Laboratoire RDP » Biophysics Team » FLORIVAR

import numpy as np

import matplotlib.pyplot as plt

import math

from scipy import optimize

from titk_tools.io import imread, imsave, SpatialImage

def center_on_point(img, cm):

        '''

        Centers the image img on the point cm

        '''

        x = np.array(np.where(img > 0) )

        xp=np.zeros_like(x)

        img1=np.zeros_like(img)

        s=img.shape

        center_img=np.array(s)/2

        for i in [0, 1, 2]:

                xp[i]=x[i]+center_img[i]-cm[i]

        for i in range(0, len(x[0])):

                if ((xp[0][i]>=0) and (xp[0][i]<s[0]) and (xp[1][i]>=0) and (xp[1][i]<s[1]) and (xp[2][i]>=0) and (xp[2][i]<s[2])):

                        img1[xp[0][i],xp[1][i],xp[2][i]]=img[x[0][i],x[1][i],x[2][i]]

        img1=SpatialImage(img1)

        img1.resolution=img.resolution

        return img1

def center_on_cm(img):

        '''

        Centers the image img on the point cm

        '''

        s=img.shape

        res=img.voxelsize

        x = np.array(np.where(img > 0) )

        cm = np.array([np.mean(x[i]) for i in [0,1,2]])

        xp=np.zeros_like(x)

        img1=np.zeros_like(img)

        center_img=np.array(s)/2

        for i in [0, 1, 2]:

                xp[i]=x[i]+center_img[i]-cm[i]

        for i in range(0, len(x[0])):

                if ((xp[0][i]>=0) and (xp[0][i]<s[0]) and (xp[1][i]>=0) and (xp[1][i]<s[1]) and (xp[2][i]>=0) and (xp[2][i]<s[2])):

                        img1[xp[0][i],xp[1][i],xp[2][i]]=img[x[0][i],x[1][i],x[2][i]]

        img1=SpatialImage(img1)

        img1.voxelsize=res

        return img1

def principal_directions(img, threshold=10):        

        '''

        Returns the first two principal eigen vectors of an input image

        Fixed threshold of 10 for a 8 bit image

        It suppposes an isotropic sampling of the image.

        '''

        x,y,z = np.where(img > threshold) ## appropriate thresholding 

        x = x - np.mean(x)

        y = y - np.mean(y)

        z = z - np.mean(z)

        coords = np.vstack([x,y,z])

        cov = np.cov(coords)

        evals,evecs = np.linalg.eig(cov)

        sort_indices = np.argsort(evals)[::-1]

        return list(evecs[:,sort_indices][0:2])

def direct_frame(pv):

        '''

        Constructs a direct frame with first two unitvectors v0 and v1

        '''

        return np.array([pv[0], pv[1], np.cross(pv[0], pv[1])])

def write_transformation(T, trsf_file):

        '''

        writes the affine transformation T (4x4 matrix) in

        a textfile read by blockmatching.

        '''

        f = open(trsf_file,'w')

        f.write("( "+"\n")

        f.write("08 "+"\n")

        for i in T:

                for j in i:

                        f.write("  "+str(j)+" ")

                f.write("\n")

        f.write(") ")

        return

def write_rigid(trsf_file, R, a):

        '''

        write a rigid transformation with rotation matrix R and translation a

        '''

        T = np.identity(4)

        T[0:3,0:3] = R

        T = np.transpose(T)

        T[0:3,3] = a

        write_transformation(T, trsf_file)

        return

def write_superposing_transfo(pv_flo, pv_ref, img, trsf_file):

        '''

        - pv_flo and pv-ref are lists of the first two principal vectors of the floating and the reference images respectively

        - img is the floating image

        '''

        # compute the rotation matrix R

        pframe_ref = direct_frame(pv_ref)

        pframe_flo = direct_frame(pv_flo)

        F = np.transpose(pframe_ref)

        G = np.transpose(pframe_flo)

        R = np.matmul(G, np.linalg.inv(F))

        # blockmatching rotates arround the origin,

        # so a rotation arround the middle of the image contains an additional translation t

        s = img.shape

        res = img.voxelsize

        com = np.array(res)*np.array(s)/2

        i = np.identity(3)

        t = np.dot((i-R),np.array(com))

        R = np.transpose(R)

        write_rigid(trsf_file, R, t)

        return

def add_side_slices(Img, x0, x1, y0, y1, z0, z1):

        """

        adds 0 value slices on different sides of the image

        """

        s=Img.shape

        ss=(s[0]+x0+x1,s[1]+y0+y1,s[2]+z0+z1)

