BINF 5040 MEDICAL IMAGE PROCESSING AND NETWORKING MORPHOLOGICAL OPERATIONS

1
BINF 5040MEDICAL IMAGE PROCESSING AND
NETWORKINGMORPHOLOGICAL OPERATIONS
2

• Following the image pre-processing, morphological
  operations work to clarify the underline
  structure of objects. This is done by further
  object boundaries to single pixel wide outlines
  or skeletons.
• Subsequent measurement operations can more easily
  quantify object shape measures for use in
  classification operations.
• There are two forms of morphological processing
  binary and gray scale.
• Binary morphological process works like spatial
  convolution, which computes a resulting pixels
  brightness value based on their neighborhood
  values.
• Morphological process logically combines pixel
  brightness with a structuring element, looking
  for spatial patterns.
• Instead of multiplying the pixel brightness by
  weights and summing the results, morphological
  process use operations such as AND, OR,
  NOT, to combine pixels logically

3

• into resulting pixel value.
• In binary morphological process, input images are
  assumed to be composed of pixels that have only
  two brightness values.
• Like spatial convolution, the morphological
  process moves across the input image, pixel by
  pixel, placing the resulting in the output image.
• At each input location, the pixel and its
  neighbors are logically compared against a
  structured element or morphological mask, to
  determine the output pixels logical value.
• The structuring element is analogous to the
  convolution mask used in spatial convolution.

4

• Binary Erosion and Dilation
• Erosion operation uniformly reduces the size of
  white objects on a black background in an
  image.The reduction is by one pixel around the
  objects perimeter.
• The binary dilation operation uniformly
  increases the size of white objects on a black
  background in an image. The objects size
  increases by one pixel around the objects
  perimeter.
• Applications Erosion is used to remove small
  anomalies such as single-pixel objects, called
  speckles, and single pixel wide spurs from the
  image. Multiple erosion operation on an image
  shrinks touching objects until they finally
  separate. This can be useful prior to object
  counting operations.
• Binary dilation operations are used to remove
  small anomalies such as single-pixel holes in
  objects and single pixel wide gaps from an image.

5

• Multiple applications of dilation process
  expands broken objects until they finally merge
  into one. This can also be useful prior to
  object counting operation.
• Implementation Define morphological structuring
  element and perform the morphological group
  process on the image.
• Structuring elements for omni-directional,
  horizontal, vertical and diagonal erosion are

Omnidirectional Horizontal Vertical
Diagonal SElement SElement SElement
SElement
6
Binary erosion and dilation process - a- original
image, b- binarized image after contrast
enhancement, c- eroded image, d- erosion
operation applied two times.
7

• Example
• Let us assume that the SE 3 x 3 with all
  elements as one.
• The erosion operation is defined as logical AND
  for all nine elements, which implies
• If the input pixel is 1 and all neighbors are 1
  ? output pixel is 1 (hit).
• If the input pixel is 1, and some of the
  neighbors are 1 and others are zero, ? output
  pixel is zero ( miss).
• If the input pixel is 0, and some of the
  neighbors are 1 and others are zero, ? output
  pixel is zero ( miss).
• If the input pixel is 0, and all of the
  neighbors are zero, ? output pixel is zero (
  miss).
• The dilation operation is inverse of erosion.

8

• Structuring elements for the dilation operation
  for omni-directional, horizontal, vertical and
  diagonal are

Omnidirectional Horizontal Vertical
Diagonal SEelement SEelement SEelement
SEelement The generalized dilation mask (SE)
all elements are zero, and the operation is
logical OR Dilation operation assumes that the
object is white and the background is black.
9

• Like the erosion operation, the dilation
  operation has four distinct input pixel cases to
  consider. These cases are

• If the input pixel is 1 and all neighbors are 1 ?
  output pixel is 1 (miss).
• If the input pixel is 1, and some of the
  neighbors are 1 and others are zero, ? output
  pixel is one( miss).
• If the input is 0, and some of the neighbors
  are 1 and others are zero, ? output pixel is
  one ( miss).
• If the input is 0, and all of the neighbors are
  zero, ? output pixel is zero ( hit ).
• BW2 erode(BW1, SE, n) n is number of times
  the erosion is to be performed and SE defines the
  Structuring element
• Dilate command is similar to erode command.

