the range 
             [         1   2     ⁢       y   ^     p       ,       y   ^     p       ]     ,         
according to relation (9) below:
 
   
     
       
         
           
             
               
                 
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   In the ideal case (no motion between the two consecutive frames), it can be derived that m 3  is close to a constant value, denoted as C m3 . This constant value is related to the block size k=H×W as well. Therefore, given thresholds t 3 (t 3 &lt;C m     3   ) and t 4 (t 4 &gt;C m     3   ), if t 3 ≦m 3 ≦t 4 , we say that there is no motion and the estimated noise variance is reliable. The third example of the reliability detector  106  ( FIG. 1 ) implements the detection function  800  in the example  FIG. 8 . The detection function comprises the functional units  802 ,  804  and  806 , which input the third characteristic value M 3  and the threshold values t 3  and t 4  to provide a reliability indication. Function units  802  and  804  are Boolean functions, and the function unit  806  is an AND function, wherein the units  802 ,  804  and  806  together determine if t 3 ≦m 3 ≦t 4 . 
   In application, the integration or summation range above is not limited to 
             [         1   2     ⁢       y   ^     p       ,       y   ^     p       ]     .         
If another value is used, the threshold values t 3  and t 4  should be adjusted correspondingly.
 
   The above implementations can be combined arbitrarily to obtain more robust result. An example system  900  which combines three reliability estimators  902 ,  904  and  906 , i.e., Reliability Estimator  1 , Reliability Estimator  2  and Reliability Estimator  3 , respectively. The system  900  inputs the histogram h(ŷ) and outputs a combined reliability indicator. The Reliability Estimator  1  implements reliability estimation according to  FIG. 1  and Example 1 above, and generates the first reliability indicator “reliability  1 ”. The Reliability Estimator  2  implements reliability estimation according to  FIG. 1  and Example 2 above, and generates the second reliability indicator “reliability  2 ”. The Reliability Estimator  3  implements reliability estimation according to  FIG. 1  and Example 3 above, and generates the third reliability indicator “reliability  3 ”. The results from the Reliability Estimator  1 , Reliability Estimator  2  and Reliability Estimator  3  (i.e., “reliability  1 ”, “reliability  2 ” and “reliability  3 ”, respectively) are combined by the Final Decision unit  908  to generate the final, combined reliability indication output for the system  900 . As those skilled in the art will recognize, other example combinations are possible according to the present invention. 
   An example implementation of the Final Decision unit  908  of  FIG. 9  is shown as the function  910  (logic AND) shown in the example of  FIG. 10 . As those skilled in the art will recognize, other examples for the function  910  are possible according to the present invention. 
   If the estimated noise variance is determined as not reliable, it will be discarded and the previous estimated reliable noise variance will be used instead indicating the noise level of the current frame. 
   As those skilled in the art will recognize, the present invention can be used on both progressive and interlaced videos. The even and odd fields in an interlaced video can be processed as two separate progressive video sequences; or the fields can be merged into a single frame prior to be processed. 
   The present invention has been described in considerable detail with reference to certain preferred versions thereof; however, other versions are possible. Therefore, the spirit and scope of the appended claims should not be limited to the description of the preferred versions contained herein.