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// 频域滤波（基于 FFT）
///|
/// 频域滤波类型
pub(all) enum FreqFilterType {
LowPass // 低通滤波（保留低频，去除高频）
HighPass // 高通滤波（保留高频，去除低频）
BandPass // 带通滤波（保留中频）
BandStop // 带阻滤波（去除中频）
}
///|
/// 频域滤波。对灰度图做 FFT，应用指定滤波器，再做 IFFT 回空域。
/// cutoff 为截止频率（像素数，从中心算起），band_width 为带宽（仅 BandPass/BandStop 使用）。
pub fn freq_filter(
img : @types.Image,
filter_type : FreqFilterType,
cutoff : Float,
band_width? : Float = 0.0F,
) -> @types.Image raise @types.LoadError {
if img.channels != 1 && img.channels != 3 && img.channels != 4 {
raise @types.LoadError::DecodeFailed("freq_filter 仅支持 channels=1/3/4")
}
let ch = img.channels
let color_ch = if ch >= 3 { 3 } else { 1 }
let ffts = fft_2d(img)
let filtered : Array[FFTResult] = []
for c in 0..<color_ch {
fft_shift_inplace(ffts[c])
let shifted = ffts[c]
let w = shifted.width
let h = shifted.height
let cx = w / 2
let cy = h / 2
let n = w * h
let out_data : Array[Complex] = Array::make(n, Complex::{
re: 0.0F,
im: 0.0F,
})
let data = shifted.data
for y in 0..<h {
let dy = y - cy
let row = y * w
for x in 0..<w {
let dx = x - cx
let dist = Float::from_int(dx * dx + dy * dy).sqrt()
let gain = filter_gain(filter_type, dist, cutoff, band_width)
let src = data[row + x]
out_data[row + x] = Complex::{ re: src.re * gain, im: src.im * gain }
}
}
let filtered_fft = FFTResult::{ width: w, height: h, data: out_data }
fft_shift_inplace(filtered_fft)
filtered.push(filtered_fft)
}
if color_ch == 1 {
return ifft_2d(filtered[0])
}
let pw = filtered[0].width
let ph = filtered[0].height
let n = pw * ph
let out : Array[Byte] = Array::make(n * ch, b'\x00')
for c in 0..<color_ch {
let channel_img = ifft_2d(filtered[c])
for i in 0..<n {
out[i * ch + c] = channel_img.data[i]
}
}
if ch == 4 {
for i in 0..<n {
out[i * 4 + 3] = img.data[i * 4 + 3]
}
}
@types.Image::{
width: pw,
height: ph,
channels: ch,
data: Bytes::from_array(out),
}
}
///|
/// 理想滤波器增益
fn filter_gain(
filter_type : FreqFilterType,
dist : Float,
cutoff : Float,
band_width : Float,
) -> Float {
match filter_type {
LowPass => if dist <= cutoff { 1.0F } else { 0.0F }
HighPass => if dist >= cutoff { 1.0F } else { 0.0F }
BandPass => {
let lo = cutoff - band_width / 2.0F
let hi = cutoff + band_width / 2.0F
if dist >= lo && dist <= hi {
1.0F
} else {
0.0F
}
}
BandStop => {
let lo = cutoff - band_width / 2.0F
let hi = cutoff + band_width / 2.0F
if dist >= lo && dist <= hi {
0.0F
} else {
1.0F
}
}
}
}
///|
/// 高斯频域滤波。使用高斯传递函数而非理想滤波器，更平滑。
pub fn freq_filter_gaussian(
img : @types.Image,
filter_type : FreqFilterType,
cutoff : Float,
band_width? : Float = 0.0F,
) -> @types.Image raise @types.LoadError {
if img.channels != 1 && img.channels != 3 && img.channels != 4 {
raise @types.LoadError::DecodeFailed(
"freq_filter_gaussian 仅支持 channels=1/3/4",
)
}
let ch = img.channels
let color_ch = if ch >= 3 { 3 } else { 1 }
let ffts = fft_2d(img)
let filtered : Array[FFTResult] = []
for c in 0..<color_ch {
fft_shift_inplace(ffts[c])
let shifted = ffts[c]
let w = shifted.width
let h = shifted.height
let cx = w / 2
let cy = h / 2
let n = w * h
let out_data : Array[Complex] = Array::make(n, Complex::{
re: 0.0F,
im: 0.0F,
})
let data = shifted.data
for y in 0..<h {
let dy = y - cy
let row = y * w
for x in 0..<w {
let dx = x - cx
let dist = Float::from_int(dx * dx + dy * dy).sqrt()
let gain = gaussian_gain(filter_type, dist, cutoff, band_width)
let src = data[row + x]
out_data[row + x] = Complex::{ re: src.re * gain, im: src.im * gain }
}
}
let filtered_fft = FFTResult::{ width: w, height: h, data: out_data }
fft_shift_inplace(filtered_fft)
filtered.push(filtered_fft)
}
if color_ch == 1 {
return ifft_2d(filtered[0])
}
let pw = filtered[0].width
let ph = filtered[0].height
let n = pw * ph
let out : Array[Byte] = Array::make(n * ch, b'\x00')
for c in 0..<color_ch {
let channel_img = ifft_2d(filtered[c])
for i in 0..<n {
out[i * ch + c] = channel_img.data[i]
}
}
if ch == 4 {
for i in 0..<n {
out[i * 4 + 3] = img.data[i * 4 + 3]
}
}
@types.Image::{
width: pw,
height: ph,
channels: ch,
data: Bytes::from_array(out),
}
}
///|
/// 高斯传递函数增益
fn gaussian_gain(
filter_type : FreqFilterType,
dist : Float,
cutoff : Float,
band_width : Float,
) -> Float {
let eps = 0.0001F
let c2 = cutoff * cutoff
match filter_type {
LowPass => @math.expf(-(dist * dist) / (c2 + eps))
HighPass => 1.0F - @math.expf(-(dist * dist) / (c2 + eps))
BandPass => {
let lp = @math.expf(-(dist * dist) / (c2 + eps))
let lo = cutoff - band_width / 2.0F
let lp2 = @math.expf(-(dist * dist) / (lo * lo + eps))
lp2 - lp
}
BandStop => {
let lp = @math.expf(-(dist * dist) / (c2 + eps))
let lo = cutoff - band_width / 2.0F
let lp2 = @math.expf(-(dist * dist) / (lo * lo + eps))
1.0F - (lp2 - lp)
}
}
}