Cutouts are often called for when doing commercial work, where a product needs to be taken out of the background it was photographed on, and placed into a more flexible background (generally transparent).
Cutouts are a very common task, and are useful for many styles of designs, where you wish to isolate objects and bring them into a montage.
This cutout how to is courtesy of Beautiful Balms an online cream & balm shop, and Poised Solutions IT consultancy. Whilst the product range was not huge, a few cutouts had to be created for the site, to show the various balms. As the cutouts were primarily of curved jars and containers, they offered quite a simple way of showing how cutouts are done, whilst still having a degree of complexity.
The photograph is fairly important, you want something where the edge of the object can be clearly seen, but also where the colour of the background can compliment the object if the object has a degree of translucency.
Web resolutions is typically screen resolution, which is 72DPI so you won't need to have a huge image, though you should try and keep the image resolutions as large as you can work comfortably with, to improve the accuracy of the cutout.
For this how to though, I will reduce the size of the image to keep downloads small.

By eye I can see that the rotation is ever so slightly off, so to make sure you are working with something level grab two rules from the rule bar and place them across the top and bottom of the object.

At a glance I would say the shot is only about 2° off the level. A quick rotation will sort out the level of the object and make the cutout easier to achieve.
Select the rotate tool
and put in 2 as the degree of rotation to
use.

It is possible to do cutouts without leveling the image first, instead rotating at the end, but with a uniform object the cutout is made simpler to do if the object is level at the start.
Crop around the object giving a little room to work with, and you should end up with something like this.

To make a cutout we use the paths tools to create a path that has the nodes on it bent using bezenier curves or kept straight.
The paths tool icon
sometimes referred to as the pen,
is a very useful tool. It is worthwhile getting comfortable
with how it works. It allows you to make a serious of joined
points that can then be looped back and joined (anchored) to
the first point.
A couple of tricks are to enlarge the image window, and
place points outside the view port of the image, and to dock
the paths dialog
, referring to it when you think you may have
lost the path (by selecting another tool).
Paths are automatically stored in the paths dock, so you should not fear about losing the path.
To make a curve you can either drag the line (not on a node) or press Ctrl and select a node at the same time. Two handles should appear that allow you to shape the curve, between the two nodes.
If you press Ctrl when not on a node, but on the line you can introduce a new node.
The way to do a cutout relatively fast and with little fuss, is to add nodes only where you actually need them. Avoid the temptation of just putting in lots of nodes, place them at points where you need a line to be made. You can always add nodes later if you find you have run out.
Begin by placing a few nodes around the object, a node for each place where you think you will need to create a line.
Zoom the image a bit to make the initial placement simpler.

Most of the nodes have been correctly placed, but just to the lower left, one node is missing that is needed to allow for the depth of the label, that will be added later.
This is where the real work of the cutout begins, zoom into the image, enough so you can easily move nodes around at the pixel level of accuracy (spare a thought for those people doing bill board cutouts at this point).

Initially work your way around the path moving the nodes into their end of line positions, adding any nodes that you may need.

Work your way around the path again, but this time curve the lines to fit the contour of the object, you may wish to zoom in even further to get the curves right.
A good technique is to start by moving the line out to create a curve, this should reveal the handles to change the shape of curve to more finely tune the line.

Once you are happy with path around the object, right click the path in the paths dock and path to selection, or Select -> From Path in the image menu (Shift+V).
Invert the selection (Select -> Invert or Ctrl+I) and clear (Edit -> Clear or Delete). Select none, and checkout your handy work.
All being well you should have something similar to what is shown below.

If you are going to make a number of cutouts, then you could now create a mask from this template to apply to photographs of similar items, and speed the process up considerably.
Once the object is cut from the background you are then free to add whatever style of background you like.

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