Image Processing Toolbox

Image Analysis

Image analysis techniques return information about the structure of an image. This section describes toolbox functions that you can use for these image analysis techniques:

• Edge detection
• Quadtree decomposition

The functions described in this section work only with intensity images.

Edge Detection

You can use the edge function to detect edges, which are those places in an image that correspond to object boundaries. To find edges, this function looks for places in the image where the intensity changes rapidly, using one of these two criteria:

• Places where the first derivative of the intensity is larger in magnitude than some threshold
• Places where the second derivative of the intensity has a zero crossing

edge provides a number of derivative estimators, each of which implements one of the definitions above. For some of these estimators, you can specify whether the operation should be sensitive to horizontal or vertical edges, or both. edge returns a binary image containing 1's where edges are found and 0's elsewhere.

The most powerful edge-detection method that edge provides is the Canny method. The Canny method differs from the other edge-detection methods in that it uses two different thresholds (to detect strong and weak edges), and includes the weak edges in the output only if they are connected to strong edges. This method is therefore less likely than the others to be "fooled" by noise, and more likely to detect true weak edges.

The example below illustrates the power of the Canny edge detector. It shows the results of applying the Sobel and Canny edge detectors to the rice.tif image.

• I = imread('rice.tif');
  BW1 = edge(I,'sobel');
  BW2 = edge(I,'canny');
  imshow(BW1)
  figure, imshow(BW2)
  
  
  

For an interactive demonstration of edge detection, try running edgedemo.

Quadtree Decomposition

Quadtree decomposition is an analysis technique that involves subdividing an image into blocks that are more homogeneous than the image itself. This technique reveals information about the structure of the image. It is also useful as the first step in adaptive compression algorithms.

You can perform quadtree decomposition using the qtdecomp function. This function works by dividing a square image into four equal-sized square blocks, and then testing each block to see if it meets some criterion of homogeneity (e.g., if all of the pixels in the block are within a specific dynamic range). If a block meets the criterion, it is not divided any further. If it does not meet the criterion, it is subdivided again into four blocks, and the test criterion is applied to those blocks. This process is repeated iteratively until each block meets the criterion. The result may have blocks of several different sizes.

For example, suppose you want to perform quadtree decomposition on a 128-by-128 intensity image. The first step is to divide the image into four 64-by-64 blocks. You then apply the test criterion to each block; for example, the criterion might be

• max(block(:)) - min(block(:)) <= 0.2
  

If one of the blocks meets this criterion, it is not divided any further; it is 64-by-64 in the final decomposition. If a block does not meet the criterion, it is then divided into four 32-by-32 blocks, and the test is then applied to each of these blocks. The blocks that fail to meet the criterion are then divided into four 16-by-16 blocks, and so on, until all blocks "pass." Some of the blocks may be as small as 1-by-1, unless you specify otherwise.

The call to qtdecomp for this example would be

• S = qtdecomp(I,0.2)
  

S is returned as a sparse matrix whose nonzero elements represent the upper-left corners of the blocks; the value of each nonzero element indicates the block size. S is the same size as I.

Note    The threshold value is specified as a value between 0 and 1, regardless of the class of I. If I is uint8, the threshold value you supply is multiplied by 255 to determine the actual threshold to use; if I is uint16, the threshold value you supply is multiplied by 65535.

The example below shows an image and a representation of its quadtree decomposition. Each black square represents a homogeneous block, and the white lines represent the boundaries between blocks. Notice how the blocks are smaller in areas corresponding to large changes in intensity in the image.

Figure 10-5: An Image (left) and a Representation of its Quadtree Decomposition

You can also supply qtdecomp with a function (rather than a threshold value) for deciding whether to split blocks; for example, you might base the decision on the variance of the block. See the reference page for qtdecomp for more information.

For an interactive demonstration of quadtree decomposition, try running qtdemo.

Region Property Measurement

Image Enhancement