        Img_new = (SpatialImage(np.zeros(ss))).astype('uint8')

        Img_new[x0:ss[0]-x1,y0:ss[1]-y1,z0:ss[2]-z1]=Img

        Img_new.voxelsize = Img.voxelsize

        return Img_new

def remove_side_slices(Img, x0, x1, y0, y1, z0, z1):

        """

        removes slices on different sides of the image

        """

        ss=Img.shape

        Img_new=Img[x0:ss[0]-x1,y0:ss[1]-y1,z0:ss[2]-z1]

        #Img_new.resolution = Img.resolution

        return Img_new

def measure_hight(a):

        b= np.where(a)

        height = 0

        if b[0].shape[0]>0 :

                height = b[0][-1]

        return height

def measure_height(a):

        b= np.where(a)

        height = [0,0]

        if b[0].shape[0]>0 :

                height = [b[0].min(),b[0].max()]

        return height

def extract_curve(x_section):

        sx = x_section.shape

        xx = np.zeros((sx[0],2))

        for i in range(0,sx[0]):

                xx[i,0] = i

                xx[i,1] = measure_hight(x_section[i,:])

        return xx

def extract_curves(x_section):

        sx = x_section.shape

        xup = np.zeros((sx[0],2))

        xdown = np.zeros((sx[0],2))

        for i in range(0,sx[0]):

                xup[i,0] = i

                xdown[i,0] = i

                xup[i,1] = measure_height(x_section[i,:])[1]

                xdown[i,1] = measure_height(x_section[i,:])[0]

        return xup, xdown

def write_curve(y, pixelsize, filename) :

        FILE = open(filename,"w")

        FILE.write('# '+str(pixelsize[0])+' '+str(pixelsize[1])+'\n')

        s = y.shape

        #FILE.write('# '+str(s[0])+'\n')

        for i in range(0,s[0]) :

                FILE.write(str(y[i,0])+' '+str(y[i,1])+'\n')

        FILE.close()

        return

def struct_element_sphere(radius):

        s=int(2*radius+1)

        structure=np.zeros((s,s,s))

        center = np.array([radius, radius, radius])

        Nl=range(s)

        for i in Nl:

                for j in Nl:

                        for k in Nl:

                                p=np.array([i,j,k])

                                d=p-center

                                dist=np.sqrt(sum(d*d))

                                if dist<=radius:

                                        structure[i,j,k]=1

        return structure

def create_artificial_sepal(AA, RR, resolution):

        # A = parameters of an ellipse, as projected on xy plane (2d array)

        # R = curvature radius in directions x and y (2d array)

        # (A and R are given in micrometers)

        # resolution = voxelsize of the output stack

        A = np.array([AA[i]/resolution[i] for i in [0,1]])

        R = np.array([RR[i]/resolution[i] for i in [0,1]])

        h = np.array([math.sqrt(R[i]**2-A[i]**2) for i in range(len(A))])

        zmax=np.array([R[i]-math.sqrt(R[i]**2-A[i]**2) for i in [0,1]])

        #zmax= int(math.sqrt(zmax[0]*zmax[1]))

        zmax=zmax.mean()

        #zmax = 5

        print(zmax)

        marge = 0.2

        # creating the stack and the surface

        s = (int(A[0]*2*(1+marge)), int(A[1]*2*(1+marge)), int(zmax*(1+2*marge)))

        cm = np.array(s)/2

        x = np.array(range(0,s[0]))

        y = np.array(range(0,s[1]))

        xx = x - cm[0]

        yy = y - cm[1]

        #xgrid, ygrid = np.meshgrid(xx, yy, sparse=True)  # make sparse output arrays

        #mask=(((xgrid**2)/float(A[0])**2+(ygrid**2)/float(A[1])**2)<1).astype('uint8')

        z = np.zeros((s[0],s[1]))

        stack= np.zeros(s).astype('uint8')

        for i in x:

                for j in range(0,s[1]):

                        if xx[i]**2/float(A[0])**2+yy[j]**2/float(A[1])**2<=1 :

                                zx = (math.sqrt(R[0]**2-xx[i]**2)-h[0])*(1-abs(yy[j])/A[1])

                                zy = (math.sqrt(R[1]**2-yy[j]**2)-h[1])*(1-abs(xx[i])/A[0])

                                z[i,j] = math.sqrt(zx*zy)

                                #z[i,j] = (zx+zy)/2

                                #z[i,j] = 5

                                stack[i,j,int(zmax*marge+z[i,j])]=1

        stack = SpatialImage(stack)

        stack.resolution = resolution

        return z, stack

def create_artificial_sepal_ellipse(AA, H, resolution):

