text: the present invention provides an intra - field interpolation deinterlacing technique that utilizes an edge directed deinterlacing technique based on pca . pca provides for the representation of shape , orientation and appearance . application of pca to the edge direction detection in deinterlacing provides accurate edge direction detection even when the edges are in noisy image areas . the detected edge directions are denoted by eigenvectors which can represent infinite number of directions including those at very steep angles . fig2 shows a functional block diagram of an example system 200 implementing a pca - based edge directed deinterlacing technique , according to an embodiment of the present invention . an interlaced input field f is processed by : ( 1 ) a v - filter 210 that performs vertical filtering on the field f to obtain a vertical filtered signal f v , ( 2 ) a pca - based edge directed interpolator 220 that performs directional interpolation on the field f to obtain a signal f d , and ( 3 ) a bisection and strong edge detector 230 that performs bisection and strong edge detection on the field f to generate a binary map bmap . the v - filter 210 interpolates the missing pixels along the vertical direction only . it is applied to the missing pixels belonging to image areas that do not include strong edges or bisection ( e . g ., textured ) areas ( i . e ., bmap = 0 ). as is known to those skilled in the art , principal component analysis is a technique for simplifying a data set , by reducing multidimensional data sets to lower dimensions for analysis . the pca - based edi 220 performs interpolation on missing pixels along a detected edge direction . pca - based edi is applied only to the missing pixels belonging to image areas that include strong edges but no bisection ( i . e ., bmap = 1 ). in effect , the missing pixels that belong to strong edges but not to bisection areas , are represented by f d , while the other remaining missing pixels are represented by f v . the binary map bmap is used by a multiplexer 240 to determine which of the resulting signals f v or f d is selected as an output signal f p of the system 200 . fig3 shows an example field 300 ( e . g ., either top field 102 or bottom field 104 in fig1 ), which is of size m * n ( e . g ., height by width ) pixels , wherein indices y and x denote the scan line number and pixel location , respectively , in the input field f 300 . for each missing scan line y = 1 , 3 , 5 , . . . , m − 1 , and missing pixel locations x = 0 , 1 , . . . , n − 1 , the multiplexer 240 generates an output according to relation ( 1 ) below : in fig3 , a missing pixel 302 is represented by f [ y ][ x ] in the field f 300 . the window 304 includes a group of neighboring existing pixels for the missing pixel 302 . the window 306 contains another group of neighboring existing pixels for the missing pixel 302 . existing pixels in the rectangular window 304 are for filtering by the v - filter 210 , and the existing pixels in the square window 306 are for pca - based calculation by the pca - based edi 220 . an example size for the window 306 is 6 - by - 11 pixels and an example size for the window 304 is 6 - by - 1 pixels . other sizes for the windows 304 and 306 are also possible . an example of calculating f v or f d by the v - filter 210 and the pca - based edi 220 , respectively , are now described . a vertical filtered result f v [ y ][ x ] is calculated by applying the v - filter 210 to the existing neighbors of the missing pixel 302 in the window 304 . the resulting vertical filtered signal f v [ y ][ x ] can be represented by relation ( 2 ) below : f v [ y ][ x ]=( f [ y − 5 ][ x ]− 12 f [ y − 3 ][ x ]+ 75 f [ y 1 ][ x ]+ 75 f [ y + 1 ][ x ]− 12 f [ y + 3 ][ x ]+ f [ y + 5 ][ x ])/ 128 . ( 2 ) in this example , the v - filter 210 utilizes a set of filter coefficients that comprise : 1 / 128 [ 1 − 12 75 75 − 12 1 ]. conceptually , a value f v [ y ][ x ] for the missing pixel 302 is calculated by the v - filter 210 from a weighted average ( according to v - filter coefficients ) of the neighboring existing pixels along a vertical direction ( i . e ., window 304 ). the set of v - filter coefficients used in relation ( 2 ) has 6 taps for low - pass filtering , but other examples are possible . other sets of coefficients with shorter or longer numbers of taps can be used in the same manner . another example of the v - filter 210 may be a vertical - temporal ( vt ) filter such as described by n . seth - smith and g . walker , “ flexible upconversion for high quality tv and multimedia displays ,” in proc . icce , chicago , ill ., june 1996 , pp . 