// Limited Best-Bin-First k-d-tree nearest neighbour search.
//
// (Using the algorithm described in the paper "Shape indexing using
// approximate nearest-neighbour search in high-dimensional spaces",
// available at http://www.cs.ubc.ca/spider/lowe/papers/cvpr97-abs.html)
//
// Find the approximate nearest neighbour to the hyperspace point 'target'
// within the kd-tree using 'searchSteps' tail recursions at most (each
// recursion deciding about one neighbours' fitness).
//
// After return 'resDist' contains the absolute distance of the
// approximate nearest neighbour from the target point. The approximate
// nearest neighbour is returned.
public ArrayList NearestNeighbourListBBF(IKDTreeDomain target,
int q, int searchSteps)
{
HyperRectangle hr =
HyperRectangle.CreateUniverseRectangle(target.DimensionCount);
SortedLimitedList best = new SortedLimitedList(q);
SortedLimitedList searchHr = new SortedLimitedList(searchSteps);
float dummyDist;
IKDTreeDomain nearest = NearestNeighbourListBBFI(best, q, target, hr,
Int32.MaxValue, out dummyDist, searchHr, ref searchSteps);
foreach (BestEntry be in best)
{
be.Distance = Math.Sqrt(be.DistanceSq);
}
return(best);
}
public ArrayList NearestNeighbourList(IKDTreeDomain target,
out double resDist, int q)
{
HyperRectangle hr =
HyperRectangle.CreateUniverseRectangle(target.DimensionCount);
SortedLimitedList best = new SortedLimitedList(q);
IKDTreeDomain nearest = NearestNeighbourListI(best, q, target, hr,
Double.PositiveInfinity, out resDist);
resDist = Math.Sqrt(resDist);
foreach (BestEntry be in best)
{
be.Distance = Math.Sqrt(be.Distance);
}
return(best);
}
private IKDTreeDomain NearestNeighbourListBBFI(SortedLimitedList best,
int q, IKDTreeDomain target, HyperRectangle hr, float maxDistSq,
out float resDistSq, SortedLimitedList searchHr, ref int searchSteps)
{
//Console.WriteLine ("C NearestNeighbourI called");
resDistSq = Int32.MaxValue;
IKDTreeDomain pivot = dr;
best.Add(new BestEntry(dr, KDTree.DistanceSq(target, dr), true));
HyperRectangle leftHr = hr;
HyperRectangle rightHr = leftHr.SplitAt(splitDim,
pivot.GetDimensionElement(splitDim));
HyperRectangle nearerHr, furtherHr;
KDTree nearerKd, furtherKd;
// step 5-7
if (target.GetDimensionElement(splitDim) <=
pivot.GetDimensionElement(splitDim))
{
nearerKd = left;
nearerHr = leftHr;
furtherKd = right;
furtherHr = rightHr;
}
else
{
nearerKd = right;
nearerHr = rightHr;
furtherKd = left;
furtherHr = leftHr;
}
// step 8
IKDTreeDomain nearest = null;
float distSq;
searchHr.Add(new HREntry(furtherHr, furtherKd, pivot,
furtherHr.Distance(target)));
// No child, bottom reached!
if (nearerKd == null)
{
distSq = Int32.MaxValue;
}
else
{
nearest = nearerKd.NearestNeighbourListBBFI(best, q, target, nearerHr,
maxDistSq, out distSq, searchHr, ref searchSteps);
}
// step 9
if (best.Count >= q)
{
maxDistSq = ((BestEntry)best[q - 1]).DistanceSq;
}
else
{
maxDistSq = Int32.MaxValue;
}
if (searchHr.Count > 0)
{
HREntry hre = (HREntry)searchHr[0];
searchHr.RemoveAt(0);
furtherHr = hre.HR;
furtherKd = hre.Tree;
pivot = hre.Pivot;
}
// step 10
searchSteps -= 1;
if (searchSteps > 0 &&
furtherHr.IsInReach(target, Math.Sqrt(maxDistSq)))
{
float ptDistSq = KDTree.DistanceSq(pivot, target);
if (ptDistSq < distSq)
{
// steps 10.1.1 to 10.1.3
nearest = pivot;
distSq = ptDistSq;
maxDistSq = distSq;
}
// step 10.2
float tempDistSq;
IKDTreeDomain tempNearest = null;
if (furtherKd == null)
{
tempDistSq = Int32.MaxValue;
}
else
{
tempNearest = furtherKd.NearestNeighbourListBBFI(best, q,
target, furtherHr, maxDistSq, out tempDistSq, searchHr,
ref searchSteps);
}
// step 10.3
if (tempDistSq < distSq)
{
nearest = tempNearest;
distSq = tempDistSq;
}
}
resDistSq = distSq;
return(nearest);
}
private IKDTreeDomain NearestNeighbourListI(SortedLimitedList best,
int q, IKDTreeDomain target, HyperRectangle hr, double maxDistSq,
out double resDistSq)
{
//Console.WriteLine ("C NearestNeighbourI called");
resDistSq = Double.PositiveInfinity;
IKDTreeDomain pivot = dr;
best.Add(new BestEntry(dr, KDTree.DistanceSq(target, dr)));
HyperRectangle leftHr = hr;
HyperRectangle rightHr = leftHr.SplitAt(splitDim,
pivot.GetDimensionElement(splitDim));
HyperRectangle nearerHr, furtherHr;
KDTree nearerKd, furtherKd;
// step 5-7
if (target.GetDimensionElement(splitDim) <=
pivot.GetDimensionElement(splitDim))
{
nearerKd = left;
nearerHr = leftHr;
furtherKd = right;
furtherHr = rightHr;
}
else
{
nearerKd = right;
nearerHr = rightHr;
furtherKd = left;
furtherHr = leftHr;
}
// step 8
IKDTreeDomain nearest = null;
double distSq;
// No child, bottom reached!
if (nearerKd == null)
{
distSq = Double.PositiveInfinity;
}
else
{
nearest = nearerKd.NearestNeighbourListI(best, q, target, nearerHr,
maxDistSq, out distSq);
}
// step 9
//maxDistSq = Math.Min (maxDistSq, distSq);
if (best.Count >= q)
{
maxDistSq = ((BestEntry)best[q - 1]).Distance;
}
else
{
maxDistSq = Double.PositiveInfinity;
}
// step 10
if (furtherHr.IsInReach(target, Math.Sqrt(maxDistSq)))
{
double ptDistSq = KDTree.DistanceSq(pivot, target);
if (ptDistSq < distSq)
{
// steps 10.1.1 to 10.1.3
nearest = pivot;
distSq = ptDistSq;
// TODO: use k-element list
/*
* best.Add (new BestEntry (pivot, ptDistSq));
* best.Sort ();
*/
maxDistSq = distSq;
}
// step 10.2
double tempDistSq;
IKDTreeDomain tempNearest = null;
if (furtherKd == null)
{
tempDistSq = Double.PositiveInfinity;
}
else
{
tempNearest = furtherKd.NearestNeighbourListI(best, q, target,
furtherHr, maxDistSq, out tempDistSq);
}
// step 10.3
if (tempDistSq < distSq)
{
nearest = tempNearest;
distSq = tempDistSq;
}
}
resDistSq = distSq;
return(nearest);
}