Is there a way to detect what Windows Store apps are installed on a system with native C# calls?

I'm trying to replicate the functionality of the Get-AppxPackage and Get-ProvisionedAppxPackage Powershell cmdlets for a C# application I'm building, but have no idea how to even get started.

I can't use the C# Powershell API because of this problem, so I'd like a native C# solution if possible.