338 - 339 , and g . de haan and e . b . bellers , “ deinterlacing — an overview ,” proceedings of the ieee , vol . 86 , no . 9 , september 1998 , pp . 1839 - 1857 . fig4 shows a functional block diagram of an embodiment of the pca - based edi 220 for calculating f d , according to a preferred embodiment of the present invention . first , based on the window 306 associated with the missing pixel f [ y ][ x ], a set of horizontal gradients g h and vertical gradients g v associated with each existing pixel within the window 306 are calculated using a horizontal gradient calculator 402 and a vertical gradient calculator 404 , respectively . the horizontal gradient calculator 402 implements relation ( 3 ) below for each existing pixel : wherein iεi ={ y − 5 , y − 3 , y − 1 , y + 1 , y + 3 , y + 5 }, and relation ( 3 ) calculates the set of horizontal gradients at each existing pixel location ( i , j ) relative to the missing pixel f [ y ][ x ] ( i and j denote vertical and horizontal indices , respectively ). the gradients represent differences between pixel values along the horizontal direction . therefore , at a location ( i , j ), the horizontal gradient is calculated by subtracting the immediate left neighboring existing pixel f [ i ] [ j − 1 ] from the existing pixel f [ i ] [ j ]. the vertical gradient calculator 404 determines the vertical gradients by implementing relation ( 4 ) below for each existing pixel : for the vertical gradients , at each location ( i , j ), the vertical gradient is calculated by subtracting the immediate above neighboring existing pixel f [ i − 1 ] [ j ] from the existing pixel f [ i ] [ j ]. next , a matrix a , which is the covariance matrix of the horizontal and vertical gradients , is determined . the matrix aεr 2 × 2 is formed by a matrix formation unit 406 according to relation ( 5 ) below : after the resulting matrix a is formed , its eigenvalues λ 1 and λ 2 and an eigenvector v 1 =[ v x v y ] t associated with the smaller eigenvalue λ 1 ( assuming λ 1 ≦ λ 2 ), are calculated by an eigen calculator 408 , according to relations ( 6 ) and ( 7 ) below : relations ( 6 ) and ( 7 ) are standard closed form relations for calculating eigenvalue and eigenvectors when the input covariance matrix is of size 2 × 2 as in relation ( 5 ). as such , the gradient calculators 402 , 404 , the matrix formation unit 406 and the eigen calculator 408 , together implement an edge detector that performs edge detection including edge direction detection which in this example provides the eigenvector v 1 that is proportional to the direction of a detected edge . once both eigenvalues λ 1 and λ 2 are obtained , a reliability factor α is calculated by a reliability calculator 410 according to relation ( 8 ) below : wherein the thresholds re_thr 1 and re_thr 2 are used for limiting the reliability factor a within the range from 0 . 0 to 1 . 0 . the ratio λ 2 / λ 1 in relation ( 8 ) indicates how reliable eigenvector v 1 is as the direction of a detected edge . the reliability factor α ranges from 0 . 0 ( not reliable ) to 1 . 0 ( very reliable ). if the ratio λ 2 / λ 1 is less than or equal to re_thr 1 , the reliability factor α is set to 0 . 0 ( not reliable ). if the ratio λ 2 / λ 1 is greater than or equal to re_thr 2 , the reliability factor α is set to 1 . 0 ( very reliable ). when the ratio λ 2 / λ 1 is in - between re_thr 1 and re_thr 2 , the reliability factor α is proportional to the ratio λ 2 / λ 1 and has a value from 0 . 0 to 1 . 0 . the typical values for re_thr 1 and re_thr 2 are set to e . g ., 4 . 0 and 12 . 0 , respectively . if the ratio λ 2 / λ 1 , is less than or equal 4 . 0 , then the detected edge direction according to eigenvector v 1 is not reliable ( α = 0 ). on the other hand , if the ratio λ 2 / λ 1 is greater than or equal to 12 . 