Image Variations: Linear and Nonlinear Brightness Changes

13 Oct.,2023

 

Image Variations: Linear and Nonlinear Brightness Changes

In a typical application, you use CNLSearch to find the location of a particular feature within each of a series of search images. In many applications, the brightness of the image changes between successive search images. These brightness changes are due to a number of factors:

  • Changes in illumination intensity
  • Changes in illumination source location
  • Changes in reflectance of part or all of the scene
  • Changes in color of part or all of the scene

The change in brightness that occurs between images can be linear, in which case all parts of the image have undergone a proportional change in brightness, or nonlinear, in which case some parts of the image have changed in brightness to a different degree than others, or some parts of the image have become brighter while others have become dimmer.

Typically, changing the intensity of light with which a scene is lit causes a linear change in the brightness of different parts of the image. The figure below shows an example of two images with a linear brightness change.

Linear brightness change

Specifically, if the brightness of two images, j and k, is linearly different, for each pixel value Pjxy in image j, the value of the corresponding pixel Pkxy in image k can be calculated using the following formula:

where A and B are constants. If the differences between all corresponding pixel values in the two images cannot be expressed with a linear function of this type, the two images are nonlinearly different.

Nonlinear brightness changes between images are often the result of changes in the reflectance of different parts of the scene. Images of an object obtained at different points during a manufacturing process can undergo nonlinear brightness changes. These changes are a result of process steps that change the surface characteristics of the object. For example, as a metal stamping is painted, the color and reflectance of the stamping changes. Search images obtained at different steps in the painting process can exhibit nonlinear brightness changes with respect to each other and with respect to the model image.

Nonlinear brightness changes in an image can take one of two forms. Different areas within the image may have changed brightness relative to each other while retaining consistent brightness within each area. This is called a uniform nonlinear brightness change. The figure below shows an image that has undergone a uniform nonlinear brightness change.

Uniform nonlinear brightness change

Nonlinear brightness changes within an image can also occur within formerly uniform areas of the image. This is called a nonuniform nonlinear brightness change. The figure below shows an image that has undergone a nonuniform nonlinear brightness change.

Nonuniform nonlinear brightness change

CNLSearch can find patterns in search images with both uniform and nonuniform nonlinear brightness changes from the model image.

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