fastaniso

# Original work: Copyright (c) 1995-2012 Peter Kovesi [email protected]
# Modified work: Copyright (c) 2012 Alistair Muldal
#
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# copies or substantial portions of the Software.
#
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# implied, including but not limited to the warranties of merchantability,
# fitness for a particular purpose and noninfringement. In no event shall the
# authors or copyright holders be liable for any claim, damages or other
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# software.

import numpy as np
import warnings

def anisodiff(img,niter=1,kappa=50,gamma=0.1,step=(1.,1.),option=1,ploton=False):
    """
    Anisotropic diffusion.

    Usage:
    imgout = anisodiff(im, niter, kappa, gamma, option)

    Arguments:
            img    - input image
            niter  - number of iterations
            kappa  - conduction coefficient 20-100 ?
            gamma  - max value of .25 for stability
            step   - tuple, the distance between adjacent pixels in (y,x)
            option - 1 Perona Malik diffusion equation No 1
                     2 Perona Malik diffusion equation No 2
            ploton - if True, the image will be plotted on every iteration

    Returns:
            imgout   - diffused image.

    kappa controls conduction as a function of gradient.  If kappa is low
    small intensity gradients are able to block conduction and hence diffusion
    across step edges.  A large value reduces the influence of intensity
    gradients on conduction.

    gamma controls speed of diffusion (you usually want it at a maximum of
    0.25)

    step is used to scale the gradients in case the spacing between adjacent
    pixels differs in the x and y axes

    Diffusion equation 1 favours high contrast edges over low contrast ones.
    Diffusion equation 2 favours wide regions over smaller ones.

    Reference:
    P. Perona and J. Malik.
    Scale-space and edge detection using ansotropic diffusion.
    IEEE Transactions on Pattern Analysis and Machine Intelligence,
    12(7):629-639, July 1990.

    Original MATLAB code by Peter Kovesi
    School of Computer Science & Software Engineering
    The University of Western Australia
    pk @ csse uwa edu au
    <http://www.csse.uwa.edu.au>

    Translated to Python and optimised by Alistair Muldal
    Department of Pharmacology
    University of Oxford
    <[email protected]>

    June 2000  original version.
    March 2002 corrected diffusion eqn No 2.
    July 2012 translated to Python
    """

    # ...you could always diffuse each color channel independently if you
    # really want
    if img.ndim == 3:
        warnings.warn("Only grayscale images allowed, converting to 2D matrix")
        img = img.mean(2)

    # initialize output array
    img = img.astype('float32')
    imgout = img.copy()

    # initialize some internal variables
    deltaS = np.zeros_like(imgout)
    deltaE = deltaS.copy()
    NS = deltaS.copy()
    EW = deltaS.copy()
    gS = np.ones_like(imgout)
    gE = gS.copy()

    # create the plot figure, if requested
    if ploton:
        import pylab as pl
        from time import sleep

        fig = pl.figure(figsize=(20,5.5),num="Anisotropic diffusion")
        ax1,ax2 = fig.add_subplot(1,2,1),fig.add_subplot(1,2,2)

        ax1.imshow(img,interpolation='nearest')
        ih = ax2.imshow(imgout,interpolation='nearest',animated=True)
        ax1.set_title("Original image")
        ax2.set_title("Iteration 0")

        fig.canvas.draw()

    for ii in xrange(niter):

        # calculate the diffs
        deltaS[:-1,: ] = np.diff(imgout,axis=0)
        deltaE[: ,:-1] = np.diff(imgout,axis=1)

        # conduction gradients (only need to compute one per dim!)
        if option == 1:
            gS = np.exp(-(deltaS/kappa)**2.)/step[0]
            gE = np.exp(-(deltaE/kappa)**2.)/step[1]
        elif option == 2:
            gS = 1./(1.+(deltaS/kappa)**2.)/step[0]
            gE = 1./(1.+(deltaE/kappa)**2.)/step[1]

        # update matrices
        E = gE*deltaE
        S = gS*deltaS

        # subtract a copy that has been shifted 'North/West' by one
        # pixel. don't as questions. just do it. trust me.
        NS[:] = S
        EW[:] = E
        NS[1:,:] -= S[:-1,:]
        EW[:,1:] -= E[:,:-1]

        # update the image
        imgout += gamma*(NS+EW)

        if ploton:
            iterstring = "Iteration %i" %(ii+1)
            ih.set_data(imgout)
            ax2.set_title(iterstring)
            fig.canvas.draw()
            # sleep(0.01)

    return imgout

def anisodiff3(stack,niter=1,kappa=50,gamma=0.1,step=(1.,1.,1.),option=1,ploton=False):
    """
    3D Anisotropic diffusion.

