You should be able to evaluate something very similar. Typing EdgeDetect[CTRL = The Edge image] (where "CTRL =" indicates "execute the key combination CTRL and Equals key") should give you the result in anything which runs the Wolfram Language. I believe that will include Mathematica and also the Wolfram Desktop. WolframAlpha is an instantiation of the Wolfram Language with a huge knowledge base and a parser - it used to be Mathematica+knowledgebase+parser, but now it's explicitly got the cloud capabilities of the Wolfram Language which I am under the impression that Mathematica will not have.
Note that you can access Alpha from Mathematica (by dint of the command WolframAlpha, or by typing two Equals signs before what you type), but you can only enter the crudest Wolfram Language commands into Alpha and have them executed. However, using the Mathematica tie-in as above, it is possible to write your own Mathematica expressions (and soon Wolfram Language expressions, when it's released properly) which make use of the Alpha knowledgebase.
You should be able to evaluate something very similar. Typing EdgeDetect[CTRL = The Edge image] (where "CTRL =" indicates "execute the key combination CTRL and Equals key") should give you the result in anything which runs the Wolfram Language. I believe that will include Mathematica and also the Wolfram Desktop. WolframAlpha is an instantiation of the Wolfram Language with a huge knowledge base and a parser - it used to be Mathematica+knowledgebase+parser, but now it's explicitly got the cloud capabilities of the Wolfram Language which I am under the impression that Mathematica will not have.
Note that you can access Alpha from Mathematica (by dint of the command WolframAlpha, or by typing two Equals signs before what you type), but you can only enter the crudest Wolfram Language commands into Alpha and have them executed. However, using the Mathematica tie-in as above, it is possible to write your own Mathematica expressions (and soon Wolfram Language expressions, when it's released properly) which make use of the Alpha knowledgebase.