Image::Leptonica::Func::numafunc2
version 0.03
numafunc2.c
numafunc2.c Morphological (min/max) operations NUMA *numaErode() NUMA *numaDilate() NUMA *numaOpen() NUMA *numaClose() Other transforms NUMA *numaTransform() l_int32 numaWindowedStats() NUMA *numaWindowedMean() NUMA *numaWindowedMeanSquare() l_int32 numaWindowedVariance() NUMA *numaConvertToInt() Histogram generation and statistics NUMA *numaMakeHistogram() NUMA *numaMakeHistogramAuto() NUMA *numaMakeHistogramClipped() NUMA *numaRebinHistogram() NUMA *numaNormalizeHistogram() l_int32 numaGetStatsUsingHistogram() l_int32 numaGetHistogramStats() l_int32 numaGetHistogramStatsOnInterval() l_int32 numaMakeRankFromHistogram() l_int32 numaHistogramGetRankFromVal() l_int32 numaHistogramGetValFromRank() l_int32 numaDiscretizeRankAndIntensity() l_int32 numaGetRankBinValues() Splitting a distribution l_int32 numaSplitDistribution() Comparing two histograms l_int32 numaEarthMoverDistance() Extrema finding NUMA *numaFindPeaks() NUMA *numaFindExtrema() l_int32 *numaCountReversals() Threshold crossings and frequency analysis l_int32 numaSelectCrossingThreshold() NUMA *numaCrossingsByThreshold() NUMA *numaCrossingsByPeaks() NUMA *numaEvalBestHaarParameters() l_int32 numaEvalHaarSum() Things to remember when using the Numa: (1) The numa is a struct, not an array. Always use accessors (see numabasic.c), never the fields directly. (2) The number array holds l_float32 values. It can also be used to store l_int32 values. See numabasic.c for details on using the accessors. (3) Occasionally, in the comments we denote the i-th element of a numa by na[i]. This is conceptual only -- the numa is not an array! Some general comments on histograms: (1) Histograms are the generic statistical representation of the data about some attribute. Typically they're not normalized -- they simply give the number of occurrences within each range of values of the attribute. This range of values is referred to as a 'bucket'. For example, the histogram could specify how many connected components are found for each value of their width; in that case, the bucket size is 1. (2) In leptonica, all buckets have the same size. Histograms are therefore specified by a numa of occurrences, along with two other numbers: the 'value' associated with the occupants of the first bucket and the size (i.e., 'width') of each bucket. These two numbers then allow us to calculate the value associated with the occupants of each bucket. These numbers are fields in the numa, initialized to a startx value of 0.0 and a binsize of 1.0. Accessors for these fields are functions numa*Parameters(). All histograms must have these two numbers properly set.
NUMA * numaClose ( NUMA *nas, l_int32 size )
numaClose() Input: nas size (of sel; greater than 0, odd; origin implicitly in center) Return: nad (opened), or null on error Notes: (1) The structuring element (sel) is linear, all "hits" (2) If size == 1, this returns a copy (3) We add a border before doing this operation, for the same reason that we add a border to a pix before doing a safe closing. Without the border, a small component near the border gets clipped at the border on dilation, and can be entirely removed by the following erosion, violating the basic extensivity property of closing.
NUMA * numaConvertToInt ( NUMA *nas )
numaConvertToInt() Input: na Return: na with all values rounded to nearest integer, or null on error
l_int32 numaCountReversals ( NUMA *nas, l_float32 minreversal, l_int32 *pnr, l_float32 *pnrpl )
numaCountReversals() Input: nas (input values) minreversal (relative amount to resolve peaks and valleys) &nr (<optional return> number of reversals &nrpl (<optional return> reversal density: reversals/length) Return: 0 if OK, 1 on error Notes: (1) The input numa is can be generated from pixExtractAlongLine(). If so, the x parameters can be used to find the reversal frequency along a line.
