Adaptive Threshold Filtering

Dynamic Boundary Detection

Adaptive threshold filtering creates intelligent boundaries that respond to local image characteristics rather than global parameters. This technique analyzes surrounding pixel values and adjusts threshold levels dynamically, producing superior visual results compared to fixed threshold approaches.

The system examines both the current value and a blurred reference, calculating optimal separation points that adapt to varying content density and lighting conditions.

ライブエディター

const fragment = () => {
      const uv = position.xy.div(iResolution)
      const time = iTime.mul(0.2)

      // Create complex noise pattern
      const noise = uv.x.mul(15).add(time).sin().mul(uv.y.mul(12).sub(time.mul(0.7)).cos())
      const blurred = uv.x.mul(3).add(time.mul(0.5)).sin().mul(uv.y.mul(2.5).sub(time.mul(0.3)).cos())

      // Apply adaptive thresholding with bias
      const threshold = adaptiveThreshold(noise, blurred, float(0.2))

      const color = vec3(threshold.mul(0.8), threshold.mul(0.6), threshold.mul(0.9))
      return vec4(color, 1)

}

Content-Aware Edge Enhancement

Advanced edge detection leverages adaptive thresholding to identify meaningful boundaries while suppressing noise artifacts. The algorithm compares fine detail against smooth background variations, highlighting significant transitions.

ライブエディター

const fragment = () => {
      const uv = position.xy.div(iResolution).sub(0.5).mul(3)
      const time = iTime.mul(0.4)

      // Generate detailed texture pattern
      const detail = uv.x.mul(20).add(time).sin().add(uv.y.mul(18).sub(time.mul(1.2)).cos())
      const background = uv.x.mul(2).add(time.mul(0.3)).sin().add(uv.y.mul(1.8).sub(time.mul(0.7)).cos())

      // Simple adaptive threshold without bias
      const edges = adaptiveThresholdSimple(detail, background)

      // Create rainbow edge coloring
      const colorShift = uv.x.add(uv.y).add(time.mul(2))
      const red = edges.mul(colorShift.sin().mul(0.5).add(0.7))
      const green = edges.mul(colorShift.mul(1.3).cos().mul(0.5).add(0.6))
      const blue = edges.mul(colorShift.mul(0.7).sin().mul(0.5).add(0.8))

      const color = vec3(red, green, blue)
      return vec4(color, 1)

}

Technical Implementation Framework

The adaptive threshold system operates through comparative analysis between target values and reference patterns. This approach enables context-sensitive decision making that adapts to local content characteristics.

Core Algorithm Structure

Function Variant	Parameters	Threshold Calculation	Application Domain
adaptiveThreshold	value, reference, bias	step(reference + bias, value)	Configurable sensitivity control
adaptiveThresholdSimple	value, reference	step(reference - 0.05, value)	Standard edge detection

Processing Architecture

The threshold comparison uses the step function to create binary decisions based on computed boundaries. Reference values provide local context, while bias parameters enable fine-tuning for specific visual requirements.

Mathematical Foundation

Adaptive thresholding implements local comparison operations through binary step functions:

For the standard adaptive threshold with bias: $\text{adaptiveThreshold}(v, b, k) = \text{step}(b + k, v)$

For the simple adaptive threshold: $\text{adaptiveThresholdSimple}(v, b) = \text{step}(b - 0.05, v)$

Where the step function is defined as:

$$\text{step}(edge, x) = \begin{cases} 0 & \text{if } x < edge \\ 1 & \text{if } x \geq edge \end{cases}$$

The parameters represent:

• $v$ = input value to be thresholded
• $b$ = blurred reference value (local neighborhood)
• $k$ = bias adjustment for sensitivity control

This approach eliminates global threshold limitations by creating dynamic boundaries that respond to content density and structural variations within the processed data.