gevd_float_operators Class Reference

#include <gevd_float_operators.h>

Detailed Description

Definition at line 42 of file gevd_float_operators.h.

Static Public Member Functions

static float Convolve (const gevd_bufferxy &from, const gevd_bufferxy &kernel, gevd_bufferxy *&to)

Convolves from image with 2D filter and stores values in to image.

static gevd_bufferxy * Read2dKernel (const char *filename)

Read 2D kernel from a file: width height k_x_y .

static float Convolve (const gevd_bufferxy &from, gevd_bufferxy *&to, const float *xkernel, const int xradius, const bool xevenp, const float *ykernel, const int yradius, const bool yevenp, const bool xwrap=false, const bool ywrap=false)

Convolves from image with two separable filters, along directions x and y, and stores values in to image.

static float Convolve (const gevd_bufferxy &from, gevd_bufferxy *&to, const float *xkernel, const int xradius, const bool xevenp, const int yradius, const bool xwrap=false, const bool ywrap=false)

Convolves from image with a filter along x, and a running sum along y-axis, then stores values in to image.

static float Convolve (const float *from, float *&to, const int len, const float *kernel, const int radius, const bool evenp, const bool wrap=false)

Convolve a linear array of data, wrapping at the 2 ends.

static float RunningSum (float *from, float *&to, const int len, const int radius, const bool wrap=false)

For large smoothing sigma, use running sum to avoid floating multiplications.

static bool Read1dKernel (const char *filename, float *&kernel, int &radius, bool &evenp)

Read 1d odd/even kernel from a file: width k_i .

static float Gaussian (gevd_bufferxy &img, gevd_bufferxy *&smooth, const float sigma=1.0, const bool xwrap=false, const bool ywrap=false)

Convolves the from image with a 2D Gaussian filter with standard deviation sigma.

static bool Find1dGaussianKernel (const float sigma, float *&kernel, int &radius, const float fuzz=0.02)

Returns the kernel array for Gaussian with given standard deviation sigma [pixel], and cutoff at min/max = fuzz.

static float Gradient (const gevd_bufferxy &smooth, gevd_bufferxy *&mag, gevd_bufferxy *&dirx, gevd_bufferxy *&diry, const bool xwrap=false, const bool ywrap=false)

Compute the gradient of the intensity surface.

static float Slope (float *from, float *&to, const int len, const bool wrap=false)

Compute slope or first-difference, in linear/circular array.

static float Hessian (const gevd_bufferxy &smooth, gevd_bufferxy *&mag, gevd_bufferxy *&dirx, gevd_bufferxy *&diry, const bool xwrap=false, const bool ywrap=false)

Compute the Hessian of the intensity surface.

static float Laplacian (const gevd_bufferxy &smooth, gevd_bufferxy *&mag, gevd_bufferxy *&dirx, gevd_bufferxy *&diry, const bool xwrap=false, const bool ywrap=false)

Compute the Laplacian of the intensity surface.

static float Curvature (float *from, float *&to, const int len, const bool wrap=false)

Compute curvature, or 2nd-difference in linear/circular array.

static float Orientation (const gevd_bufferxy &smooth, gevd_bufferxy *&theta, gevd_bufferxy *&coherence, const int frame=1)

Compute the local orientation at each pixel in the image, and returns 2 images: twice the angle, and coherence measure (0,1).

static void NonMaximumSuppression (const gevd_bufferxy &magnitude, const gevd_bufferxy &directionx, const gevd_bufferxy &directiony, const float threshold, gevd_bufferxy *&contour, gevd_bufferxy *&direction, gevd_bufferxy *&locationx, gevd_bufferxy *&locationy, const bool xwrap=false, const bool ywrap=false)

Detect contour pixels as strict local maxima, and interpolate the strength/location with a parabola through 3 points.

static int NonMaximumSuppression (const float *from, const int len, const float threshold, int *&index, float *&mag, float *&locs, const bool wrap=false)

Detect local maxima in linear/circular array.

static float InterpolateParabola (float y1, float y0, float y2, float &y)

Fit a parabola through 3 points with strict local max/min.

static float BilinearInterpolate (const gevd_bufferxy &img, float x, float y)

Return the float value of pixel (x, y) in float buffer, using bilinear interpolation.

static void SupportAngle (const gevd_bufferxy &dirx, const gevd_bufferxy &diry, const gevd_bufferxy &magnitude, gevd_bufferxy *&angle)

Find angle of the line of support, in degrees.

static void SurfaceNormal (const gevd_bufferxy &range, gevd_bufferxy *&normal)

Find local surface normal at all pixels in the range z(x,y) image.

static void SurfaceCurvature (const gevd_bufferxy &normal, gevd_bufferxy *&curvature)

Find local gaussian curvature at all pixels from the local surface normals, previously computed from the range z(x,y) image.

static void SurfaceNormalD (const gevd_bufferxy &range, gevd_bufferxy *&normal, float no_value, float pixel_distance=1.0)

Same as gevd_float_operators::SurfaceNormal with two exceptions.

static void SurfaceCurvatureD (const gevd_bufferxy &normal, const gevd_bufferxy &surface, gevd_bufferxy *&curvature, float dflt, float pixel_distance=1.0)

Estimate the maximum curvature at all pixels from the local surface normals, previously computed from the range z(x,y) image.

static float ShrinkBy2 (const gevd_bufferxy &cfrom, gevd_bufferxy *&to, const float burt_ka=0.359375)

Shrinks the from image by 2 and stores into to image, using Burt-Adelson reduction algorithm.

static float ExpandBy2 (const gevd_bufferxy &cfrom, gevd_bufferxy *&to, const float burt_ka=0.359375)

Expands the from image by 2 and store into to image, using Burt-Adelson expansion algorithm.

