Data and images are not meant to be stored in Azure Web Site web root directory. It could cause problems doing so, few ideas discussed in below links.
To store a image or other files in Azure blob container, the below class can be used, with ASP.NET Core 1.0. This class creates the blob container if it does not exist, with required access level (Blob) to allow store and retrieve images to the web site. (Class and interface can be downloaded from here)
The above class can be used in an ASP.NET Core 1.0 web application as shown below.
In startup class Startup.cs of ASP.NET Core 1.0 web application, add the class to SerivcesCollection as shown below to make it available for MVC 6.0 controllers.
Then in a controller, this can be used. MVC 6.0 will auto inject it to controller.
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