iaconv

iaconv
2D convolution.

Synopsis

g = iaconv( f, h )

Implemented in Python.

Input

f	Image. Gray-scale (uint8 or uint16) or binary image (logical). input image.
h	Image. Gray-scale (uint8 or uint16) or binary image (logical). PSF (point spread function), or kernel. The origin is at the array center.

Output

g	Image. Gray-scale (uint8 or uint16) or binary image (logical).

Description

Perform a 2D discrete convolution. The kernel origin is at the center of image h.

Examples

>>> import Numeric

>>> f = Numeric.zeros((5,5))

>>> f[2,2] = 1

>>> print f

[[0 0 0 0 0]
 [0 0 0 0 0]
 [0 0 1 0 0]
 [0 0 0 0 0]
 [0 0 0 0 0]]

>>> h = Numeric.array([[1,2,3],[4,5,6]])

>>> print h

[[1 2 3]
 [4 5 6]]

>>> a = iaconv(f,h)

>>> print a

[[0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0]
 [0 0 1 2 3 0 0]
 [0 0 4 5 6 0 0]
 [0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0]]

>>> f = Numeric.array([[1,0,0,0],[0,0,0,0]])

>>> print f

[[1 0 0 0]
 [0 0 0 0]]

>>> h = Numeric.array([1,2,3])

>>> print h

[1 2 3]

>>> a = iaconv(f,h)

>>> print a

[[1 2 3 0 0 0]
 [0 0 0 0 0 0]]

>>> f = Numeric.array([[1,0,0,0,0,0],[0,0,0,0,0,0]])

>>> print f

[[1 0 0 0 0 0]
 [0 0 0 0 0 0]]

>>> h = Numeric.array([1,2,3,4])

>>> print h

[1 2 3 4]

>>> a = iaconv(f,h)

>>> print a

[[1 2 3 4 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]]

>>> f = iaread('cameraman.pgm')

>>> h = [[1,2,1],[0,0,0],[-1,-2,-1]]

>>> g = iaconv(f,h)

>>> gn = ianormalize(g, [0,255])

>>> iashow(gn)

(258, 258) Min= 0.0 Max= 255.0 Mean=131.495 Std=19.08


gn

Limitations

Both image and kernel are internally converted to double.

Equation

where AxB and CxD are the dimensions of f(x,y) and h(x,y) respectively.

Source Code

def iaconv(f, h):
    from Numeric import asarray, NewAxis, zeros, array, product
    f, h = asarray(f), asarray(h)
    if len(f.shape) == 1: f = f[NewAxis,:]
    if len(h.shape) == 1: h = h[NewAxis,:]
    if product(f.shape) < product(h.shape):
        f, h = h, f
    g = zeros(array(f.shape) + array(h.shape) - 1)
    for i in range(h.shape[0]):
        for j in range(h.shape[1]):
            g[i:i+f.shape[0], j:j+f.shape[1]] += h[i,j] * f
    return g

iaconv 2D convolution.