static void ShrinkBy2_D (const gevd_bufferxy &from, gevd_bufferxy *&to, float no_value, float burt_ka=0.359375)

Shrinks the from image by 2 and stores into to image.

static int Pyramid (const float *from, const int length, float *&to, int &nlevels, int trim=0, const float burt_ka=0.359375)

Compute the pyramid by shrinking data sequence by 2, nlevels-1 times, and return final shrunk length, and reset number of levels in pyramid.

static int ShrinkBy2 (const float *from, const int length, float *&to, const float burt_ka=0.359375)

static bool WaveletTransform (float *array, const int n, const bool forwardp, int nlevels, const int waveletno=4)

Compute the forward/inverse wavelet transform of a 1d array of data.

static bool WaveletTransformByBlock (float *array, const int *dims, const int ndim, const bool forwardp, int nlevels, const int waveletno=4)

n-dimensional wavelet transform of an n-dimensional array.

static bool WaveletTransformByIndex (float *array, const int *dims, const int ndim, const bool forwardp, int nlevels, const int waveletno=4)

n-dimensional wavelet transform of an n-dimensional array.

static bool FindWavelet (const int waveletno, float *&cc, float *&cr, int &ncof)

Looks up and stores the wavelet pair in (lo_filter, hi_filter).

static void LowHighPyramid (float *highPass, float *lowPass, int n, int nlevels, const float *lo_filter, const float *hi_filter, int ncof, float *wksp)

Find pyramid of low/high pass components, using wavelet transform.

static bool WaveletTransformByBlock (const gevd_bufferxy &cfrom, gevd_bufferxy *&to, const bool forwardp, int nlevels, const int waveletno=4)

Compute the Fast Wavelet Transform of the image.

static bool WaveletTransformByIndex (const gevd_bufferxy &cfrom, gevd_bufferxy *&to, const bool forwardp, int nlevels, const int waveletno=4)

Compute the Fast Wavelet Transform of the 2d array.

static int DeleteMixedComponents (gevd_bufferxy &wave, const int nlevels)

Delete all wavelet components, which have high frequency along both x- and y- axes.

static int TruncateHighFrequencies (gevd_bufferxy &wave, const int nlevels, const float threshold=0.1)

Truncate to 0, all wavelet components with high frequency along either x- or y- axes only, not both.

static int TruncateLowestFrequency (gevd_bufferxy &wave, const int nlevels)

Truncate to average value, the lowest frequency component.

static int DeleteBoundaryArtifacts (float *wave, const int n, const int nlevels)

Delete boundary artifacts in 1d-array, because its length is not a power of 2, and so wrapping will skip the last odd element.

static int DeleteBoundaryArtifacts (gevd_bufferxy &wave, const int nlevels)

Delete boundary artifacts because the dimension of the image is not a power of 2, and so wrapping will skip the last odd element.

static void ProjectWaveOntoX (const gevd_bufferxy &buf, float *&proj, const int nlevels=0)

Project wavelet components onto the axes.

static void ProjectWaveOntoY (const gevd_bufferxy &buf, float *&proj, const int nlevels=0)

static void ProjectOntoX (const gevd_bufferxy &buf, float *&proj, int sizeX=0, int sizeY=0, int origX=0, int origY=0)

Project the image data in ROI onto the x- and y- axes.

static void ProjectOntoY (const gevd_bufferxy &buf, float *&proj, int sizeX=0, int sizeY=0, int origX=0, int origY=0)

static float Correlation (const gevd_bufferxy &from, const gevd_bufferxy &kernel, gevd_bufferxy *&to)

Correlate from image with 2D filter and stores values in to image.

static float CorrelationAlongAxis (const gevd_bufferxy &from, const gevd_bufferxy &kernel, gevd_bufferxy *&to)

Correlate from image with 2D filter and stores values in to image.

static float Correlation (const float *data, const int length, const float *pattern, const int radius, const int index)

Find correlation of given pattern to data, matching pattern[radius+i] with data[index+i].

static float * Correlations (const float *data, const int length, const float *pattern, const int radius, const int index, const int search)

Find correlations of given pattern to data, given maximum search from index.

static float BestCorrelation (const float *data, const int length, const float *pattern, const int radius, int &shift, const int search)

Find correlation, and return correlation and shift values.

static float CoarseFineCorrelation (const float *dataPyr, const int dlength, const float *patternPyr, const int plength, float &shift, const int coarse, const int fine, const float cutoff=0, const float overlap=0.75, float *matches=0)

Search for best correlation, from coarse to fine, starting at a priori shift, and requiring minimum overlap.

static void Apply (gevd_bufferxy &buf, float(*func)(float))

Apply function to all elements in buffer.

static gevd_bufferxy * AbsoluteDifference (const gevd_bufferxy &buf1, const gevd_bufferxy &buf2)

static gevd_bufferxy * Allocate (gevd_bufferxy *space, const gevd_bufferxy &model, int bits_per_pixel=0, int sizeX=0, int sizeY=0)

Allocate new space if desired depth and sizes are not the same.

static gevd_bufferxy * SimilarBuffer (const gevd_bufferxy &buffer, int bits_per_pixel=0, int sizeX=0, int sizeY=0)

Creates a new buffer similar to buf, unless dimension and precision are given.

static bool IsSimilarBuffer (const gevd_bufferxy &buf1, const gevd_bufferxy &buf2)

Two buffers are similar if they have the same dimensions, and precision (bits_per_pixel).

static gevd_bufferxy * Extract (const gevd_bufferxy &buf, int sizeX=0, int sizeY=0, int origX=0, int origY=0)

Extract from buf, a float sub-buffer with dimensions (sizeX, sizeY), from top-left corner (origX, origY).

static void Update (gevd_bufferxy &old_buf, const gevd_bufferxy &new_buf, int origX=0, int origY=0)

