reconstruction

reconstruction

skimage.morphology.reconstruction(seed, mask, method='dilation', selem=None, offset=None) [source]

Perform a morphological reconstruction of an image.

Morphological reconstruction by dilation is similar to basic morphological dilation: high-intensity values will replace nearby low-intensity values. The basic dilation operator, however, uses a structuring element to determine how far a value in the input image can spread. In contrast, reconstruction uses two images: a “seed” image, which specifies the values that spread, and a “mask” image, which gives the maximum allowed value at each pixel. The mask image, like the structuring element, limits the spread of high-intensity values. Reconstruction by erosion is simply the inverse: low-intensity values spread from the seed image and are limited by the mask image, which represents the minimum allowed value.

Alternatively, you can think of reconstruction as a way to isolate the connected regions of an image. For dilation, reconstruction connects regions marked by local maxima in the seed image: neighboring pixels less-than-or-equal-to those seeds are connected to the seeded region. Local maxima with values larger than the seed image will get truncated to the seed value.

Parameters:

seed : ndarray The seed image (a.k.a. marker image), which specifies the values that are dilated or eroded. mask : ndarray The maximum (dilation) / minimum (erosion) allowed value at each pixel. method : {‘dilation’|’erosion’} Perform reconstruction by dilation or erosion. In dilation (or erosion), the seed image is dilated (or eroded) until limited by the mask image. For dilation, each seed value must be less than or equal to the corresponding mask value; for erosion, the reverse is true. selem : ndarray The neighborhood expressed as a 2-D array of 1’s and 0’s.

Returns:

reconstructed : ndarray The result of morphological reconstruction.

Notes

The algorithm is taken from [R297]. Applications for greyscale reconstruction are discussed in [R298] and [R299].

References

[R297]

(1, 2) Robinson, “Efficient morphological reconstruction: a downhill filter”, Pattern Recognition Letters 25 (2004) 1759-1767.

[R298]

(1, 2) Vincent, L., “Morphological Grayscale Reconstruction in Image Analysis: Applications and Efficient Algorithms”, IEEE Transactions on Image Processing (1993)

[R299]

(1, 2) Soille, P., “Morphological Image Analysis: Principles and Applications”, Chapter 6, 2nd edition (2003), ISBN 3540429883.

Examples

>>> import numpy as np
>>> from skimage.morphology import reconstruction

First, we create a sinusoidal mask image with peaks at middle and ends.

>>> x = np.linspace(0, 4 * np.pi)
>>> y_mask = np.cos(x)

Then, we create a seed image initialized to the minimum mask value (for reconstruction by dilation, min-intensity values don’t spread) and add “seeds” to the left and right peak, but at a fraction of peak value (1).

>>> y_seed = y_mask.min() * np.ones_like(x)
>>> y_seed[0] = 0.5
>>> y_seed[-1] = 0
>>> y_rec = reconstruction(y_seed, y_mask)

The reconstructed image (or curve, in this case) is exactly the same as the mask image, except that the peaks are truncated to 0.5 and 0. The middle peak disappears completely: Since there were no seed values in this peak region, its reconstructed value is truncated to the surrounding value (-1).

As a more practical example, we try to extract the bright features of an image by subtracting a background image created by reconstruction.

>>> y, x = np.mgrid[:20:0.5, :20:0.5]
>>> bumps = np.sin(x) + np.sin(y)

To create the background image, set the mask image to the original image, and the seed image to the original image with an intensity offset, h.

>>> h = 0.3
>>> seed = bumps - h
>>> background = reconstruction(seed, bumps)

The resulting reconstructed image looks exactly like the original image, but with the peaks of the bumps cut off. Subtracting this reconstructed image from the original image leaves just the peaks of the bumps

>>> hdome = bumps - background

This operation is known as the h-dome of the image and leaves features of height h in the subtracted image.