10

• Binary Opening and Closing
• The Binary opening operation is a binary erosion
  operation followed by binary dilation. Objects
  generally remain in their original size.
• The binary closing operation is a binary
  dilation operation followed by as binary erosion
  operation. Objects retain size.
• Applications Opening operation- eliminates
  small anomalies, such as single pixel objects and
  single pixel wide spurs from an image. Since the
  erosion reduces object size, the following
  dilation expands object back to original size.
  This operation is useful to clean-up images with
  noise and other anomalies.
• Closing - the dilation process eliminates single
  pixel holes and single pixel wide gaps. Since the
  dilation increases size, the following erosion
  reduces object back to original size. It gets
  rid of object holes and other small anomalies.

11

• Outlining
• Outlining operation operates on binary images by
  subtracting the eroded version of the image from
  the original one.The resulting image shows a
  single pixel wide outline of the original image.
• Applications The outlining operation is useful
  as a precursor to object measurement. It produces
  outline of the object. Using omnidirectional
  erosion structuring element, this operation
  produces outlines of all objects, regardless of
  their orientation.
• Multiple erosion operations can be applied prior
  to subtracting the eroded image from the
  original. Additional erosion produces a resulting
  outline of an image with wider outline widths.
• Directional outlines can also be produced using
  directional elements.

12
a- original chip image b- eroded image c-
original image minus eroded image yielding an
outline image
13

• Gray Scale Erosion and Dilation
• This operation reduces the brightness ( and
  therefore the size) of bright objects on a dark
  background.
• The gray-scale dilation process increases the
  brightness ( and therefore the size) of bright
  object on a black background .
• Applications
• The erosion operation is used to eliminate small
  anomalies such as single pixel bright spots.
  Multiple application of this operation shrinks
  the touching objets for counting purpose.
• The dilation operation is used to eliminate small
  anomalies such as single pixel dark spots from an
  image. Multiple dilation application of the
  operation expands broken objects by brightening
  their perimeters until they finally merge into
  one.
• Masks are similar to binary erosion and dilation
  process.

14

• In Gray-scale morphological processing, input and
  output images are of gray scale form, rather than
  binary form.
• Gray-scale morphological operations do not
  generally produce images with single pixel
  object boundaries or skeletons. They are usually
  followed by some binarization operation like
  contrast enhancement.
• Like spatial convolution and binary morphological
  process, the gray-scale morphological process
  moves across the input image, pixel-by-pixel,
  placing the resultant pixels in output image.
• The structuring element (SE) for the gray-scale
  morphological process is is an array of values
  ranging from 255 to 255. Alternately a value
  can be assigned as dont care. SE is normally a
  square matrix of size 3x3 or 5x5 or larger.

15

• Every pixel in the input image is evaluated with
  its eight neighbors to produce a resulting pixel
  value.
• Evaluation method is defined as
• Placing a mask(SE) over input pixel.
• For the erosion, mask values can range from 0 to
  255, but will be generally 0. For the dilation
  case the values are from 0 to 255 but will be
  generally 0.
• The center mask value and the values of its eight
  neighbors are each added to the corresponding
  input pixel and its eight neighbors. If there are
  dont cares in the mask, no addition is made in
  dont care position of the mask.
• The output value is determined as the minimum
  value of all nine addends.
• This process repeats pixel by pixel in the input
  image.

16

• O(x,y)
• min all the intensity values of center pixel
  plus its all 8 neighbors after adding the values
  of mask .
• Similarly for the dilation operation
• O(x,y)
• max all the intensity values of center pixel
  plus its all 8 neighbors after adding the values
  of mask .
• O(x,y) is the output value of the pixel after
  performing the morphological operation.
• The erosion operation has the effect of
  darkening the object thus making it look smaller,
  while
• The dilation has opposite effect.

17

• Morphological Gradient
• This operation operates on gray-scale images.
  Both the eroded and dilated version are created.
  Then the eroded version of the image is
  subtracted from the dilated version. The
  resulting image shows the edges of the objects in
  the original image.
• Applications The morphological gradient
  operation is used to produce the edges of the
  object in an image. Using the omni-directional
  erosion and dilation structuring element, this
  operation produces edges of all objects,
  regardless of their orientation.
• Other structuring elements as horizontal,
  vertical or diagonal can be used to obtain
  directional edges.
• Multiple erosion and dilation operations can be
  applied prior to subtracting. This operation
  provides wider edge widths.

18
a- eroded gray scale image , b- dilated image
minus eroded image, yielding a morphological
gradient image