Update a float sub-buffer of buf, from top-left corner (origX, origY), with values in sub.

static gevd_bufferxy * TransposeExtract (const gevd_bufferxy &buf, int sizeX, int sizeY, int origX, int origY)

static void TransposeUpdate (gevd_bufferxy &buf, const gevd_bufferxy &sub, int origX, int origY)

static void Fill (gevd_bufferxy &buf, const float value, int sizeX=0, int sizeY=0, int origX=0, int origY=0)

Set all pixels in ROI to value.

static void FillFrameX (gevd_bufferxy &buf, const float value, const int width=1)

Sets all pixels in the frame region to value (default = 0).

static void FillFrameY (gevd_bufferxy &buf, const float value, const int width=1)

static void DrawFrame (gevd_bufferxy &buf, const int loc, const float value=0)

Sets all pixels on frame contour, such as buf(loc, i), to value.

static gevd_bufferxy * PadToPowerOf2 (gevd_bufferxy &buf)

Pad the buffer by repeating values at the border, so that the new buffer has dimensions being powers of 2.

static gevd_bufferxy * UnpadFromPowerOf2 (gevd_bufferxy &padded, int sizeX, int sizeY)

Inverse of the above operation.

static float Maximum (const gevd_bufferxy &buf, int sizeX=0, int sizeY=0, int origX=0, int origY=0)

Returns the maximum value in float buffer.

static float Minimum (const gevd_bufferxy &buf, int sizeX=0, int sizeY=0, int origX=0, int origY=0)

Returns the minimum value in float buffer.

static bool Maximum (const float *data, const int length, int &index, float &value)

Detect maximum in 1d-array of values.

static float Sum (const gevd_bufferxy &buf, int sizeX=0, int sizeY=0, int origX=0, int origY=0)

Returns the sum of all values in float buffer.

static int Threshold (gevd_bufferxy &buf, float noise, int sizeX=0, int sizeY=0, int origX=0, int origY=0)

Truncate all values in ROI to 0, if below noise.

static float TruncateToPositive (gevd_bufferxy &buf)

Zeros out all negative values.

static float TruncateToCeiling (gevd_bufferxy &buf, float ceil)

static void Absolute (gevd_bufferxy &buf)

Replace with absolute values.

static void Negate (gevd_bufferxy &buf)

Negate all values.

static void Scale (gevd_bufferxy &buf, float factor)

Scale all values by factor.

static void ShiftToPositive (gevd_bufferxy &buf)

Shift to positive values, by adding 30.0000, and truncate all values to 0-60.000.

static void Normalize (gevd_bufferxy &buf, const float lo, const float hi)

Normalizes a float buffer so that the pixel values range from lo to hi, inclusive.

static bool BufferToFloat (const gevd_bufferxy &from, gevd_bufferxy &floatto)

Converts from a unsigned char (8-bit) or a short (16-bit) buffer to a float buffer to avoid overflow/underflow and conversion for subsequent math computations.

static bool FloatToBuffer (const gevd_bufferxy &floatfrom, gevd_bufferxy &to)

Static Protected Member Functions

static int SetupPipeline (const float *data, const int len, const int kradius, const bool wrap, float *&cache, float *&pipeline)

Setup the cache for reflection/wrapping at the borders, and the center pipeline.

static gevd_bufferxy * WrapAlongX (const gevd_bufferxy &img)

Create a buffer that wraps rows/columns.

static gevd_bufferxy * WrapAlongY (const gevd_bufferxy &img)

static float Gaussian (const float x, const float sigma)

static float ShrinkBy2AlongX (const gevd_bufferxy &cfrom, const int y, float *yline, const int len, const float ka, const float kb, const float kc)

Shrinks the yline by 2 along the x-axis.

static void ShrinkBy2AlongX_D (const gevd_bufferxy &from, int from_sizeX, int sizeX, int y, float kernel[], float no_value, float *yline, float *wline)

Create a smoothed and subsampled array of x values in the given row.

static float ExpandBy2AlongX (const gevd_bufferxy &cfrom, const int y, float *yline, const int len, const float ka, const float kb, const float kc)

Expands the yline by 2 along the x-axis.

static void WaveletTransformStep (float *array, const int n, const bool forwardp, const float *lo_filter, const float *hi_filter, const int ncof, float *wksp)

Convolution with wavelets (lo_filter, hi_filter) and gather results into consecutive blocks, with convolution of lo_filter (resp.

static void WaveletTransformStep (float *array, const int *dims, const int ndim, const bool forwardp, const float *lo_filter, const float *hi_filter, const int ncof, float *buffer, float *wksp)

static void CopyNdRecursive (const float *from_array, const int from_size, const int *from_dims, float *to_array, const int to_size, const int *to_dims, const int ndim, const bool fullp=true)

Recursively copies elements of n-dimensional arrays.

static void TestWavelets ()

Private Member Functions

gevd_float_operators ()

Constructor & Destructor Documentation

gevd_float_operators::gevd_float_operators ( ) [private]

Member Function Documentation

void gevd_float_operators::Absolute ( gevd_bufferxy & buf ) [static]

Replace with absolute values.

Definition at line 3809 of file gevd_float_operators.cxx.

gevd_bufferxy * gevd_float_operators::AbsoluteDifference ( const gevd_bufferxy & buf1,

const gevd_bufferxy & buf2

) [static]

Definition at line 4083 of file gevd_float_operators.cxx.

gevd_bufferxy * gevd_float_operators::Allocate ( gevd_bufferxy * space,

const gevd_bufferxy & model,

int bits_per_pixel = 0,

int sizeX = 0,

int sizeY = 0

) [static]

Allocate new space if desired depth and sizes are not the same.