0 , the detected edge direction according to eigenvector v 1 is highly reliable ( α = 1 ). when the ratio λ 2 / λ 1 is in between 4 . 0 and 12 . 0 , the reliability factor is proportional to the ratio and has a value from 0 . 0 to 1 . 0 . the two threshold values were selected by the inventors as default values , based on extensive experimentation . it is noted that when λ 1 ≦ λ 2 , the orientation of the eigenvector v 1 =[ v x v y ] t associated with the smaller eigenvalue λ 1 is proportional to the dominant edge direction in the window 306 whose center is the missing pixel f [ y ][ x ]( 302 in fig3 ). the directional interpolator 412 determines an edge direction proportional to v 1 =[ v x v y ] t and generates a directional interpolated value d ( i . e ., d [ y ][ x ]) associated with the missing pixel f [ y ][ x ] along the edge direction . at the final stage , the vertical filtered signal f v [ y ][ x ] from the v - filter 210 ( fig2 ) and the directional interpolated signal d [ y ][ x ] are mixed together using a mixer 414 based on the reliability factor α to obtain a mixed directional interpolated signal f d [ y ][ x ], according to relation ( 9 ) below : as such , the signal f d [ y ][ x ] is calculated by mixing between d [ y ][ x ] and f v [ y ][ x ] with a contribution ratio of αand its complement , 1 − α , respectively . fig5 shows another view of the field 300 including a set of 13 edge direction candidates { 510 , 511 , . . . , 522 } associated with the missing pixel 302 in the window 306 . a method of selecting the edge direction closest to the direction of eigenvector v 1 , by the directional interpolator 412 is now described by example . suppose an eigenvector 502 is the vector pointing to the same direction as the eigenvector v 1 whose starting point is at the missing pixel 302 . among the set of all edge directions { 510 , 511 , . . . , 522 }, the edge direction 515 is the closest direction to the direction of eigenvector 502 . therefore , the edge directed interpolated value d [ y ][ x ] in accordance with the edge direction 515 , is calculated by averaging between the existing pixels at both ends the edge direction 515 ( i . e ., pixels 530 and 540 ). the set of 13 edge directions { 510 , 511 , . . . , 522 } in fig5 is by way of example , and those skilled in the art recognize that other sets with smaller or larger number of edge directions can also be used wherein the method of selecting the edge direction closest to the direction of eigenvector is adjusted accordingly . fig6 shows a functional block diagram of an embodiment of the bisection and strong edge detector 230 of fig2 that generates the binary map bmap . the detector 230 includes a bisection detector 602 and a strong edge detector 604 . bisection detection and strong edge detection functions are independent and can be performed in a parallel manner . the bisection detector 602 generates a binary decision bbs ( 0 or 1 ) indicating whether or not the missing pixel f [ y ][ x ] ( 302 in fig3 ) belongs to a bisection area . the bisection area is defined as the area whose pixel values can be clearly separated into two sections . an example of detecting a bisection pattern for use in conjunction with the deinterlacing is briefly described . for each missing pixel in a current input field , a window w is constructed , whose center pixel is at the considered missing pixel . a binary map is generated which includes rows of values corresponding to pixels in the window , wherein the values indicate if each element of the window is greater than the sample mean of the area surrounding the missing pixel . the number of value changes in the values in each row of the binary map is counted . it is then determined whether or not the missing pixel is within the bisection pattern based on said counts ( there are two sets of value change counts corresponding to two rows ). in order to maintain both the low angle edge direction detection capability and low misdetection probability , complicated areas are identified by the bisection pattern detection method . then deinterlacing is performed . bisection detection examples are described in the related u . s . patent application ser . no . 