NUMA * numaCrossingsByPeaks ( NUMA *nax, NUMA *nay, l_float32 delta )
numaCrossingsByPeaks() Input: nax (<optional> numa of abscissa values) nay (numa of ordinate values, corresponding to nax) delta (parameter used to identify when a new peak can be found) Return: nad (abscissa pts at threshold), or null on error Notes: (1) If nax == NULL, we use startx and delx from nay to compute the crossing values in nad.
NUMA * numaCrossingsByThreshold ( NUMA *nax, NUMA *nay, l_float32 thresh )
numaCrossingsByThreshold() Input: nax (<optional> numa of abscissa values; can be NULL) nay (numa of ordinate values, corresponding to nax) thresh (threshold value for nay) Return: nad (abscissa pts at threshold), or null on error Notes: (1) If nax == NULL, we use startx and delx from nay to compute the crossing values in nad.
NUMA * numaDilate ( NUMA *nas, l_int32 size )
numaDilate() Input: nas size (of sel; greater than 0, odd; origin implicitly in center) Return: nad (dilated), or null on error Notes: (1) The structuring element (sel) is linear, all "hits" (2) If size == 1, this returns a copy
l_int32 numaDiscretizeRankAndIntensity ( NUMA *na, l_int32 nbins, NUMA **pnarbin, NUMA **pnam, NUMA **pnar, NUMA **pnabb )
numaDiscretizeRankAndIntensity() Input: na (normalized histogram of probability density vs intensity) nbins (number of bins at which the rank is divided) &pnarbin (<optional return> rank bin value vs intensity) &pnam (<optional return> median intensity in a bin vs rank bin value, with @nbins of discretized rank values) &pnar (<optional return> rank vs intensity; this is a cumulative norm histogram) &pnabb (<optional return> intensity at the right bin boundary vs rank bin) Return: 0 if OK, 1 on error Notes: (1) We are inverting the rank(intensity) function to get the intensity(rank) function at @nbins equally spaced values of rank between 0.0 and 1.0. We save integer values for the intensity. (2) We are using the word "intensity" to describe the type of array values, but any array of non-negative numbers will work. (3) The output arrays give the following mappings, where the input is a normalized histogram of array values: array values --> rank bin number (narbin) rank bin number --> median array value in bin (nam) array values --> cumulative norm = rank (nar) rank bin number --> array value at right bin edge (nabb)
l_int32 numaEarthMoverDistance ( NUMA *na1, NUMA *na2, l_float32 *pdist )
numaEarthMoverDistance() Input: na1, na2 (two numas of the same size, typically histograms) &dist (<return> EM distance) Return: 0 if OK, 1 on error Notes: (1) The two numas must have the same size. They do not need to be normalized to the same sum before applying the function. (2) For a 1D discrete function, the implementation of the EMD is trivial. Just keep filling or emptying buckets in one numa to match the amount in the other, moving sequentially along both arrays. (3) We divide the sum of the absolute value of everything moved (by 1 unit at a time) by the sum of the numa (amount of "earth") to get the average distance that the "earth" was moved. Further normalization, by the number of buckets (minus 1), gives the distance as a fraction of the maximum possible distance, which is n-1. This fraction is 1.0 for the situation where all the 'earth' in the first array is at one end, and all in the second array is at the other end.
NUMA * numaErode ( NUMA *nas, l_int32 size )
numaErode() Input: nas size (of sel; greater than 0, odd; origin implicitly in center) Return: nad (eroded), or null on error Notes: (1) The structuring element (sel) is linear, all "hits" (2) If size == 1, this returns a copy (3) General comment. The morphological operations are equivalent to those that would be performed on a 1-dimensional fpix. However, because we have not implemented morphological operations on fpix, we do this here. Because it is only 1 dimensional, there is no reason to use the more complicated van Herk/Gil-Werman algorithm, and we do it by brute force.