Definition at line 3495 of file gevd_float_operators.cxx.

void gevd_float_operators::Apply ( gevd_bufferxy & buf,

float(*)(float) func

) [static]

Apply function to all elements in buffer.

Definition at line 3483 of file gevd_float_operators.cxx.

float gevd_float_operators::BestCorrelation ( const float * data,

const int length,

const float * pattern,

const int radius,

int & shift,

const int search

) [static]

Find correlation, and return correlation and shift values.

Definition at line 3340 of file gevd_float_operators.cxx.

float gevd_float_operators::BilinearInterpolate ( const gevd_bufferxy & img,

float x,

float y

) [static]

Return the float value of pixel (x, y) in float buffer, using bilinear interpolation.

Definition at line 1441 of file gevd_float_operators.cxx.

bool gevd_float_operators::BufferToFloat ( const gevd_bufferxy & from,

gevd_bufferxy & to

) [static]

Converts from a unsigned char (8-bit) or a short (16-bit) buffer to a float buffer to avoid overflow/underflow and conversion for subsequent math computations.
O(n*m).
Definition at line 3854 of file gevd_float_operators.cxx.

float gevd_float_operators::CoarseFineCorrelation ( const float * dataPyr,

const int dlength,

const float * patternPyr,

const int plength,

float & shift,

const int coarse,

const int fine,

const float cutoff = 0,

const float overlap = 0.75,

float * matches = 0

) [static]

Search for best correlation, from coarse to fine, starting at a priori shift, and requiring minimum overlap.
O(n) time. Return last best correlation, and its corresponding shift. The search is cutoff early, if no maximum is found, or maximum correlation <= cutoff. Accumulate match values if matches non null. Assumes data and pattern are pyramids. Compile with -DDEBUG to trace the coarse-to-fine search of the best correlation,
Definition at line 3372 of file gevd_float_operators.cxx.

float gevd_float_operators::Convolve ( const float * from,

float *& to,

const int len,

const float * kernel,

const int kradius,

const bool evenp,

const bool wrap = false

) [static]

Convolve a linear array of data, wrapping at the 2 ends.
Special care is taken when to and from are identical - Peter Vanroose.
Definition at line 493 of file gevd_float_operators.cxx.

float gevd_float_operators::Convolve ( const gevd_bufferxy & from,

gevd_bufferxy *& to,

const float * xkernel,

const int xradius,

const bool xevenp,

const int yradius,

const bool xwrap = false,

const bool ywrap = false

) [static]

Convolves from image with a filter along x, and a running sum along y-axis, then stores values in to image.
O(m*n*k).
Definition at line 379 of file gevd_float_operators.cxx.

float gevd_float_operators::Convolve ( const gevd_bufferxy & from,

gevd_bufferxy *& to,

const float * xkernel,

const int xradius,

const bool xevenp,

const float * ykernel,

const int yradius,

const bool yevenp,

const bool xwrap = false,

const bool ywrap = false

) [static]

Convolves from image with two separable filters, along directions x and y, and stores values in to image.
O(m*n*k). The filter kernel has length 2*radius + 1, and is either even or odd. Assume image data is in row-major order.
Special care is taken when to and from are identical - Peter Vanroose.
Definition at line 229 of file gevd_float_operators.cxx.

float gevd_float_operators::Convolve ( const gevd_bufferxy & from,

const gevd_bufferxy & kernel,

gevd_bufferxy *& to

) [static]

Convolves from image with 2D filter and stores values in to image.
O(m*n*k). The filter kernel has odd width and height, and is either even or odd along x- or y-axis. Assume image data is in row-major order.
Special care is taken when to and from are identical - Peter Vanroose.
Definition at line 48 of file gevd_float_operators.cxx.

void gevd_float_operators::CopyNdRecursive ( const float * from_array,

const int from_size,

const int * from_dims,

float * to_array,

const int to_size,

const int * to_dims,

const int ndim,

const bool fullp = true

) [static, protected]

Recursively copies elements of n-dimensional arrays.
Extra elements that can not fit in both arrays are not read or written. A flag fullp (default = true) is used to copy from/to a full n-dimensional array or only a sub-block of the array.
Definition at line 2794 of file gevd_float_operators.cxx.

float gevd_float_operators::Correlation ( const float * data,

const int length,

const float * pattern,

const int radius,

const int index

) [static]

Find correlation of given pattern to data, matching pattern[radius+i] with data[index+i].
The linear correlation coefficient, also called Pearson r, is computed, O(|pattern|). Assumed pattern has length = 2*radius + 1.
Definition at line 3273 of file gevd_float_operators.cxx.

float gevd_float_operators::Correlation ( const gevd_bufferxy & from,

const gevd_bufferxy & kernel,

gevd_bufferxy *& to

) [static]

Correlate from image with 2D filter and stores values in to image.
O(m*n*k). The filter kernel has odd width and height, and is either even or odd along x- or y-axis. Assume image data is in row-major order.
Special care is taken when to and from are identical - Peter Vanroose.
Definition at line 90 of file gevd_float_operators.cxx.

float gevd_float_operators::CorrelationAlongAxis ( const gevd_bufferxy & from,

const gevd_bufferxy & kernel,

gevd_bufferxy *& to

) [static]

Correlate from image with 2D filter and stores values in to image.
Special care is taken when to and from are identical - Peter Vanroose.
Definition at line 140 of file gevd_float_operators.cxx.

float * gevd_float_operators::Correlations ( const float * data,

const int length,

const float * pattern,

const int radius,

const int index,

const int search

) [static]

Find correlations of given pattern to data, given maximum search from index.
O(|pattern|*shift). Returns the array of correlation values, with positive translation starting from result[search+1], and negative translation starting from result[search-1].
Definition at line 3310 of file gevd_float_operators.cxx.

float gevd_float_operators::Curvature ( float * from,

float *& to,

const int len,

const bool wrap = false

) [static]

Compute curvature, or 2nd-difference in linear/circular array.
Special care is taken when to and from are identical - Peter Vanroose.
Definition at line 1137 of file gevd_float_operators.cxx.

int gevd_float_operators::DeleteBoundaryArtifacts ( gevd_bufferxy & wave,

const int nlevels

) [static]

Delete boundary artifacts because the dimension of the image is not a power of 2, and so wrapping will skip the last odd element.

