I am using the Extract by Mask tool in ArcGIS. The tool is extracting all the cell that intersect the masking layer. Is there a process to mask only the cells that fall completely within the making layer ! That means cells which have some-part outside the masking layer should be excluded. As per request by Hornbydd I have added this image. It looks like cells with approximately 50% or more overlap with the masking layer are selected in the process.
This rule cannot be applied by default, but the workaround is to use negative buffer.
if your mask is a raster, you can shrink you mask by one pixel with the shrink tool.
if your mask is a feature class, the cells whose center are within the feature class will be taken. If you apply a negative buffer of "square root of 2" time the pixel size, then none of the pixels will be outside of the original mask.
The extract by mask tool that you used gave you the correct result based on the raster resolution of your image. The cell size or raster resolution of the image is coarse compared to the mask polygon, and if the raster pixel center is located within the polygon, it will be presented in the result after running extract by mask. However, if the raster pixel center is not located within the polygon, it will be excluded from the result.
You may need to use Resample tool to change the spatial resolution of the raster image by decreasing the pixel size. After changing the spatial resolution, you can run extract by mask to include more pixels with the mask polygon.