Lecture 4

Question 1

Segmentation

Answer 1

Dividing an image into biologically meaningful segments for further analysis.

Question 2

Object vs Background

Answer 2

Intensity thresholding can be applied if sufficiently and consistently higher intenstiy.

Question 3

Selected automatic thresholding

Answer 3

Based on the histogram. Hard to figure out yourself sometimes, so automatic methods:

• Isodata
• Otsu
• Triangle

Question 4

Isodata thresholding

Answer 4

Goal: converge to mean of the class intensity mean

1. Compute the normalized histogram to get intensity probabilities: P(i)=H(i)/N
2. Select arbitraty initial threshold and compute class means
3. Iteratively update the threshold and class means until convergence (no more change)

Question 5

Otsu thresholding

Answer 5

Goal: Minimize total intra-class intenstiy variance.
Useful in bimodal histogram with similar objects and background volumes.
1. Compute the variance in two classes defined by the threshold
2. Minimize the total intra-class variance over all possible thresholds

Question 6

Triangle thresholding

Answer 6

Goal: find the kinks between two class distributions

1. Construct a line between (ip,h(ip)) and (im,h(im)) -> l(i)=h(ip)*(im-i)/(im-ip)
2. Find the maximum histogram-to-line distance max d(i)=max(l(i)-h(i))

Useful in cases where the object pixels constitute only weak histogram peaks. Right after highest peak

Question 7

Improvement of processing methods

Answer 7

• Preprocessing by gaussian smoothing or median smoothing to reduce noise.
• Postprocessing by morphological image filtering by binary watershed for example
• Apply threshold of diameter

Question 8

Binary watershed

Answer 8

Makes sure you can distuingish the different particles.

Question 9

Connectivity

Answer 9

Determine whether segmented pixels belong together. The number of objects depends on the chosen connectivity. Put some sort of structuring element over to determine.

Question 10

Connected component labelling

Answer 10

Assign unique labels to segmented regions:
First pass: Check each pixel: if it is an object and has no neighbors, assign new label. If do neighbors, assign smallest label.
Second pass: Check each pixel and replace each label with smallest equivalent. All background pixels default to zero.

Question 11

Boundary chain coding

Answer 11

If you know the starting pixel, the chain code gives you the next pixel and you can figure out the image.

Question 12

Selected advanced segmentation methods

Answer 12

• Kmeans clustering
• Watershed-based segmentation
• Segmentation by seeded region growing

Question 13

k-means clustering

Answer 13

1. Assume there are k clusters of pixels and initialize their intensity means
2. Assign pixels to clusters by minimum squared intensity distance
3. Update the cluster intensity means for the next iteration
4. Iteratively compute Ci and meann=1 until convergence

Suitible if total number of intensity classes is known priori

Question 14

Watershed segmentation

Answer 14

Start with local maxima by reverting the image. And let the water flow higher till you have all different objects.

Question 15

Active contour segmentation

Answer 15

• Explicit: Incorporate larger context and prior knowledge
  1. Define a suitable contour model
  2. Define suitable energy functional
  3. Minimize the energy functional.
  Want to fit the contour model over the image.

Question 16

Level-set segmentation

Answer 16

• Implicit active countour segmentation
  1. Define a level-set function for each object
  2. Define suitable energy functional
  3. Iteratively minimize the energy using Euler-Langrange equations

Question 17

Tracing line-like structures

Answer 17

Common in neuron segmentation.

Image -> soma segmentation -> tree segmentation -> spine segmentation -> reconstruction -> image

Question 18

Problems segmentation

Answer 18

• Segmentation of image regions into labeled objects
• Segmentation of line-like image structures into labelled paths
• No single method that can correctly segment all different microscopic images
• Boundary of objects is locally not so evident.

Question 19

Segmentation by seeded region growing

Answer 19

Goal: completely partition an image into selected regions

1. Select a representative blob of pixels for each region of interest
2. Make a ist of all (4 or 8) connected neighbor pixels of these regions
3. Define a measure of distance of any pixel to any region
4. Define a closest region index for candidate pixels
5. Iterativly do the following until cadidate list is empty:
   - Add all-closest candidate pixel to its corresponding region
   - Remove that pixel from the candidate list but add its new neighbors

Question 20

Watershed based segmentation problems

Answer 20

• Images often have many local minima, leading to heavy oversegmentation
• Preprocessing may be needed to reduce false minima
• Postprocessing may lbe needed to reduce fragmentation

Question 21

Advanced segmentation methods

Answer 21

Incorporate knowledge to get a better idea of the boundary.

• Explicit active contour segmentation
• Implicit active contour segmentation

Question 22

Hessian

Answer 22

Local approcimation to approximate more difficult underlying function. It is a vector pair where one of them shows the direction orthogonal to the neuro direction and the other toward the neuron.
Hessian matrix =
Ixx Ixy
Ixy Iyy