Definition at line 3159 of file gevd_float_operators.cxx.

int gevd_float_operators::DeleteBoundaryArtifacts ( float * wave,

const int n,

const int nlevels

) [static]

Delete boundary artifacts in 1d-array, because its length is not a power of 2, and so wrapping will skip the last odd element.

Definition at line 3134 of file gevd_float_operators.cxx.

int gevd_float_operators::DeleteMixedComponents ( gevd_bufferxy & wave,

const int nlevels

) [static]

Delete all wavelet components, which have high frequency along both x- and y- axes.
They are diagonal blocks, except the lowest frequency block. This will throw away high frequency point-like features. Return the number of coefficients deleted.
Definition at line 3057 of file gevd_float_operators.cxx.

void gevd_float_operators::DrawFrame ( gevd_bufferxy & buf,

const int loc,

const float value = 0

) [static]

Sets all pixels on frame contour, such as buf(loc, i), to value.
O(n+m).
Definition at line 3630 of file gevd_float_operators.cxx.

float gevd_float_operators::ExpandBy2 ( const gevd_bufferxy & from,

gevd_bufferxy *& to,

const float burt_ka = 0.359375

) [static]

Expands the from image by 2 and store into to image, using Burt-Adelson expansion algorithm.
Convolution with a 5-point kernel [(0.5-ka), 0.5, 2*ka, 0.5, (0.5-ka)] ka = 0.6 maximum decorrelation, low-pass filter for image compression. ka = 0.5 linear interpolation, ka = 0.4 Gaussian filter, smoothing at tail. ka = 0.3 wider than Gaussian, for more smoothing. The image indexes are mapped with: to.ij = from.ij * 2 The image sizes are related by: to.size = from.size * 2.
Special care is taken when to and from are identical - Peter Vanroose.
Definition at line 2140 of file gevd_float_operators.cxx.

float gevd_float_operators::ExpandBy2AlongX ( const gevd_bufferxy & from,

const int y,

float * yline,

const int sizeX,

const float ka,

const float kb,

const float kc

) [static, protected]

Expands the yline by 2 along the x-axis.
Interpolation is done by convolution with pixels at integral indexes only.
Definition at line 2188 of file gevd_float_operators.cxx.

gevd_bufferxy * gevd_float_operators::Extract ( const gevd_bufferxy & buf,

int sizeX = 0,

int sizeY = 0,

int origX = 0,

int origY = 0

) [static]

Extract from buf, a float sub-buffer with dimensions (sizeX, sizeY), from top-left corner (origX, origY).
Faster copying can be done with read/write chunks of memory.
Definition at line 3548 of file gevd_float_operators.cxx.

void gevd_float_operators::Fill ( gevd_bufferxy & buf,

const float value,

int sizeX = 0,

int sizeY = 0,

int origX = 0,

int origY = 0

) [static]

Set all pixels in ROI to value.

Definition at line 3578 of file gevd_float_operators.cxx.

void gevd_float_operators::FillFrameX ( gevd_bufferxy & buf,

const float value,

const int width = 1

) [static]

Sets all pixels in the frame region to value (default = 0).
O((n+m)*width). The frame region is a rectangular band with given width, framing at two ends of x/y axes.
Definition at line 3598 of file gevd_float_operators.cxx.

void gevd_float_operators::FillFrameY ( gevd_bufferxy & buf,

const float value,

const int width = 1

) [static]

Definition at line 3613 of file gevd_float_operators.cxx.

bool gevd_float_operators::Find1dGaussianKernel ( const float sigma,

float *& kernel,

int & radius,

const float fuzz = 0.02

) [static]

Returns the kernel array for Gaussian with given standard deviation sigma [pixel], and cutoff at min/max = fuzz.
The area under the discrete Gaussian is normalized to 1.
Definition at line 689 of file gevd_float_operators.cxx.

bool gevd_float_operators::FindWavelet ( const int waveletno,

float *& lo_filter,

float *& hi_filter,

int & ncof

) [static]

Looks up and stores the wavelet pair in (lo_filter, hi_filter).
The wavelet number is 2 for Haar wavelet, 4-20 even numbers for Daubechies wavelet, and 9-15 odd numbers for symmetric Coifman wavelets.
Definition at line 2438 of file gevd_float_operators.cxx.

bool gevd_float_operators::FloatToBuffer ( const gevd_bufferxy & floatfrom,

gevd_bufferxy & to

) [static]

Definition at line 3899 of file gevd_float_operators.cxx.

float gevd_float_operators::Gaussian ( const float x,

const float sigma

) [static, protected]

Definition at line 717 of file gevd_float_operators.cxx.

float gevd_float_operators::Gaussian ( gevd_bufferxy & from,

gevd_bufferxy *& to,

const float sigma = 1.0,

const bool xwrap = false,

const bool ywrap = false

) [static]

Convolves the from image with a 2D Gaussian filter with standard deviation sigma.
O(m*n*k). The 2D convolution is decomposed into 2 1D convolutions: Gxy * I = Gy * (Gx * I). The frame with width equal to the radius of the Gaussian kernel is filled with zero.
Definition at line 661 of file gevd_float_operators.cxx.

float gevd_float_operators::Gradient ( const gevd_bufferxy & smooth,

gevd_bufferxy *& magnitude,

gevd_bufferxy *& gradx,

gevd_bufferxy *& grady,

const bool xwrap = false,

const bool ywrap = false

) [static]