l_int32 numaEvalBestHaarParameters ( NUMA *nas, l_float32 relweight, l_int32 nwidth, l_int32 nshift, l_float32 minwidth, l_float32 maxwidth, l_float32 *pbestwidth, l_float32 *pbestshift, l_float32 *pbestscore )
numaEvalBestHaarParameters() Input: nas (numa of non-negative signal values) relweight (relative weight of (-1 comb) / (+1 comb) contributions to the 'convolution'. In effect, the convolution kernel is a comb consisting of alternating +1 and -weight.) nwidth (number of widths to consider) nshift (number of shifts to consider for each width) minwidth (smallest width to consider) maxwidth (largest width to consider) &bestwidth (<return> width giving largest score) &bestshift (<return> shift giving largest score) &bestscore (<optional return> convolution with "Haar"-like comb) Return: 0 if OK, 1 on error Notes: (1) This does a linear sweep of widths, evaluating at @nshift shifts for each width, computing the score from a convolution with a long comb, and finding the (width, shift) pair that gives the maximum score. The best width is the "half-wavelength" of the signal. (2) The convolving function is a comb of alternating values +1 and -1 * relweight, separated by the width and phased by the shift. This is similar to a Haar transform, except there the convolution is performed with a square wave. (3) The function is useful for finding the line spacing and strength of line signal from pixel sum projections. (4) The score is normalized to the size of nas divided by the number of half-widths. For image applications, the input is typically an array of pixel projections, so one should normalize by dividing the score by the image width in the pixel projection direction.
l_int32 numaEvalHaarSum ( NUMA *nas, l_float32 width, l_float32 shift, l_float32 relweight, l_float32 *pscore )
numaEvalHaarSum() Input: nas (numa of non-negative signal values) width (distance between +1 and -1 in convolution comb) shift (phase of the comb: location of first +1) relweight (relative weight of (-1 comb) / (+1 comb) contributions to the 'convolution'. In effect, the convolution kernel is a comb consisting of alternating +1 and -weight.) &score (<return> convolution with "Haar"-like comb) Return: 0 if OK, 1 on error Notes: (1) This does a convolution with a comb of alternating values +1 and -relweight, separated by the width and phased by the shift. This is similar to a Haar transform, except that for Haar, (1) the convolution kernel is symmetric about 0, so the relweight is 1.0, and (2) the convolution is performed with a square wave. (2) The score is normalized to the size of nas divided by twice the "width". For image applications, the input is typically an array of pixel projections, so one should normalize by dividing the score by the image width in the pixel projection direction. (3) To get a Haar-like result, use relweight = 1.0. For detecting signals where you expect every other sample to be close to zero, as with barcodes or filtered text lines, you can use relweight > 1.0.
NUMA * numaFindExtrema ( NUMA *nas, l_float32 delta )
numaFindExtrema() Input: nas (input values) delta (relative amount to resolve peaks and valleys) Return: nad (locations of extrema), or null on error Notes: (1) This returns a sequence of extrema (peaks and valleys). (2) The algorithm is analogous to that for determining mountain peaks. Suppose we have a local peak, with bumps on the side. Under what conditions can we consider those 'bumps' to be actual peaks? The answer: if the bump is separated from the peak by a saddle that is at least 500 feet below the bump. (3) Operationally, suppose we are looking for a peak. We are keeping the largest value we've seen since the last valley, and are looking for a value that is delta BELOW our current peak. When we find such a value, we label the peak, use the current value to label the valley, and then do the same operation in reverse (looking for a valley).