        '''

        # A = parameters of an ellipse, as projected on xy plane (2d array)

        # R = curvature radius in directions x and y (2d array)

        # (A and R are given in micrometers)

        # resolution = voxelsize of the output stack

        '''

        A = np.array([AA[i]/resolution[i] for i in [0,1]])

        h = H/resolution[2]

        zmax=h

        marge = 0.2

        # creating the stack and the surface

        s = (int(A[0]*2*(1+marge)), int(A[1]*2*(1+marge)), int(zmax*(1+5*marge)))

        cm = np.array(s)/2

        x = np.array(range(0,s[0]))

        y = np.array(range(0,s[1]))

        xx = x - cm[0]

        yy = y - cm[1]

        #xgrid, ygrid = np.meshgrid(xx, yy, sparse=True)  # make sparse output arrays

        #mask=(((xgrid**2)/float(A[0])**2+(ygrid**2)/float(A[1])**2)<1).astype('uint8')

        z = np.zeros((s[0],s[1]))

        #z = -h*((xgrid**2)/float(A[0])**2+(ygrid**2)/float(A[1])**2)

        stack= np.zeros(s).astype('uint8')

        for i in x:

                for j in y:

                        if xx[i]**2/float(A[0])**2+yy[j]**2/float(A[1])**2<=1 :

                                z[i,j] = -h*((xx[i]**2)/float(A[0])**2+(yy[j]**2)/float(A[1])**2-1)

                                stack[i,j,int(zmax*4*marge+z[i,j])]=1

        stack = SpatialImage(stack)

        stack.voxelsize = resolution

        return z, stack

# -------------------------------------------------------------------

def read_curve(filename) :

        """

        Reads the coordinates of the point-list defining a 2D curve.

        **Returns**

        y : 2-column array

                defines a curve as an ordered list of points, 

                each row of the array represents a point on the curve and contains

                its 2D cartesian coordinates

        pixelsize : tuple (res0, res1) in micrometers

        """        

        x0 = []

        pixelsize = (1.0,1.0)

        for line in file(filename):

                if line[0] == "#" :

                        line = line.lstrip('# ')

                        line = line.rstrip('\n')

                        line_list = [float(x) for x in line.split(' ')]

                        pixelsize = (line_list[0], line_list[1])

                else :

                        line = line.rstrip('\n')

                        line_list = [float(x) for x in line.split(' ')]

                        x0.append(line_list)

        y = np.array(x0)

        return y, pixelsize

def distance(p1, p2):

        return np.sqrt((p1[0]-p2[0])**2+(p1[1]-p2[1])**2)

def distance_to_line(p1, p2, p0):

        '''

        gives the distance of point p0 to the line defined by points p1 and p2 (in 2d)

        '''

        return abs((p2[1]-p1[1])*p0[0]-(p2[0]-p1[0])*p0[1]+p2[0]*p1[1]-p2[1]*p1[0])/distance(p1,p2)

def curvature(p1,p2,p3):

        t1 = (p3[0]**2-p2[0]**2+p3[1]**2-p2[1]**2)/(2.0*(p3[1]-p2[1]))

        t2 = (p2[0]**2-p1[0]**2+p2[1]**2-p1[1]**2)/(2.0*(p2[1]-p1[1]))

        n1 = (p3[0]-p2[0])/(p3[1]-p2[1])

        n2 = (p2[0]-p1[0])/(p2[1]-p1[1])

        pcx = (t1-t2+p3[1]-p1[1])/(n1-n2)

        pc = [pcx, -n1*pcx+t1/2+p3[1]/2+p1[1]/2]

        R = distance(p1, pc)

        return 1.0/R, pc

def curvature2(p1,p2,p3):

        # http://www.ambrsoft.com/TrigoCalc/Circle3D.htm

        A = p1[0]*(p2[1]-p3[1])-p1[1]*(p2[0]-p3[0])+p2[0]*p3[1]-p3[0]*p2[1]

        B = (p1[0]**2+p1[1]**2)*(p3[1]-p2[1])+(p2[0]**2+p2[1]**2)*(p1[1]-p3[1])+(p3[0]**2+p3[1]**2)*(p2[1]-p1[1])

        C = (p1[0]**2+p1[1]**2)*(p3[0]-p2[0])+(p2[0]**2+p2[1]**2)*(p1[0]-p3[0])+(p3[0]**2+p3[1]**2)*(p2[0]-p1[0])