11 / 121 , 815 , entitled “ a method for detecting bisection pattern in deinterlacing ,” filed on may 2 , 2005 , incorporated herein by reference . suppose the sample mean of all existing pixels within the window 306 ( fig3 ) is denoted by μ . then , a binary matrix b =[ b ij ] of the same size as the window 306 is determined by comparing each pixel value to mean μ , according to relation ( 10 ) below : as such , for each existing pixel location ( i , j ) within the window 306 , the associated binary value b ij is set to 1 if f [ i ][ j ] is greater than or equal to the mean value of at least a plurality of the existing pixel values within the window 306 neighboring the missing pixel 302 , otherwise b ij is set to 0 . for each row iεi in binary matrix b , the number of sign changes are counted along the horizontal direction according to relation ( 11 ) below : similarly , for each column jεj , the number of sign changes are counted along the vertical direction according to relation ( 12 ) below : then , the binary decisions bs h and bs v in the horizontal and vertical directions are obtained in accordance to relations ( 13 ) and ( 14 ), respectively : wherein the sets i ′ and j ′ can be equal to , or a subset of , respectively , i ={ y − 5 , y − 3 , y − 1 , y + 1 , y + 3 , y + 5 } and j ={ x − 5 , x − 4 , x − 3 , . . . , x + 5 }. in this description , i ′={ y − 1 , y + 1 } and j ′={ x − 1 , x + 1 }. if the number of sign changes in every row i in set i ′ is not greater than 1 , then the missing pixel at location ( x , y ) belongs to a bisection area along the horizontal direction ( i . e ., bs h = 1 ). otherwise , the missing pixel does not belong to the bisection area ( i . e ., bs h = 0 ). in a similar fashion , if the number of sign changes in every column j in set j ′ is not greater than 1 , then the missing pixel at location ( x , y ) belongs to a bisection area along the vertical direction ( i . e ., bs v = 1 ). otherwise , the missing pixel does not belong to the bisection area ( i . e ., bs v = 0 ). in this example , the set i ′ contains row indices immediately above and below the missing pixel , and the set j ′ contains column indices immediately to the left and right of the missing pixel . once both the horizontal binary decision bs h and the vertical binary decision bs v are determined , the binary decision bbs in both directions is determined by the bisection detector 602 according to relation ( 15 ) below : preferably , in parallel to operation of the bisection detector 602 described above , the strong edge detector 604 detects strong edges in the input field f . suppose the mean and approximated local variance of the window 306 whose center pixel 302 is f [ y ][ x ], are denoted by μ and σ , respectively . the approximate local variance σ is determined according to relation ( 16 ) below : relation ( 16 ) provides calculation of an approximate local variance for the missing pixel 302 , by averaging the absolute difference between the pixel values within the window 306 and the sample mean of the missing pixel 302 . in this example , the window 306 is of size 6 - by - 11 pixels , such that the total number of pixels within the window 306 is 66 . the binary decision bse from the strong edge detector 604 indicates whether or not the missing pixel 302 belongs to a strong edge area . the binary decision bse is determined according to relation ( 17 ) below : as such , the binary decision bse is determined by using a hard threshold se_thr . that is , if the local variance σis greater than or equal to se_thr , then the missing pixel 302 is considered to belong to the strong edge area ( bse = 1 ), otherwise , it is not ( bse = 0 ). after both binary decisions from detectors 602 and 604 are determined , they are input to a combiner ( e . g ., logical and gate ) 606 to obtain the final resulting binary decision map bmap from the detector 230 . as is known to those skilled in the art , the aforementioned example architectures described above , according to the present invention , can be implemented in many ways , such as program instructions for execution by a processor , as logic circuits , as an application specific integrated circuit , as firmware , etc . 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 .