NUMA * numaFindPeaks ( NUMA *nas, l_int32 nmax, l_float32 fract1, l_float32 fract2 )
numaFindPeaks() Input: source na max number of peaks to be found fract1 (min fraction of peak value) fract2 (min slope) Return: peak na, or null on error. Notes: (1) The returned na consists of sets of four numbers representing the peak, in the following order: left edge; peak center; right edge; normalized peak area
l_int32 numaGetHistogramStats ( NUMA *nahisto, l_float32 startx, l_float32 deltax, l_float32 *pxmean, l_float32 *pxmedian, l_float32 *pxmode, l_float32 *pxvariance )
numaGetHistogramStats() Input: nahisto (histogram: y(x(i)), i = 0 ... nbins - 1) startx (x value of first bin: x(0)) deltax (x increment between bins; the bin size; x(1) - x(0)) &xmean (<optional return> mean value of histogram) &xmedian (<optional return> median value of histogram) &xmode (<optional return> mode value of histogram: xmode = x(imode), where y(xmode) >= y(x(i)) for all i != imode) &xvariance (<optional return> variance of x) Return: 0 if OK, 1 on error Notes: (1) If the histogram represents the relation y(x), the computed values that are returned are the x values. These are NOT the bucket indices i; they are related to the bucket indices by x(i) = startx + i * deltax
l_int32 numaGetHistogramStatsOnInterval ( NUMA *nahisto, l_float32 startx, l_float32 deltax, l_int32 ifirst, l_int32 ilast, l_float32 *pxmean, l_float32 *pxmedian, l_float32 *pxmode, l_float32 *pxvariance )
numaGetHistogramStatsOnInterval() Input: nahisto (histogram: y(x(i)), i = 0 ... nbins - 1) startx (x value of first bin: x(0)) deltax (x increment between bins; the bin size; x(1) - x(0)) ifirst (first bin to use for collecting stats) ilast (last bin for collecting stats; use 0 to go to the end) &xmean (<optional return> mean value of histogram) &xmedian (<optional return> median value of histogram) &xmode (<optional return> mode value of histogram: xmode = x(imode), where y(xmode) >= y(x(i)) for all i != imode) &xvariance (<optional return> variance of x) Return: 0 if OK, 1 on error Notes: (1) If the histogram represents the relation y(x), the computed values that are returned are the x values. These are NOT the bucket indices i; they are related to the bucket indices by x(i) = startx + i * deltax
l_int32 numaGetRankBinValues ( NUMA *na, l_int32 nbins, NUMA **pnarbin, NUMA **pnam )
numaGetRankBinValues() Input: na (just an array of values) nbins (number of bins at which the rank is divided) &pnarbin (<optional return> rank bin value vs array value) &pnam (<optional return> median intensity in a bin vs rank bin value, with @nbins of discretized rank values) Return: 0 if OK, 1 on error Notes: (1) Simple interface for getting a binned rank representation of an input array of values. This returns two mappings: array value --> rank bin number (narbin) rank bin number --> median array value in each rank bin (nam)
l_int32 numaGetStatsUsingHistogram ( NUMA *na, l_int32 maxbins, l_float32 *pmin, l_float32 *pmax, l_float32 *pmean, l_float32 *pvariance, l_float32 *pmedian, l_float32 rank, l_float32 *prval, NUMA **phisto )
numaGetStatsUsingHistogram() Input: na (an arbitrary set of numbers; not ordered and not a histogram) maxbins (the maximum number of bins to be allowed in the histogram; use 0 for consecutive integer bins) &min (<optional return> min value of set) &max (<optional return> max value of set) &mean (<optional return> mean value of set) &variance (<optional return> variance) &median (<optional return> median value of set) rank (in [0.0 ... 1.0]; median has a rank 0.5; ignored if &rval == NULL) &rval (<optional return> value in na corresponding to @rank) &histo (<optional return> Numa histogram; use NULL to prevent) Return: 0 if OK, 1 on error Notes: (1) This is a simple interface for gathering statistics from a numa, where a histogram is used 'under the covers' to avoid sorting if a rank value is requested. In that case, by using a histogram we are trading speed for accuracy, because the values in @na are quantized to the center of a set of bins. (2) If the median, other rank value, or histogram are not requested, the calculation is all performed on the input Numa. (3) The variance is the average of the square of the difference from the mean. The median is the value in na with rank 0.5. (4) There are two situations where this gives rank results with accuracy comparable to computing stastics directly on the input data, without binning into a histogram: (a) the data is integers and the range of data is less than @maxbins, and (b) the data is floats and the range is small compared to @maxbins, so that the binsize is much less than 1. (5) If a histogram is used and the numbers in the Numa extend over a large range, you can limit the required storage by specifying the maximum number of bins in the histogram. Use @maxbins == 0 to force the bin size to be 1. (6) This optionally returns the median and one arbitrary rank value. If you need several rank values, return the histogram and use numaHistogramGetValFromRank(nah, rank, &rval) multiple times.
