Patent Application: US-58243904-A

Abstract:
a method is proposed for binarising an image by deriving an intensity threshold and classifying pixels according to whether their intensity is below or above the threshold . in the derivation of the threshold , prior konwledge is used to define a region of interest in the image . furthermore , prior knowledge is used to select a range in the frequency distribution of the intensities of the pixels in the roi , and that only data within this frequency range is used to derive the threshold . these techniques provide a highly effective mechanism for incorporating prior knowledge into the threshold selection which is critical whether the image is a medical image or not . in particular , a threshold can be found to binarise images which exhibits high robustness to imaging artefacts such a gray level inhomogeneity and noise .

Description:
referring firstly to fig1 , the overall steps of a method which is an embodiment of the invention are shown . in step 2 , prior knowledge of the image is used to define a region of interest ( roi ) which is a subset of the image . this process can be done by whatever means , either automatic , semi - automatic , or even manual . in step 3 an analysis is performed on the frequency of occurrence of intensities within the roi , and a range of frequencies is defined , again using prior knowledge . for example , without losing generality , we denote the image to be processed as f ( x ), where f ( x ) is the gray level at a pixel labelled x . it is further supposed that the processed image has l gray levels denoted by r i where i is an integer in the range 0 to l - 1 and r 0 & lt ; r 1 & lt ; . . . r l - 1 . it is also assumed that the object of interest has higher intensity values than the background . suppose that due to prior knowledge or test we know that the proportion of the region of interest which is occupied by the object is in the percentage range per 0 to per 1 . let h ( i ) denote the frequency of gray level r i , and let h ( i ) denote the cumulative frequency which is ∑ i ′ = 0 i ⁢ h ⁡ ( i ′ ) , where i ′ is an integer dummy index . considering two values of i written as m and n , the frequency of intensities in the range r m to r n is ∑ i ′ = n n ⁢ h ⁡ ( i ′ ) . thus , we can use per 0 to calculate a gray level r low , such that we are sure that all the pixels having lower intensity represent background . r low can be written as : r low = min i ⁢ { i ❘ h ⁡ ( i ) ≥ per 0 } . ( 1 ) similarly , we can use per 1 to calculate a gray level r high such that we are sure that all pixels having higher intensity represent the object : r high = min i ⁢ { i ❘ h ⁡ ( i ) ≥ per 1 } . ( 2 ) in a step 4 of the method of fig1 , the threshold is selected using an algorithm which operates on the frequencies within the selected range from r low to r high . the details of several ways in which this can be carried out within the scope of the invention are given below . thus , a selected threshold is output in step 5 . image binarisation is then performed using this threshold , to create an image in which all pixels ( at least in the roi ) are classified into two classes . further image processing steps may optionally be performed at this stage . we now turn to a discussion of three techniques by which step 4 can be carried out . if the frequency range derived in step 3 is correctly estimated then it will include a valley in the frequency distribution of intensities . this valley separates the background and the object . thus , valley detection can be exploited to select the threshold . this has the following steps : 2 ) the gray level range [ r low , r high ] is partitioned into k + 1 intervals with an equal frequency range δh . for an interval labelled by integer index j , the lower end of its intensity range is denoted r 1 j and the upper end is denoted r 2 j . thus : r 1 0 = r low , r 2 0 = min i ⁢ { i ❘ h ⁡ ( i ) ≥ ( per 0 + δ ⁢ ⁢ h ) } , r 1 1 = r 2 0 , r 2 1 = min i ⁢ { i ❘ h ⁡ ( i ) ≥ ( h ⁡ ( r 1 1 ) + δ ⁢ ⁢ h ) } , … r 1 k = r 2 k - 1 , r 2 k = min i ⁢ { i ❘ h ⁡ ( i ) ≥ ( h ⁡ ( r 1 k ) + δ ⁢ ⁢ h ) . h ⁢ ( r 1 k + δ ⁢ ⁢ h ) ≥ per 1 ⁢ ⁢ and ⁢ ⁢ h ⁡ ( r 1 k ) & lt ; per 1 . 