    Usage:
    stackout = anisodiff(stack, niter, kappa, gamma, option)

    Arguments:
            stack  - input stack
            niter  - number of iterations
            kappa  - conduction coefficient 20-100 ?
            gamma  - max value of .25 for stability
            step   - tuple, the distance between adjacent pixels in (z,y,x)
            option - 1 Perona Malik diffusion equation No 1
                     2 Perona Malik diffusion equation No 2
            ploton - if True, the middle z-plane will be plotted on every
                 iteration

    Returns:
            stackout   - diffused stack.

    kappa controls conduction as a function of gradient.  If kappa is low
    small intensity gradients are able to block conduction and hence diffusion
    across step edges.  A large value reduces the influence of intensity
    gradients on conduction.

    gamma controls speed of diffusion (you usually want it at a maximum of
    0.25)

    step is used to scale the gradients in case the spacing between adjacent
    pixels differs in the x,y and/or z axes

    Diffusion equation 1 favours high contrast edges over low contrast ones.
    Diffusion equation 2 favours wide regions over smaller ones.

    Reference:
    P. Perona and J. Malik.
    Scale-space and edge detection using ansotropic diffusion.
    IEEE Transactions on Pattern Analysis and Machine Intelligence,
    12(7):629-639, July 1990.

    Original MATLAB code by Peter Kovesi
    School of Computer Science & Software Engineering
    The University of Western Australia
    pk @ csse uwa edu au
    <http://www.csse.uwa.edu.au>

    Translated to Python and optimised by Alistair Muldal
    Department of Pharmacology
    University of Oxford
    <[email protected]>

    June 2000  original version.
    March 2002 corrected diffusion eqn No 2.
    July 2012 translated to Python
    """

    # ...you could always diffuse each color channel independently if you
    # really want
    if stack.ndim == 4:
        warnings.warn("Only grayscale stacks allowed, converting to 3D matrix")
        stack = stack.mean(3)

    # initialize output array
    stack = stack.astype('float32')
    stackout = stack.copy()

    # initialize some internal variables
    deltaS = np.zeros_like(stackout)
    deltaE = deltaS.copy()
    deltaD = deltaS.copy()
    NS = deltaS.copy()
    EW = deltaS.copy()
    UD = deltaS.copy()
    gS = np.ones_like(stackout)
    gE = gS.copy()
    gD = gS.copy()

    # create the plot figure, if requested
    if ploton:
        import pylab as pl
        from time import sleep

        showplane = stack.shape[0]//2

        fig = pl.figure(figsize=(20,5.5),num="Anisotropic diffusion")
        ax1,ax2 = fig.add_subplot(1,2,1),fig.add_subplot(1,2,2)

        ax1.imshow(stack[showplane,...].squeeze(),interpolation='nearest')
        ih = ax2.imshow(stackout[showplane,...].squeeze(),interpolation='nearest',animated=True)
        ax1.set_title("Original stack (Z = %i)" %showplane)
        ax2.set_title("Iteration 0")

        fig.canvas.draw()

    for ii in xrange(niter):

        # calculate the diffs
        deltaD[:-1,: ,:  ] = np.diff(stackout,axis=0)
        deltaS[:  ,:-1,: ] = np.diff(stackout,axis=1)
        deltaE[:  ,: ,:-1] = np.diff(stackout,axis=2)

        # conduction gradients (only need to compute one per dim!)
        if option == 1:
            gD = np.exp(-(deltaD/kappa)**2.)/step[0]
            gS = np.exp(-(deltaS/kappa)**2.)/step[1]
            gE = np.exp(-(deltaE/kappa)**2.)/step[2]
        elif option == 2:
            gD = 1./(1.+(deltaD/kappa)**2.)/step[0]
            gS = 1./(1.+(deltaS/kappa)**2.)/step[1]
            gE = 1./(1.+(deltaE/kappa)**2.)/step[2]

        # update matrices
        D = gD*deltaD
        E = gE*deltaE
        S = gS*deltaS

        # subtract a copy that has been shifted 'Up/North/West' by one
        # pixel. don't as questions. just do it. trust me.
        UD[:] = D
        NS[:] = S
        EW[:] = E
        UD[1:,: ,: ] -= D[:-1,:  ,:  ]
        NS[: ,1:,: ] -= S[:  ,:-1,:  ]
        EW[: ,: ,1:] -= E[:  ,:  ,:-1]

        # update the image
        stackout += gamma*(UD+NS+EW)

        if ploton:
            iterstring = "Iteration %i" %(ii+1)
            ih.set_data(stackout[showplane,...].squeeze())
            ax2.set_title(iterstring)
            fig.canvas.draw()
            # sleep(0.01)

    return stackout