l_int32 numaHistogramGetRankFromVal ( NUMA *na, l_float32 rval, l_float32 *prank )
numaHistogramGetRankFromVal() Input: na (histogram) rval (value of input sample for which we want the rank) &rank (<return> fraction of total samples below rval) Return: 0 if OK, 1 on error Notes: (1) If we think of the histogram as a function y(x), normalized to 1, for a given input value of x, this computes the rank of x, which is the integral of y(x) from the start value of x to the input value. (2) This function only makes sense when applied to a Numa that is a histogram. The values in the histogram can be ints and floats, and are computed as floats. The rank is returned as a float between 0.0 and 1.0. (3) The numa parameters startx and binsize are used to compute x from the Numa index i.
l_int32 numaHistogramGetValFromRank ( NUMA *na, l_float32 rank, l_float32 *prval )
numaHistogramGetValFromRank() Input: na (histogram) rank (fraction of total samples) &rval (<return> approx. to the bin value) Return: 0 if OK, 1 on error Notes: (1) If we think of the histogram as a function y(x), this returns the value x such that the integral of y(x) from the start value to x gives the fraction 'rank' of the integral of y(x) over all bins. (2) This function only makes sense when applied to a Numa that is a histogram. The values in the histogram can be ints and floats, and are computed as floats. The val is returned as a float, even though the buckets are of integer width. (3) The numa parameters startx and binsize are used to compute x from the Numa index i.
NUMA * numaMakeHistogram ( NUMA *na, l_int32 maxbins, l_int32 *pbinsize, l_int32 *pbinstart )
numaMakeHistogram() Input: na maxbins (max number of histogram bins) &binsize (<return> size of histogram bins) &binstart (<optional return> start val of minimum bin; input NULL to force start at 0) Return: na consisiting of histogram of integerized values, or null on error. Note: (1) This simple interface is designed for integer data. The bins are of integer width and start on integer boundaries, so the results on float data will not have high precision. (2) Specify the max number of input bins. Then @binsize, the size of bins necessary to accommodate the input data, is returned. It is one of the sequence: {1, 2, 5, 10, 20, 50, ...}. (3) If &binstart is given, all values are accommodated, and the min value of the starting bin is returned. Otherwise, all negative values are discarded and the histogram bins start at 0.
NUMA * numaMakeHistogramAuto ( NUMA *na, l_int32 maxbins )
numaMakeHistogramAuto() Input: na (numa of floats; these may be integers) maxbins (max number of histogram bins; >= 1) Return: na consisiting of histogram of quantized float values, or null on error. Notes: (1) This simple interface is designed for accurate binning of both integer and float data. (2) If the array data is integers, and the range of integers is smaller than @maxbins, they are binned as they fall, with binsize = 1. (3) If the range of data, (maxval - minval), is larger than @maxbins, or if the data is floats, they are binned into exactly @maxbins bins. (4) Unlike numaMakeHistogram(), these bins in general have non-integer location and width, even for integer data.
