The mosaicked image displayed from a mosaic dataset can be created from a number of input rasters that are often overlapping. The mosaic method defines how the mosaicked image is created from these input rasters.
For example, when using the By Attribute method, the values in an attribute field are used to sort the images, and when using Closest to Center, the image closest to the center of the display is positioned as the top image in the mosaic. Additionally, the mosaic operator allows you to define how to resolve the overlapping cells, such as choosing a blending operation.
When working with the mosaic dataset, there are two places to modify the mosaic method. If you're editing the mosaic dataset and you need to set the default mosaic method (or limit the options), you will modify the mosaic dataset properties. This permanently alters the mosaic dataset. However, if you're viewing the mosaic dataset as a data source and not modifying it for the benefit of others, you can change the mosaic method from the Image layer. This way, you only impact your display and do not permanently impact others when viewing or accessing the mosaic dataset.
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Understanding the mosaicking rules for a mosaic dataset