The email part is a little unusual, but webcams are inexpensive these days and so is the software to monitor them. Several software packages support motion detection as well as publishing the results in different ways.
Let’s review the pieces you need.
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First, of course, you need a webcam. That’s nothing more than a video camera attached to your computer. Many digital video cameras, for example, can be used as webcams. More realistically, webcams from popular manufacturers like Logitech are not only inexpensive, but often come complete with the drivers and software required to do everything you need.
Once you have a webcam, the next step is software. Most will actually come with software that will allow you some sort of webcam functionality, but possibly not motion detection. It’s often an option – the default might be the more common behavior of taking a picture every so many seconds. Look for options under surveillance or motion detection to see if the accompanying software has this feature. If it does, you’re almost done.
If not, there are some very good packages out there. One I’ve used in the past is ISpy. A quick search also turns up WebCam Monitor – while I’ve not used this product, it promises to do pretty much everything you might want. In fact, quick search for “webcam motion detection software” turns up many possibilities. If you’re on a budget, “free webcam motion detection software” also has several hits, but I’m always very cautious downloading so-called “free” software.
Finally, there’s what to do with the motion captured images. Realize, of course, that your computer needs to be on and connected to the internet in order for you to be able to view your web cam remotely. The most common approach is to have the webcam take a snapshot every few seconds and automatically upload that to a website. With motion detection involved, the cam might only upload the snapshot if, or when, motion has been detected. You would then simply visit the website periodically to see what your cam’s been looking at. (If you don’t already have a website of your own, check with your ISP. You may already have space available from them that you can use for things like this.)
The scenario mentioned in the original question is an interesting one: once motion is detected, take a snapshot and immediately email them to you. Not all webcam software supports this, so make sure to check for the feature as you evaluate what package to use. The aforementioned WebCam Monitor, for example, lists email as one of its options.
All in all, using a webcam for some simple surveillance is fairly inexpensive, quite possible, and quite popular.