C# 718 bytes
I realize that c# is terrible for golfing, but here's my attempt at 718 bytes
namespace System{using Collections.Generic;using Drawing;using Linq;using O=Convert;class P{int j,i;List<S> s=new List<S>();Image G(string t){var l=t.Replace("\r","").Split('\n');var w=O.ToInt32(l[0].Split(' ')[0]);var h=O.ToInt32(l[0].Split(' ')[1]);for(i=1;i < l.Length;i++){var p=l[i].Split(' ');s.Add(new S{X=O.ToInt32(p[0]),Y=O.ToInt32(p[1]),I=O.ToSingle(p[2]),R=O.ToByte(p[3]),G=O.ToByte(p[4]),B=O.ToByte(p[5])});}var b=new Bitmap(w,h);for(j=0;j<h;j++)for(i=0;i<w;i++)b.SetPixel(i,j,C());return b;}Color C(){return Color.FromArgb(X(x=>x.R),X(x=>x.G),X(x=>x.B));}int X(Func<S,float>f){return(int)Math.Min(s.Sum(x=>x.I*f(x)/(Math.Sqrt((x.X-i)*(x.X-i)+(x.Y-j)*(x.Y-j))+1)),255);}class S{public float X,Y,R,G,B,I;}}}
If anyone has any suggestions to shorten it, feel free to let me know.