NUMA * numaMakeHistogramClipped ( NUMA *na, l_float32 binsize, l_float32 maxsize )
numaMakeHistogramClipped() Input: na binsize (typically 1.0) maxsize (of histogram ordinate) Return: na (histogram of bins of size @binsize, starting with the na[0] (x = 0.0) and going up to a maximum of x = @maxsize, by increments of @binsize), or null on error Notes: (1) This simple function generates a histogram of values from na, discarding all values < 0.0 or greater than min(@maxsize, maxval), where maxval is the maximum value in na. The histogram data is put in bins of size delx = @binsize, starting at x = 0.0. We use as many bins as are needed to hold the data.
l_int32 numaMakeRankFromHistogram ( l_float32 startx, l_float32 deltax, NUMA *nasy, l_int32 npts, NUMA **pnax, NUMA **pnay )
numaMakeRankFromHistogram() Input: startx (xval corresponding to first element in nay) deltax (x increment between array elements in nay) nasy (input histogram, assumed equally spaced) npts (number of points to evaluate rank function) &nax (<optional return> array of x values in range) &nay (<return> rank array of specified npts) Return: 0 if OK, 1 on error
NUMA * numaNormalizeHistogram ( NUMA *nas, l_float32 tsum )
numaNormalizeHistogram() Input: nas (input histogram) tsum (target sum of all numbers in dest histogram; e.g., use @tsum= 1.0 if this represents a probability distribution) Return: nad (normalized histogram), or null on error
NUMA * numaOpen ( NUMA *nas, l_int32 size )
numaOpen() Input: nas size (of sel; greater than 0, odd; origin implicitly in center) Return: nad (opened), or null on error Notes: (1) The structuring element (sel) is linear, all "hits" (2) If size == 1, this returns a copy
NUMA * numaRebinHistogram ( NUMA *nas, l_int32 newsize )
numaRebinHistogram() Input: nas (input histogram) newsize (number of old bins contained in each new bin) Return: nad (more coarsely re-binned histogram), or null on error
l_int32 numaSelectCrossingThreshold ( NUMA *nax, NUMA *nay, l_float32 estthresh, l_float32 *pbestthresh )
numaSelectCrossingThreshold() Input: nax (<optional> numa of abscissa values; can be NULL) nay (signal) estthresh (estimated pixel threshold for crossing: e.g., for images, white <--> black; typ. ~120) &bestthresh (<return> robust estimate of threshold to use) Return: 0 if OK, 1 on error Note: (1) When a valid threshold is used, the number of crossings is a maximum, because none are missed. If no threshold intersects all the crossings, the crossings must be determined with numaCrossingsByPeaks(). (2) @estthresh is an input estimate of the threshold that should be used. We compute the crossings with 41 thresholds (20 below and 20 above). There is a range in which the number of crossings is a maximum. Return a threshold in the center of this stable plateau of crossings. This can then be used with numaCrossingsByThreshold() to get a good estimate of crossing locations.
l_int32 numaSplitDistribution ( NUMA *na, l_float32 scorefract, l_int32 *psplitindex, l_float32 *pave1, l_float32 *pave2, l_float32 *pnum1, l_float32 *pnum2, NUMA **pnascore )
numaSplitDistribution() Input: na (histogram) scorefract (fraction of the max score, used to determine the range over which the histogram min is searched) &splitindex (<optional return> index for splitting) &ave1 (<optional return> average of lower distribution) &ave2 (<optional return> average of upper distribution) &num1 (<optional return> population of lower distribution) &num2 (<optional return> population of upper distribution) &nascore (<optional return> for debugging; otherwise use null) Return: 0 if OK, 1 on error Notes: (1) This function is intended to be used on a distribution of values that represent two sets, such as a histogram of pixel values for an image with a fg and bg, and the goal is to determine the averages of the two sets and the best splitting point. (2) The Otsu method finds a split point that divides the distribution into two parts by maximizing a score function that is the product of two terms: (a) the square of the difference of centroids, (ave1 - ave2)^2 (b) fract1 * (1 - fract1) where fract1 is the fraction in the lower distribution. (3) This works well for images where the fg and bg are each relatively homogeneous and well-separated in color. However, if the actual fg and bg sets are very different in size, and the bg is highly varied, as can occur in some scanned document images, this will bias the split point into the larger "bump" (i.e., toward the point where the (b) term reaches its maximum of 0.25 at fract1 = 0.5. To avoid this, we define a range of values near the maximum of the score function, and choose the value within this range such that the histogram itself has a minimum value. The range is determined by scorefract: we include all abscissa values to the left and right of the value that maximizes the score, such that the score stays above (1 - scorefract) * maxscore. The intuition behind this modification is to try to find a split point that both has a high variance score and is at or near a minimum in the histogram, so that the histogram slope is small at the split point. (4) We normalize the score so that if the two distributions were of equal size and at opposite ends of the numa, the score would be 1.0.