Compute the gradient of the intensity surface.
O(m*n). The intensity surface is assumed smoothed by a Gaussian filter, or convolved with a low-pass filter. Return at each pixel, the magnitude, the vector (dG * I), and the multiplication factor to normalize the magnitude. The product of detection |dG * I| and localization |dddG * I| of the step relative to noise is invariant to filter-size for the ideal step edge, and depends only on the shape of the step edge. As the filter size (sigma) increases by k, detection or signal-to-noise ratio increases by sqrt(k), but localization decreases by 1/sqrt(k). This invariance is consistent with the uncertainty principle.
Definition at line 806 of file gevd_float_operators.cxx.

float gevd_float_operators::Hessian ( const


Static Public Member Functions
static float	Convolve (const gevd_bufferxy &from, const gevd_bufferxy &kernel, gevd_bufferxy *&to)
	Convolves from image with 2D filter and stores values in to image.
static gevd_bufferxy *	Read2dKernel (const char *filename)
	Read 2D kernel from a file: width height k_x_y .
static float	Convolve (const gevd_bufferxy &from, gevd_bufferxy &to, const float xkernel, const int xradius, const bool xevenp, const float *ykernel, const int yradius, const bool yevenp, const bool xwrap=false, const bool ywrap=false)
	Convolves from image with two separable filters, along directions x and y, and stores values in to image.
static float	Convolve (const gevd_bufferxy &from, gevd_bufferxy &to, const float xkernel, const int xradius, const bool xevenp, const int yradius, const bool xwrap=false, const bool ywrap=false)
	Convolves from image with a filter along x, and a running sum along y-axis, then stores values in to image.
static float	Convolve (const float from, float &to, const int len, const float *kernel, const int radius, const bool evenp, const bool wrap=false)
	Convolve a linear array of data, wrapping at the 2 ends.
static float	RunningSum (float from, float &to, const int len, const int radius, const bool wrap=false)
	For large smoothing sigma, use running sum to avoid floating multiplications.
static bool	Read1dKernel (const char filename, float &kernel, int &radius, bool &evenp)
	Read 1d odd/even kernel from a file: width k_i .
static float	Gaussian (gevd_bufferxy &img, gevd_bufferxy *&smooth, const float sigma=1.0, const bool xwrap=false, const bool ywrap=false)
	Convolves the from image with a 2D Gaussian filter with standard deviation sigma.
static bool	Find1dGaussianKernel (const float sigma, float *&kernel, int &radius, const float fuzz=0.02)
	Returns the kernel array for Gaussian with given standard deviation sigma [pixel], and cutoff at min/max = fuzz.
static float	Gradient (const gevd_bufferxy &smooth, gevd_bufferxy &mag, gevd_bufferxy &dirx, gevd_bufferxy *&diry, const bool xwrap=false, const bool ywrap=false)
	Compute the gradient of the intensity surface.
static float	Slope (float from, float &to, const int len, const bool wrap=false)
	Compute slope or first-difference, in linear/circular array.
static float	Hessian (const gevd_bufferxy &smooth, gevd_bufferxy &mag, gevd_bufferxy &dirx, gevd_bufferxy *&diry, const bool xwrap=false, const bool ywrap=false)
	Compute the Hessian of the intensity surface.
static float	Laplacian (const gevd_bufferxy &smooth, gevd_bufferxy &mag, gevd_bufferxy &dirx, gevd_bufferxy *&diry, const bool xwrap=false, const bool ywrap=false)
	Compute the Laplacian of the intensity surface.
static float	Curvature (float from, float &to, const int len, const bool wrap=false)
	Compute curvature, or 2nd-difference in linear/circular array.
static float	Orientation (const gevd_bufferxy &smooth, gevd_bufferxy &theta, gevd_bufferxy &coherence, const int frame=1)
	Compute the local orientation at each pixel in the image, and returns 2 images: twice the angle, and coherence measure (0,1).
static void	NonMaximumSuppression (const gevd_bufferxy &magnitude, const gevd_bufferxy &directionx, const gevd_bufferxy &directiony, const float threshold, gevd_bufferxy &contour, gevd_bufferxy &direction, gevd_bufferxy &locationx, gevd_bufferxy &locationy, const bool xwrap=false, const bool ywrap=false)
	Detect contour pixels as strict local maxima, and interpolate the strength/location with a parabola through 3 points.
static int	NonMaximumSuppression (const float from, const int len, const float threshold, int &index, float &mag, float &locs, const bool wrap=false)
	Detect local maxima in linear/circular array.
static float	InterpolateParabola (float y1, float y0, float y2, float &y)
	Fit a parabola through 3 points with strict local max/min.
static float	BilinearInterpolate (const gevd_bufferxy &img, float x, float y)
	Return the float value of pixel (x, y) in float buffer, using bilinear interpolation.
static void	SupportAngle (const gevd_bufferxy &dirx, const gevd_bufferxy &diry, const gevd_bufferxy &magnitude, gevd_bufferxy *&angle)
	Find angle of the line of support, in degrees.
static void	SurfaceNormal (const gevd_bufferxy &range, gevd_bufferxy *&normal)
	Find local surface normal at all pixels in the range z(x,y) image.
static void	SurfaceCurvature (const gevd_bufferxy &normal, gevd_bufferxy *&curvature)
	Find local gaussian curvature at all pixels from the local surface normals, previously computed from the range z(x,y) image.
static void	SurfaceNormalD (const gevd_bufferxy &range, gevd_bufferxy *&normal, float no_value, float pixel_distance=1.0)
	Same as gevd_float_operators::SurfaceNormal with two exceptions.