3 ) the average frequency h j for each of the intervals j is calculated given by h j =( h ( r 2 j )− h ( r 1 j ))/( r 2 j − r 1 j ) 4 ) let j denote the interval for which h j is a minimum . the threshold of this rcvld method , which is denoted θ rcvld , may be selected to be any value in the range r 1 j to r 2 j , such as θ rcvld =( r 2 j + r 1 j )/ 2 . let r k fall within the range r low to r high , and suppose that the pixels of the roi are in two classes c 1 and c 2 , where c 1 is pixels of the background class and consists of pixels with gray levels r low to r k , and c 2 is pixels of the object class and is composed of pixels with gray levels r k + 1 to r high . the range - constrained weighted variance method maximises the “ weighted between - class variance ” defined as : θ rcwv ⁡ ( w 1 , w 2 ) = max r k ⁢ ( pr ⁡ ( c 1 ) ⁢ d ⁡ ( c 1 ) ⁢ w 1 + pr ⁡ ( c 2 ) ⁢ d ⁡ ( c 2 ) ⁢ w 2 ) , where w 1 and w 2 are two positive constants selected by the user and representing the weights of the two respective class variances , pr (.) denotes the class probability , i . e . pr ⁡ ( c 1 ) = ∑ i = r low r k ⁢ h ⁡ ( i ) , ⁢ pr ⁡ ( c 2 ) = ∑ i = r k + 1 r high ⁢ h ⁡ ( i ) , d ⁡ ( c 1 ) = ( μ 0 - μ t ) 2 ⁢ ⁢ and ⁢ ⁢ d ⁡ ( c 2 ) = ( μ 1 - μ t ) 2 , where ⁢ ⁢ μ t = ∑ i = r low r high ⁢ i × h ⁡ ( i ) μ 0 = ∑ i = r low r k ⁢ i × h ⁡ ( i ) ⁢ ⁢ and ⁢ ⁢ μ 1 = ∑ i = r k + 1 r high ⁢ i × h ⁡ ( i ) . when w 1 is bigger than w 2 , background homogeneity is emphasised . this third method is related to the technique used in [ 7 ], and the justification for it is as given there . in general terms , let a b / a 0 be the fuzzy sets of fuzzy events “ background / object ” ( which denotes a fuzzy partition of the set { r low , . . . , r high with a membership function μ a b / μ a 0 respectively ). the probability of these fuzzy events are given by : p ⁡ ( a i ) = ∑ j = r low r high ⁢ μ a i ⁡ ( j ) × h j , where a i ∈{ a b , a 0 , and the weighted entropy with this fuzzy partition can be calculated as : s ( w 1 , w 2 )= w 1 × p ( a b )× log p ( a b )+ w 2 × p ( a 0 )× log p ( a 0 ) where w 1 and w 2 are two positive constants , and log (.) is the natural logarithm . let r low ≦ a & lt ; c ≦ r high . the membership functions can be defined as follows : μ a b ⁡ ( x ) = { 1 , r low ≤ x ≤ a ( x - c ) / ( a - c ) a & lt ; x & lt ; c 0 c & lt ; x ≤ r high ⁢ ⁢ μ a 0 ⁡ ( x ) = { 1 , r low ≤ x ≤ a ( x - a ) / ( c - a ) a & lt ; x & lt ; c 0 c & lt ; x ≤ r high . the optimum parameters a * and c * are chosen to maximise the entropy s ( w 1 , w 2 ), and the optimum threshold is θ rcfcp =( a *+ c *)/ 2 . having now presented the steps of the embodiment in principle , we turn to an example of the embodiment in operation . this example uses the form of step 4 referred to above as rclvd . the starting point of the method is the image shown in fig2 , an mr ( magnetic resonance ) image which is a t 1 - weighted or spgr ( spoiled gradient recalled acquisition ) axial slice around the intercommissural plane . this image is input in step 1 of the method . in step 2 of the method , we calculate the pixels enclosed by the skull ( i . e . find the roi ) using the following steps : the usual histogram - based thresholding method is used to binarise the axial slice ; a morphological closing operation is used to connect small gaps ; the largest connected component is identified ; and the holes within the component are filled . the resulting roi ( the pixels enclosed by the skull ) is shown in fig3 . in step 3 , the two percentages pero and per , are set as 14 % and 28 %. this selection is based on previous experiments and / or other prior knowledge . in step 4 of the method ( rclvd ), we select the δh to be 1 % ( alternatively any value in the range 1 % to 5 % would be suitable ). fig4 shows the histogram of frequencies in the roi , and the calculated threshold θ rclvd is shown as the line indicated . this completes the procedure of the embodiment . the output threshold of the method is used as in conventional techniques to binarise the image . the binarised image is shown in fig5 . although only a single embodiment of the invention has been described , many variations are possible within the scope of the invention as will be clear to a skilled reader . the disclosure of the following references is incorporated herein by reference in their entirety : otsu n ., “ a threshold selection method from gray - level histograms ”, ieee transactions on systems , man and cybernetics , 1979 ; 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