BOUNDARY ESTIMATION in .NET Integration qrcode in .NET BOUNDARY ESTIMATION BOUNDARY ESTIMATIONUse qr code iso/iec18004 in .netuse visual studio .net qr development topaint qr barcode for .net14.7.1 Number of RDPs in P Set P of RDPs consists of all RDPs resulting from pruning PJ , the uniform partition of the unit square into n squares of sidelength 1/ n. We need to determine how many RDPs there are in P or, more speci cally, we need to know how many partitions there are with exactly squares/leafs. Since the RDP is based on recursive splits into four, the number of leafs in every partition in P is of the form = 3m + 1, for some integer 0 m (n 1)/3. The integer m corresponds to the number of recursive splits. For each RDP having 3m + 1 leafs there is a corresponding partially ordered sequence of m split points (at dyadic positions in the plane). In general, there are n m n! (n m)!m!Qr-codes scanner with .netUsing Barcode reader for visual .net Control to read, scan read, scan image in visual .net applications.possible selections of m points from n (n corresponding to the vertices of the nest resolution partition, PJ ). This number is an upper bound on the number of partitions in P with = 3m + 1 leafs (since RDPs can only have dyadic split points). 14.7.2 Kraft inequality Let n denote the set of all possible models of the eld. This set contains piecewise constant models (constant on the dyadic squares corresponding to one of the partitions in Pn ). The constant values are in a prescribed range [ R,R], and are quantized to k bits. The range corresponds to the upper and lower limits of the amplitude range of the sensors. The set n consists of a nite number of models derived in the previous section. Here we show that with the number of bits k employed per transmission and p(n) properly calibrated, we have e p(n)| | 1Bar Code barcode library with .netUsing Barcode reader for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.(14.3)Visual .net bar code generating for .netusing visual studio .net tocompose bar code on asp.net web,windows applicationwhere for simplicity notation N (P) = | | is used. If (m) denotes the subset of n of models based on = 3m + 1 leaf partitions, then we haveControl quick response code size on visual c#to connect qrcode and qr barcode data, size, image with c#.net barcode sdke p(n)| | = Control qr-code size for .net qr code size in .netconsisting Control qr codes size in vbto build qr code iso/iec18004 and qr-code data, size, image with visual basic.net barcode sdk(n 1)/3 m=0 (n 1)/3.net Framework bar code implement with .netusing vs .net toproduce barcode in asp.net web,windows application(m) n Compose qr codes with .netusing barcode printing for vs .net crystal control to generate, create qr code image in vs .net crystal applications.e (3m+1) p(n) Embed ean13 with .netusing barcode generator for visual studio .net control to generate, create gs1 - 13 image in visual studio .net applications.(n 1)/3 m=0 Assign data matrix in .netusing .net crystal tobuild data matrix barcode with asp.net web,windows applicationn (2k )3m+1 e (3m+1) p(n) m Isbn 13 generating in .netusing .net framework crystal toproduce international standard book number with asp.net web,windows applicationm=0 (n 1)/3Encode code 39 full ascii with .netusing barcode maker for reporting service 2008 control to generate, create code-39 image in reporting service 2008 applications.n m k 3m+1 (3m+1) p(n) e (2 ) m! 1 [m log n+(3m+1) log(2k ) (3m+1) p(n)] e m!Control code 3/9 data with vb.net code 3 of 9 data on vb.netIf A m log n + (3m + 1) log(2k ) (3m + 1) p(n) < 1 (then e A < e 1 ), then we have e p(n)| | 1/eControl 2d data matrix barcode size on excelto make data matrix barcode and data matrix data, size, image with office excel barcode sdk(n 1)/3 m=0 Gs1 Datamatrix Barcode barcode library on visual c#generate, create barcode data matrix none in .net c# projects1 1 m!Control qr-codes data for .netqr code data for .net(14.4)Control datamatrix 2d barcode image with .netgenerate, create data matrix ecc200 none on .net projectsTo guarantee A < 1, we must have p(n) growing at least like log n. Therefore, set p(n) = log n, for some > 0. Also, as we will see later in the next section, to guarantee that the quantization of our models is suf ciently ne to contribute a negligible amount to theControl barcode 3 of 9 image on visual c#using visual .net touse uss code 39 with asp.net web,windows applicationSENSOR NETWORKS Control pdf-417 2d barcode data in javato paint pdf 417 and pdf417 data, size, image with java barcode sdkoverall error we must select 2k : n 1/4 . With these calibrations we have A = [(7/4 3 ) m + (1/4 )] log n. In order to guarantee that the MSE converges to zero, we will see in the next section that m must be a monotonically increasing function of n. Therefore, for n suf ciently large, the term involving ( 1 ) is negligible, and the condition A < 1 is 4 satis ed by > 7/12. In References [119 125] = 2/3 is used. 14.7.3 Upper bounds on achievable accuracy Assume that p(n) satis es the condition de ned by Equation (14.4) where again | | denotes the number of squares (alternatively we shall call this the number of leafs in the pruned tree description of the boundary) in the partition . It is shown in the above section that p(n) log n satis es Equation (14.4). Let n denote the solution to n = arg min