This is not "purist" propaganda. This is an attempt to help correct increasingly widespread gross marketing-driven misconception about what vector graphics is all about, in the context of auto-tracing routines.
There is no "conversion" between a raster image and a vector graphic. Strictly speaking, a true "conversion" would be a grid array of vector rectangles, which would have no practical advantage whatsoever over a raster image. Generating a vector version of a raster image is not a "conversion" in the sense of converting a TIF to a PNG. There is no "translation" of a raster image into a vector graphic in the sense of translating a Corel Draw file into an Illustrator file.
There is only redrawing what is represented by a raster image as paths, in the same sense that you can redraw an oil painting with a pencil. Autotrace routines (like Illustrator's so-called LiveTrace feature) try to automate that re-drawing by detecting regions of similarly-colored pixels. There is no shape-detection intelligence involved. The autotrace routine doesn't know that the eye's pupil is round or that a football is symmetrical (thus, the "distortion" you are taking about).
PNG is a raster image format. In a raster image, there is no shape to speak of, other than the rectangular bounds of the image.
The "image" you are talking about being distorted only exists in your human intelligence. You think of a region of similarly-colored pixels or related-color pixels as a particular shape. The auto-trace routine only sees the adjacent colors and tries to draw paths around them. LiveTrace knows nothing about what you perceive as a shape or an object, or an image.
You see a repeating pattern of intricate colors which you recognize as flowers, distorted by visual perspective on compound surfaces, overlaid by a pattern of shadows and highlights, and you recognize it as a couch. You see a few jagged edges that merely suggest a discrete shape and recognize it as the letter A.
An auto-trace routine sees only blotches of color with absolutely no meaningful correlation. You make settings to force it to "take a closer look" and it obligingly re-creates the inaccuracies of the blotches. It doesn't know that the distortion of the flowers and the shades of the lighting work together to describe the outline of a couch. It doesn't know that the top of the A is pointed and that its legs are diagonal.
There is huge benefit to be derived from re-drawing what is represented by a raster image as a set of accurate and economical vector paths--Those are the advantages people seek when they launch Illustrator and run LiveTrace, just because they've heard somewhere something like "vector is scaleable and raster isn't."
But in the vast majority of cases, there is no benefit whatsoever in "automatically" drawing those paths just on the basis of colors. Merely "being vector" doesn't necessarily yield the advantages of vector-based artwork; Being properly-drawn vector artwork does. Upscaling auto-traced results is usually just as ugly--or uglier--than merely upsampling the original raster image.
Use the camera icon to attach the image.
In the Live Trace Options pick select your preset or make custom settings including color.
Tat wow answer you go tis nothing more then a misunderstanding of how to use the live trace feature.
It really depends on what your point of view is and true the settings are difficult to understand and require a lot of experience to make work well but the standard tracing will give you good results.
One thing I want to point so you understand the the wow answer is way off track and that is that it is call LIve Trace because it is not converting anything to vector it is not intended convert anything to vector does not say or imply it converts raster images to vector art as it is only a tracing feature for creating vector art based on a raster image.
This might help you see it from another point of view that does not have issues to confuse the matter.
Note that hough the word conversion is used it does not imply the same notion as the wow answer suggest it implies, it simply means you are using a raster image as a basis for creating vector form of that raster art.
Nothing more and nothing less.
BTW the straight forward answer to your questions are contained in the two above links.
There is no quick way to do this.
You can use the live trace in illustrator or different free convertes on the net.. but you have alot more control over the convertion in adobe illustrator.
When using the live trace, you can change the mode from black and white to color 256 is max. and then remove the 2 px pathfitting. It will make the traceing and vector you are making jaggy in the edges but it wil come the closest to the thing you are tracing.
Then you have to redaw it when you have convertet it with the pen or the pencil tool to get the exact form it takes time, but if you put your back into it, it's deffinetly worth the effort..
I must repeat there is no easy way
It often depends on the picture form and so on. Also you can clean up a form an animal whatever shape on photoshop first by making the color edges more sharp og make a bigger contrast in a picture, make it black and white at make the motive the black sharp against the baggrund, well you get the picture.
Then you make the canvas of illustrator the size you want the picture to have ans save it as a svg, eps or illustrator.