static void	SurfaceCurvatureD (const gevd_bufferxy &normal, const gevd_bufferxy &surface, gevd_bufferxy *&curvature, float dflt, float pixel_distance=1.0)
	Estimate the maximum curvature at all pixels from the local surface normals, previously computed from the range z(x,y) image.
static float	ShrinkBy2 (const gevd_bufferxy &cfrom, gevd_bufferxy *&to, const float burt_ka=0.359375)
	Shrinks the from image by 2 and stores into to image, using Burt-Adelson reduction algorithm.
static float	ExpandBy2 (const gevd_bufferxy &cfrom, gevd_bufferxy *&to, const float burt_ka=0.359375)
	Expands the from image by 2 and store into to image, using Burt-Adelson expansion algorithm.
static void	ShrinkBy2_D (const gevd_bufferxy &from, gevd_bufferxy *&to, float no_value, float burt_ka=0.359375)
	Shrinks the from image by 2 and stores into to image.
static int	Pyramid (const float from, const int length, float &to, int &nlevels, int trim=0, const float burt_ka=0.359375)
	Compute the pyramid by shrinking data sequence by 2, nlevels-1 times, and return final shrunk length, and reset number of levels in pyramid.
static int	ShrinkBy2 (const float from, const int length, float &to, const float burt_ka=0.359375)
static bool	WaveletTransform (float *array, const int n, const bool forwardp, int nlevels, const int waveletno=4)
	Compute the forward/inverse wavelet transform of a 1d array of data.
static bool	WaveletTransformByBlock (float array, const int dims, const int ndim, const bool forwardp, int nlevels, const int waveletno=4)
	n-dimensional wavelet transform of an n-dimensional array.
static bool	WaveletTransformByIndex (float array, const int dims, const int ndim, const bool forwardp, int nlevels, const int waveletno=4)
	n-dimensional wavelet transform of an n-dimensional array.
static bool	FindWavelet (const int waveletno, float &cc, float &cr, int &ncof)
	Looks up and stores the wavelet pair in (lo_filter, hi_filter).
static void	LowHighPyramid (float highPass, float lowPass, int n, int nlevels, const float lo_filter, const float hi_filter, int ncof, float *wksp)
	Find pyramid of low/high pass components, using wavelet transform.
static bool	WaveletTransformByBlock (const gevd_bufferxy &cfrom, gevd_bufferxy *&to, const bool forwardp, int nlevels, const int waveletno=4)
	Compute the Fast Wavelet Transform of the image.
static bool	WaveletTransformByIndex (const gevd_bufferxy &cfrom, gevd_bufferxy *&to, const bool forwardp, int nlevels, const int waveletno=4)
	Compute the Fast Wavelet Transform of the 2d array.
static int	DeleteMixedComponents (gevd_bufferxy &wave, const int nlevels)
	Delete all wavelet components, which have high frequency along both x- and y- axes.
static int	TruncateHighFrequencies (gevd_bufferxy &wave, const int nlevels, const float threshold=0.1)
	Truncate to 0, all wavelet components with high frequency along either x- or y- axes only, not both.
static int	TruncateLowestFrequency (gevd_bufferxy &wave, const int nlevels)
	Truncate to average value, the lowest frequency component.
static int	DeleteBoundaryArtifacts (float *wave, const int n, const int nlevels)
	Delete boundary artifacts in 1d-array, because its length is not a power of 2, and so wrapping will skip the last odd element.
static int	DeleteBoundaryArtifacts (gevd_bufferxy &wave, const int nlevels)
	Delete boundary artifacts because the dimension of the image is not a power of 2, and so wrapping will skip the last odd element.
static void	ProjectWaveOntoX (const gevd_bufferxy &buf, float *&proj, const int nlevels=0)
	Project wavelet components onto the axes.
static void	ProjectWaveOntoY (const gevd_bufferxy &buf, float *&proj, const int nlevels=0)
static void	ProjectOntoX (const gevd_bufferxy &buf, float *&proj, int sizeX=0, int sizeY=0, int origX=0, int origY=0)
	Project the image data in ROI onto the x- and y- axes.
static void	ProjectOntoY (const gevd_bufferxy &buf, float *&proj, int sizeX=0, int sizeY=0, int origX=0, int origY=0)
static float	Correlation (const gevd_bufferxy &from, const gevd_bufferxy &kernel, gevd_bufferxy *&to)
	Correlate from image with 2D filter and stores values in to image.
static float	CorrelationAlongAxis (const gevd_bufferxy &from, const gevd_bufferxy &kernel, gevd_bufferxy *&to)
	Correlate from image with 2D filter and stores values in to image.
static float	Correlation (const float data, const int length, const float pattern, const int radius, const int index)
	Find correlation of given pattern to data, matching pattern[radius+i] with data[index+i].
static float *	Correlations (const float data, const int length, const float pattern, const int radius, const int index, const int search)
	Find correlations of given pattern to data, given maximum search from index.
static float	BestCorrelation (const float data, const int length, const float pattern, const int radius, int &shift, const int search)
	Find correlation, and return correlation and shift values.
static float	CoarseFineCorrelation (const float dataPyr, const int dlength, const float patternPyr, const int plength, float &shift, const int coarse, const int fine, const float cutoff=0, const float overlap=0.75, float *matches=0)
	Search for best correlation, from coarse to fine, starting at a priori shift, and requiring minimum overlap.
static void	Apply (gevd_bufferxy &buf, float(*func)(float))
	Apply function to all elements in buffer.
static gevd_bufferxy *	AbsoluteDifference (const gevd_bufferxy &buf1, const gevd_bufferxy &buf2)
