Image Analysis is a broad description of converting the 2D spatial information in images into other forms that can be used to characterize their content.
The most basic form of image analysis is global or partial computation of statistical quantities such as average, standard deviation and higher statistical moments. ImageStats is very similar to WaveStats except it can also work on an 2D or 3D ROI or on "beams" (the beami,j is the ordered vector of values taken by pixeli,j in consecutive images) of a 3D wave.
ImageHistogram is an operation that computes the histogram for an image or any part of an image as defined by an ROI. When the image has RGB components, the operation computes the histogram on channel by channel basis. ImageHistogram uses 256 bins when image pixels components are 8 bits. If the data type are larger than 8 bits (including float and double precision) the operation can use 65536 bins.
If you are interested in cross-sections or line profiles you can use the ImageLineProfile operation which provides a numerical value for samples along an arbitrary path in the image.
The previous analysis operations apply to any type of image. By contrast, the most detailed analysis operation applies to binary images. ImageAnalyzeParticles measures particles in 2D or 3D binary images. The result of the operation include the position, area, perimeter, circularity, rectangularity and other measures of the particles.
A very different form of analysis can be found in the ImageSnake operation which implements a form of an active contour that is used to automatically find object boundaries inside an image.