Segmentation via Thresholding

• Gray level thresholding is the simplest segmentation process.

• Many objects or image regions are characterized by constant reflectivity or light absorption of their surface.

• Thresholding is computationally inexpensive and fast.

• Thresholding can easily be done in real time using specialized hardware.

• Complete segmentation can result from thresholding in simple scenes.

Algorithm

for(each pixel f(i,j) of image)



   if f(i,j) >= T

 	  is an object pixel

   else

          is a background pixel

• Correct threshold selection is crucial for successful threshold segmentation
• Threshold selection can be interactive or can be the result of some threshold detection method

Single global threshold

• Successful only under very unusual circumstances
• gray level variations are likely - due to non-uniform lighting, non-uniform input device parameters or a number of other factors.

Variable thresholding

• (also adaptive thresholding), in which the threshold value varies over the image as a function of local image characteristics, can produce the solution in these cases.
• image f is divided into subimages f_c
• a threshold is determined independently in each subimage
• if a threshold cannot be determined in some subimage, it can be interpolated from thresholds determined in neighboring subimages.
• each subimage is then processed with respect to its local threshold.

Band-thresholding

• segment an image into regions of pixels with gray levels from a set D and into background otherwise

  
  

• Can also serve as border detection

Multithresholding

• resulting image is no longer binary

Semithresholding

• aims to mask out the image background leaving gray level information present in the objects

Threshold detection methods

• If some property of an image after segmentation is known a priori, the task of threshold selection is simplified, since the threshold is chosen to ensure this property is satisfied.
  
  
• Example A printed text sheet where we know that characters of the text cover 1/p of the sheet area.

P-tile-thresholding

• choose a threshold T (based on the image histogram) such that 1/p of the image area has gray values less than T and the rest has gray values larger than T
• in text segmentation, prior information about the ratio between the sheet area and character area can be used
• if such a priori information is not available - another property, for example the average width of lines in drawings, etc. can be used - the threshold can be determined to provide the required line width in the segmented image

More complex methods of threshold detection

• based on histogram shape analysis
• bimodal histogram - if objects have approximately the same gray level that differs from the gray level of the background

  

• Bimodality of histograms
• to decide if a histogram is bimodal or multimodal may not be so simple in reality
• it is often impossible to interpret the significance of local histogram maxima
• Bimodal histogram threshold detection algorithms
  • Mode method - find the highest local maxima first and detect the threshold as a minimum between them
    • to avoid detection of two local maxima belonging to the same global maximum, a minimum distance in gray levels between these maxima is usually required
    • or techniques to smooth histograms are applied
• Histogram bimodality itself does not guarantee correct threshold segmentation

Optimal thresholding

• based on approximation of the histogram of an image using a weighted sum of two or more probability densities with normal distribution
• The threshold is set as the closest gray level corresponding to the minimum probability between the maxima of two or more normal distributions, which results in minimum error segmentation

  

• Problems - estimating normal distribution parameters together with the uncertainty that the distribution may be considered normal.

• Motivation algorithm
  

• The method performs well under a large variety of image contrast conditions

Example - Brain MR image segmentation

• A combination of optimal and adaptive thresholding
• determines optimal gray level segmentation parameters in local subregions for which local histograms are constructed
• gray-level distributions corresponding to n individual (possibly non-contiguous) regions are fitted to each local histogram that is modeled as a sum of n Gaussian distributions so that the difference between the modeled and the actual histograms is minimized