        D = (p1[0]**2+p1[1]**2)*(p3[0]*p2[1]-p2[0]*p3[1])+(p2[0]**2+p2[1]**2)*(p1[0]*p3[1]-p3[0]*p1[1])+(p3[0]**2+p3[1]**2)*(p2[0]*p1[1]-p1[0]*p2[1])

        x = -B/(2*A)

        y = C/(2*A)

        pc = [x, y]

        R = distance(p1, pc)

        return 1.0/R, pc

def curve_perle(y, first, last, step):

        yy=[]

        for i in range(first, last, step):

                if y[i][1]>0:

                        yy.append(y[i])

        if i<last:

                yy.append(y[last])

        return np.array(yy)

def compute_curvature_radius(x,y):

        # coordinates of the barycenter

        x_m = np.mean(x)

        y_m = np.mean(y)

        def calc_R(c):

                """ calculate the distance of each 2D points from the center c=(xc, yc) """

                return np.sqrt((x-c[0])**2 + (y-c[1])**2)

        #

        def calc_ecart(c):

                """ calculate the algebraic distance between the 2D points and the mean circle centered at c=(xc, yc) """

                Ri = calc_R(c)

                return Ri - Ri.mean()

        #

        center_estimate = x_m, y_m

        center_2, ier = optimize.leastsq(calc_ecart, center_estimate)

        #

        xc_2, yc_2 = center_2

        Ri_2       = calc_R(center_2)

        R_2        = Ri_2.mean()

        residu_2   = sum((Ri_2 - R_2)**2)

        pc=[xc_2, yc_2]

        return R_2, pc

def analyze_curve1(name, y, pixelsize, outfilename, graph_name='graph.png'):

        # isotropic pixels

        y[:,0] = y[:,0]*pixelsize[0]

        y[:,1] = y[:,1]*pixelsize[1]

        maxv = [y[:,i].max() for i in [0,1]]

        # find first and last points on the curve

        step = 5

        sep_indices = np.where(y[:,1])[0]

        first = sep_indices[0]#+step/2

        last = sep_indices[-1]#-step/2

        # compute flat length

        flatlength = distance(y[first],y[last])

        print("flat length =", flatlength," um")

        # compute curved length and height (maximal distance to the base)

        yy = curve_perle(y, first, last, step)

        length = 0

        height = 0

        height_index = 0

        p1 = yy[0]

        p2 = yy[-1]

        for i in range(0, len(yy)-1):

                length = length + distance(yy[i+1],yy[i])

                d = distance_to_line(p1, p2, yy[i])

                if d>height :

                        height = d

                        height_index = i

        print("length = ",length," um")

        print("height = ",height," um")

        middle_point = yy[int(len(yy)/2)]

        # compute curvature radius by fitting the sepal section to a circle

        yyy=y[first:last]

        R, pc = compute_curvature_radius(yyy[:,0],yyy[:,1])

        print("R=",R," um")

        # cutting curve in pieces in order to estimate curvature radius on portions of the curve

        slength=len(yyy)

        y21=yyy[0:int(slength/2)]

        y22=yyy[int(slength/2):slength]

        y41=yyy[0:int(slength/4)]

        y423=yyy[int(slength/4):3*int(slength/4)]

        y44=yyy[3*int(slength/4):slength]

        # and computing the curvature radius for each portion

        R21, pc = compute_curvature_radius(y21[:,0],y21[:,1])

        R22, pc = compute_curvature_radius(y22[:,0],y22[:,1])

        R41, pc = compute_curvature_radius(y41[:,0],y41[:,1])

        R423, pc = compute_curvature_radius(y423[:,0],y423[:,1])

        R44, pc = compute_curvature_radius(y44[:,0],y44[:,1])

        fig = plt.figure()

        plt.plot(yy[:,0], yy[:,1], 'bo')

        plt.plot(y[:,0], y[:,1], 'r')

        plt.plot(y[first][0], y[first][1], 'ro')

        plt.plot(middle_point[0], middle_point[1], 'ro')

        plt.plot(y[last][0], y[last][1], 'ro')

        plt.plot(yy[height_index][0], yy[height_index][1], 'go')

        plt.plot(pc[0], pc[1], 'bx')

        plt.gca().set_aspect('equal', adjustable='box')

        #plt.show()

        fig.savefig(graph_name)

        #plt.close()

        # write the data into a file

        FILE = open(outfilename,"a")

        FILE.write(name+';'+str(length)+';'+str(R)+';'+str(flatlength)+';'+str(height)+'\n')

        FILE.close()

        return length, flatlength, height, R, R21, R22, R41, R423, R44

def imsave2D(filename, matrix):

        fig = plt.figure()

        plt.gca().imshow(np.transpose(matrix), interpolation='none')

        fig.savefig(filename)

        return