static gevd_bufferxy *	Allocate (gevd_bufferxy *space, const gevd_bufferxy &model, int bits_per_pixel=0, int sizeX=0, int sizeY=0)
	Allocate new space if desired depth and sizes are not the same.
static gevd_bufferxy *	SimilarBuffer (const gevd_bufferxy &buffer, int bits_per_pixel=0, int sizeX=0, int sizeY=0)
	Creates a new buffer similar to buf, unless dimension and precision are given.
static bool	IsSimilarBuffer (const gevd_bufferxy &buf1, const gevd_bufferxy &buf2)
	Two buffers are similar if they have the same dimensions, and precision (bits_per_pixel).
static gevd_bufferxy *	Extract (const gevd_bufferxy &buf, int sizeX=0, int sizeY=0, int origX=0, int origY=0)
	Extract from buf, a float sub-buffer with dimensions (sizeX, sizeY), from top-left corner (origX, origY).
static void	Update (gevd_bufferxy &old_buf, const gevd_bufferxy &new_buf, int origX=0, int origY=0)
	Update a float sub-buffer of buf, from top-left corner (origX, origY), with values in sub.
static gevd_bufferxy *	TransposeExtract (const gevd_bufferxy &buf, int sizeX, int sizeY, int origX, int origY)
static void	TransposeUpdate (gevd_bufferxy &buf, const gevd_bufferxy &sub, int origX, int origY)
static void	Fill (gevd_bufferxy &buf, const float value, int sizeX=0, int sizeY=0, int origX=0, int origY=0)
	Set all pixels in ROI to value.
static void	FillFrameX (gevd_bufferxy &buf, const float value, const int width=1)
	Sets all pixels in the frame region to value (default = 0).
static void	FillFrameY (gevd_bufferxy &buf, const float value, const int width=1)
static void	DrawFrame (gevd_bufferxy &buf, const int loc, const float value=0)
	Sets all pixels on frame contour, such as buf(loc, i), to value.
static gevd_bufferxy *	PadToPowerOf2 (gevd_bufferxy &buf)
	Pad the buffer by repeating values at the border, so that the new buffer has dimensions being powers of 2.
static gevd_bufferxy *	UnpadFromPowerOf2 (gevd_bufferxy &padded, int sizeX, int sizeY)
	Inverse of the above operation.
static float	Maximum (const gevd_bufferxy &buf, int sizeX=0, int sizeY=0, int origX=0, int origY=0)
	Returns the maximum value in float buffer.
static float	Minimum (const gevd_bufferxy &buf, int sizeX=0, int sizeY=0, int origX=0, int origY=0)
	Returns the minimum value in float buffer.
static bool	Maximum (const float *data, const int length, int &index, float &value)
	Detect maximum in 1d-array of values.
static float	Sum (const gevd_bufferxy &buf, int sizeX=0, int sizeY=0, int origX=0, int origY=0)
	Returns the sum of all values in float buffer.
static int	Threshold (gevd_bufferxy &buf, float noise, int sizeX=0, int sizeY=0, int origX=0, int origY=0)
	Truncate all values in ROI to 0, if below noise.
static float	TruncateToPositive (gevd_bufferxy &buf)
	Zeros out all negative values.
static float	TruncateToCeiling (gevd_bufferxy &buf, float ceil)
static void	Absolute (gevd_bufferxy &buf)
	Replace with absolute values.
static void	Negate (gevd_bufferxy &buf)
	Negate all values.
static void	Scale (gevd_bufferxy &buf, float factor)
	Scale all values by factor.
static void	ShiftToPositive (gevd_bufferxy &buf)
	Shift to positive values, by adding 30.0000, and truncate all values to 0-60.000.
static void	Normalize (gevd_bufferxy &buf, const float lo, const float hi)
	Normalizes a float buffer so that the pixel values range from lo to hi, inclusive.
static bool	BufferToFloat (const gevd_bufferxy &from, gevd_bufferxy &floatto)
	Converts from a unsigned char (8-bit) or a short (16-bit) buffer to a float buffer to avoid overflow/underflow and conversion for subsequent math computations.
static bool	FloatToBuffer (const gevd_bufferxy &floatfrom, gevd_bufferxy &to)
Static Protected Member Functions
static int	SetupPipeline (const float data, const int len, const int kradius, const bool wrap, float &cache, float *&pipeline)
	Setup the cache for reflection/wrapping at the borders, and the center pipeline.
static gevd_bufferxy *	WrapAlongX (const gevd_bufferxy &img)
	Create a buffer that wraps rows/columns.
static gevd_bufferxy *	WrapAlongY (const gevd_bufferxy &img)
static float	Gaussian (const float x, const float sigma)
static float	ShrinkBy2AlongX (const gevd_bufferxy &cfrom, const int y, float *yline, const int len, const float ka, const float kb, const float kc)
	Shrinks the yline by 2 along the x-axis.
static void	ShrinkBy2AlongX_D (const gevd_bufferxy &from, int from_sizeX, int sizeX, int y, float kernel[], float no_value, float yline, float wline)
	Create a smoothed and subsampled array of x values in the given row.
static float	ExpandBy2AlongX (const gevd_bufferxy &cfrom, const int y, float *yline, const int len, const float ka, const float kb, const float kc)
	Expands the yline by 2 along the x-axis.
static void	WaveletTransformStep (float array, const int n, const bool forwardp, const float lo_filter, const float hi_filter, const int ncof, float wksp)
	Convolution with wavelets (lo_filter, hi_filter) and gather results into consecutive blocks, with convolution of lo_filter (resp.
static void	WaveletTransformStep (float array, const int dims, const int ndim, const bool forwardp, const float lo_filter, const float hi_filter, const int ncof, float buffer, float wksp)
static void	CopyNdRecursive (const float from_array, const int from_size, const int from_dims, float to_array, const int to_size, const int to_dims, const int ndim, const bool fullp=true)
	Recursively copies elements of n-dimensional arrays.
static void	TestWavelets ()
Private Member Functions
	gevd_float_operators ()