NUMA * numaTransform ( NUMA *nas, l_float32 shift, l_float32 scale )
numaTransform() Input: nas shift (add this to each number) scale (multiply each number by this) Return: nad (with all values shifted and scaled, or null on error) Notes: (1) Each number is shifted before scaling. (2) The operation sequence is opposite to that for Box and Pta: scale first, then shift.
NUMA * numaWindowedMean ( NUMA *nas, l_int32 wc )
numaWindowedMean() Input: nas wc (half width of the convolution window) Return: nad (after low-pass filtering), or null on error Notes: (1) This is a convolution. The window has width = 2 * @wc + 1. (2) We add a mirrored border of size @wc to each end of the array.
NUMA * numaWindowedMeanSquare ( NUMA *nas, l_int32 wc )
numaWindowedMeanSquare() Input: nas wc (half width of the window) Return: nad (containing windowed mean square values), or null on error Notes: (1) The window has width = 2 * @wc + 1. (2) We add a mirrored border of size @wc to each end of the array.
l_int32 numaWindowedStats ( NUMA *nas, l_int32 wc, NUMA **pnam, NUMA **pnams, NUMA **pnav, NUMA **pnarv )
numaWindowedStats() Input: nas (input numa) wc (half width of the window) &nam (<optional return> mean value in window) &nams (<optional return> mean square value in window) &pnav (<optional return> variance in window) &pnarv (<optional return> rms deviation from the mean) Return: 0 if OK, 1 on error Notes: (1) This is a high-level convenience function for calculating any or all of these derived arrays. (2) These statistical measures over the values in the rectangular window are: - average value: <x> (nam) - average squared value: <x*x> (nams) - variance: <(x - <x>)*(x - <x>)> = <x*x> - <x>*<x> (nav) - square-root of variance: (narv) where the brackets < .. > indicate that the average value is to be taken over the window. (3) Note that the variance is just the mean square difference from the mean value; and the square root of the variance is the root mean square difference from the mean, sometimes also called the 'standard deviation'. (4) Internally, use mirrored borders to handle values near the end of each array.
l_int32 numaWindowedVariance ( NUMA *nam, NUMA *nams, NUMA **pnav, NUMA **pnarv )
numaWindowedVariance() Input: nam (windowed mean values) nams (windowed mean square values) &pnav (<optional return> numa of variance -- the ms deviation from the mean) &pnarv (<optional return> numa of rms deviation from the mean) Return: 0 if OK, 1 on error Notes: (1) The numas of windowed mean and mean square are precomputed, using numaWindowedMean() and numaWindowedMeanSquare(). (2) Either or both of the variance and square-root of variance are returned, where the variance is the average over the window of the mean square difference of the pixel value from the mean: <(x - <x>)*(x - <x>)> = <x*x> - <x>*<x>
Zakariyya Mughal <zmughal@cpan.org>
This software is copyright (c) 2014 by Zakariyya Mughal.
This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.
To install Image::Leptonica, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Image::Leptonica
CPAN shell
perl -MCPAN -e shell install Image::Leptonica
For more information on module installation, please visit the detailed CPAN module installation guide.