If you are talking about 2d and 3D (volume) images, the answer is "Yes" it can be applied without significant change if you are not considering any spatial information about the points. As what u need to calculate is distance only. However, running time will be significantly increased.

Regards.

Increasing the dimensionality of the problem does not prevent you in principle the application of the k-means algorithm. However, there will be more computations to be performed. Adding only one dimension the computation is not a real problem, adding many more dimensions would be a problem though.

If you want to apply such an algorithm effectively, you will have to take into consideration various aspects of your original data set (number of points, their distribution in 3D space, etc.). Even though that distance metric is the core parameter of this algorithm, the generated cluster centers and their corresponding data have to be reevaluated, in order to ensure that each point has been properly assigned to that cluster. The simplest methodology is to validate that each cluster's point is indeed closest to its own cluster -in terms of distance- compared to the mean value of any other generated cluster. However, as Ahmed mentioned above complexity is greatly inrceased, so you may have to resort to more sophisticated algorithms that apply heuristic solutions (Lloyd's algorithm).

The k-means algorithms do not depend upon the dimensions of data. All that you need is to find a suitable metric to measure the similarity. Only problem will be the time taken as the more the dimensions the more is the computation time for similarity. Since this is to be done repeatedly, it requires a lot of time.

You can also use a DBSCAN algorithm which is suitable for spatial data.

For multi-dimension data, multi SVM can be useful for the classification. This concept already implemented in many research papers.