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kdtree.go
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kdtree.go
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package main
import (
"container/heap"
"math"
"sort"
)
// ColorNode represents a node in a KD-tree that stores RGB colors. Each node
// contains a color, a left child, a right child, and the axis along which the
// colors are split.
type ColorNode struct {
Color RGB
Left, Right *ColorNode
SplitAxis int
}
// buildKDTree constructs a KD-tree from a list of RGB colors. The function
// takes a list of colors, the current depth, and the maximum depth of the
// tree as arguments, and returns the root node of the KD-tree.
func buildKDTree(colors []RGB, depth int, maxDepth int) *ColorNode {
if len(colors) == 0 || depth >= maxDepth {
return nil
}
// Choose splitting axis based on the dimension with the largest variance
axis := chooseSplitAxis(colors)
// Sort colors along the chosen axis
sort.Slice(colors, func(i, j int) bool {
return getColorComponent(colors[i], axis) <
getColorComponent(colors[j], axis)
})
median := len(colors) / 2
return &ColorNode{
Color: colors[median],
Left: buildKDTree(colors[:median], depth+1, maxDepth),
Right: buildKDTree(colors[median+1:], depth+1, maxDepth),
SplitAxis: axis,
}
}
// chooseSplitAxis selects the axis along which to split the colors in a
// KD-tree. The function takes a list of RGB colors as input and returns
// the index of the axis with the largest variance.
func chooseSplitAxis(colors []RGB) int {
var varR, varG, varB float64
var meanR, meanG, meanB float64
for _, c := range colors {
meanR += float64(c.r)
meanG += float64(c.g)
meanB += float64(c.b)
}
meanR /= float64(len(colors))
meanG /= float64(len(colors))
meanB /= float64(len(colors))
for _, c := range colors {
varR += math.Pow(float64(c.r)-meanR, 2)
varG += math.Pow(float64(c.g)-meanG, 2)
varB += math.Pow(float64(c.b)-meanB, 2)
}
if varR > varG && varR > varB {
return 0 // R axis
} else if varG > varB {
return 1 // G axis
}
return 2 // B axis
}
// getColorComponent returns the color component of an RGB color along the
// specified axis. The function takes an RGB color and an axis index as input
// and returns the corresponding color component.
func getColorComponent(color RGB, axis int) uint8 {
switch axis {
case 0:
return color.r
case 1:
return color.g
default:
return color.b
}
}
// getCandidateColors finds the k-nearest neighbors of the colors in a block
// using a KD-tree. The function takes a block of colors, the depth of the
// search, and the number of neighbors to find as input, and returns a slice
// of colors sorted by distance.
func (node *ColorNode) getCandidateColors(
block [4]RGB,
depth int,
) colorDistanceSlice {
// Find initial candidates using KD-tree and sort by distance
var candidateColors colorDistanceSlice
seenColors := make(map[RGB]bool)
// Process block colors in a consistent order
sortedBlockColors := make(sortableRGB, len(block))
for i, c := range block {
sortedBlockColors[i] = c
}
sort.Sort(sortedBlockColors)
for _, color := range sortedBlockColors {
nearest := node.kNearestNeighbors(color, depth)
for _, c := range nearest {
if _, seen := seenColors[c]; !seen {
distance := color.colorDistance(c)
candidateColors = append(candidateColors,
colorWithDistance{
c,
distance,
len(candidateColors)})
seenColors[c] = true
}
}
}
return candidateColors
}
// nearestNeighbor finds the nearest neighbor of a target color in a KD-tree.
// The function takes the root node of the KD-tree, the target color, the best
// color found so far, the best distance found so far, and the depth of the
// search as input, and returns the nearest neighbor and the distance to it.
func (node *ColorNode) nearestNeighbor(
target RGB, best RGB, bestDist float64, depth int) (RGB, float64) {
if node == nil {
return best, bestDist
}
dist := node.Color.colorDistance(target)
if dist < bestDist {
best = node.Color
bestDist = dist
}
axis := depth % 3
var next, other *ColorNode
switch axis {
case 0:
if target.r < node.Color.r {
next, other = node.Left, node.Right
} else {
next, other = node.Right, node.Left
}
case 1:
if target.g < node.Color.g {
next, other = node.Left, node.Right
} else {
next, other = node.Right, node.Left
}
default:
if target.b < node.Color.b {
next, other = node.Left, node.Right
} else {
next, other = node.Right, node.Left
}
}
best, bestDist = next.nearestNeighbor(target, best, bestDist, depth+1)
// Check if we need to search the other branch
var axisDistance float64
switch axis {
case 0:
axisDistance = float64(target.r - node.Color.r)
case 1:
axisDistance = float64(target.g - node.Color.g)
default:
axisDistance = float64(target.b - node.Color.b)
}
if axisDistance*axisDistance < bestDist {
best, bestDist = other.nearestNeighbor(
target, best, bestDist, depth+1)
}
return best, bestDist
}
// ColorDistance is a helper struct to keep track of colors and their
// distances
type ColorDistance struct {
color RGB
distance float64
}
// kNearestNeighbors finds the k-nearest neighbors of a target color in a
// KD-tree. The function takes the root node of the KD-tree, the target color,
// and the number of neighbors to find as input, and returns a slice of colors
// sorted by distance.
func (node *ColorNode) kNearestNeighbors(target RGB, k int) []RGB {
pq := make(PriorityQueue, 0)
heap.Init(&pq)
var search func(*ColorNode, int)
search = func(node *ColorNode, depth int) {
if node == nil {
return
}
dist := node.Color.colorDistance(target)
if pq.Len() < k {
heap.Push(&pq, ColorDistance{node.Color, dist})
} else if dist < pq[0].distance {
heap.Pop(&pq)
heap.Push(&pq, ColorDistance{node.Color, dist})
}
axis := depth % 3
var firstChild, secondChild *ColorNode
var axisDist float64
switch axis {
case 0:
axisDist = float64(target.r) - float64(node.Color.r)
if axisDist < 0 {
firstChild, secondChild = node.Left, node.Right
} else {
firstChild, secondChild = node.Right, node.Left
}
case 1:
axisDist = float64(target.g) - float64(node.Color.g)
if axisDist < 0 {
firstChild, secondChild = node.Left, node.Right
} else {
firstChild, secondChild = node.Right, node.Left
}
case 2:
axisDist = float64(target.b) - float64(node.Color.b)
if axisDist < 0 {
firstChild, secondChild = node.Left, node.Right
} else {
firstChild, secondChild = node.Right, node.Left
}
}
search(firstChild, depth+1)
if pq.Len() < k || axisDist*axisDist < pq[0].distance {
search(secondChild, depth+1)
}
}
search(node, 0)
result := make([]RGB, k)
for i := k - 1; i >= 0; i-- {
result[i] = heap.Pop(&pq).(ColorDistance).color
}
return result
}