scirs2_ndimage/advanced_fusion_algorithms/

temporal_causality.rs

//! # Temporal Causality Analysis Module
//!
//! This module provides advanced temporal causality analysis capabilities for image sequences,
//! enabling the detection and analysis of causal relationships over time. It implements:
//!
//! ## Key Features
//! - **Temporal Pattern Analysis**: Detection of temporal patterns in image sequences
//! - **Granger Causality**: Classical statistical causality detection between temporal signals
//! - **Transfer Entropy**: Information-theoretic causality measurement
//! - **Causal Graph Construction**: Building and maintaining causal relationship graphs
//! - **Multi-scale Temporal Analysis**: Analysis across different temporal windows
//!
//! ## Core Algorithms
//! - Cross-correlation based causal strength measurement
//! - Variance-based entropy approximation
//! - Confidence scoring for causal relationships
//! - Dynamic temporal memory management
//!
//! ## Applications
//! - Video sequence analysis for motion causality
//! - Time-series medical imaging analysis
//! - Dynamic system monitoring in scientific imaging
//! - Predictive analysis in image-based monitoring systems

use scirs2_core::ndarray::{Array2, Array3, ArrayView2};
use scirs2_core::numeric::{Float, FromPrimitive};
use std::cmp::Ordering;
use std::collections::{BTreeMap, VecDeque};

use super::config::*;
use crate::error::NdimageResult;

/// Temporal-Causal Analysis
///
/// Analyzes temporal patterns and causal relationships in image sequences
/// to understand the flow of information and causality over time.
///
/// This function implements a comprehensive temporal causality analysis system that:
/// 1. Converts current image to temporal representation
/// 2. Maintains a sliding window of temporal memory
/// 3. Detects causal relationships using multiple algorithms
/// 4. Builds and updates a causal graph
/// 5. Calculates causal influence for each pixel
///
/// # Arguments
/// * `image` - Current image frame to analyze
/// * `advancedstate` - Mutable state containing temporal memory and causal graph
/// * `config` - Configuration parameters for causality analysis
///
/// # Returns
/// A 2D array representing the causal influence strength for each pixel
#[allow(dead_code)]
pub fn analyze_temporal_causality<T>(
    image: &ArrayView2<T>,
    advancedstate: &mut AdvancedState,
    config: &AdvancedConfig,
) -> NdimageResult<Array2<f64>>
where
    T: Float + FromPrimitive + Copy,
{
    let (height, width) = image.dim();
    let mut causal_output = Array2::zeros((height, width));

    // Convert current image to temporal representation
    let current_temporal = image_to_temporal_representation(image)?;

    // Add to temporal memory
    advancedstate
        .temporal_memory
        .push_back(current_temporal.clone());

    // Maintain temporal window size
    while advancedstate.temporal_memory.len() > config.temporal_window {
        advancedstate.temporal_memory.pop_front();
    }

    // Analyze causal relationships if we have sufficient temporal data
    if advancedstate.temporal_memory.len() >= config.causal_depth {
        for y in 0..height {
            for x in 0..width {
                let pixel_id = y * width + x;

                // Extract temporal sequence for this pixel
                let temporal_sequence =
                    extract_pixel_temporal_sequence(&advancedstate.temporal_memory, (y, x))?;

                // Detect causal relationships
                let causal_relationships =
                    detect_causal_relationships(&temporal_sequence, pixel_id, config)?;

                // Update causal graph
                advancedstate
                    .causal_graph
                    .insert(pixel_id, causal_relationships.clone());

                // Calculate causal influence on current pixel
                let causal_influence = calculate_causal_influence(
                    &causal_relationships,
                    &advancedstate.causal_graph,
                    config,
                )?;

                causal_output[(y, x)] = causal_influence;
            }
        }
    }

    Ok(causal_output)
}

/// Converts a 2D image to temporal representation
///
/// Creates a 3D temporal representation of the input image by analyzing
/// spatial gradients, edge patterns, and local statistics that can be
/// tracked over time.
///
/// # Arguments
/// * `image` - Input 2D image
///
/// # Returns
/// A 3D array containing temporal features for the image
#[allow(dead_code)]
fn image_to_temporal_representation<T>(image: &ArrayView2<T>) -> NdimageResult<Array3<f64>>
where
    T: Float + FromPrimitive + Copy,
{
    let (height, width) = image.dim();
    let mut temporal_features = Array3::zeros((height, width, 4));

    for y in 0..height {
        for x in 0..width {
            let pixel_val = image[(y, x)].to_f64().unwrap_or(0.0);

            // Basic intensity feature
            temporal_features[(y, x, 0)] = pixel_val;

            // Horizontal gradient
            let h_grad = if x > 0 && x < width - 1 {
                let left = image[(y, x - 1)].to_f64().unwrap_or(0.0);
                let right = image[(y, x + 1)].to_f64().unwrap_or(0.0);
                (right - left) / 2.0
            } else {
                0.0
            };
            temporal_features[(y, x, 1)] = h_grad;

            // Vertical gradient
            let v_grad = if y > 0 && y < height - 1 {
                let up = image[(y - 1, x)].to_f64().unwrap_or(0.0);
                let down = image[(y + 1, x)].to_f64().unwrap_or(0.0);
                (down - up) / 2.0
            } else {
                0.0
            };
            temporal_features[(y, x, 2)] = v_grad;

            // Local variance feature
            let mut local_vals = Vec::new();
            for dy in -1..=1i32 {
                for dx in -1..=1i32 {
                    let ny = y as i32 + dy;
                    let nx = x as i32 + dx;
                    if ny >= 0 && ny < height as i32 && nx >= 0 && nx < width as i32 {
                        let val = image[(ny as usize, nx as usize)].to_f64().unwrap_or(0.0);
                        local_vals.push(val);
                    }
                }
            }

            let local_variance = if local_vals.len() > 1 {
                let mean = local_vals.iter().sum::<f64>() / local_vals.len() as f64;
                local_vals.iter().map(|&v| (v - mean).powi(2)).sum::<f64>()
                    / local_vals.len() as f64
            } else {
                0.0
            };
            temporal_features[(y, x, 3)] = local_variance;
        }
    }

    Ok(temporal_features)
}

/// Extracts temporal sequence for a specific pixel from temporal memory
///
/// Retrieves the temporal evolution of features for a specific pixel position
/// across all frames in the temporal memory.
///
/// # Arguments
/// * `temporal_memory` - Queue of temporal feature arrays
/// * `position` - (y, x) coordinates of the pixel to extract
///
/// # Returns
/// Vector containing the temporal sequence of feature values for the pixel
#[allow(dead_code)]
fn extract_pixel_temporal_sequence(
    temporal_memory: &VecDeque<Array3<f64>>,
    position: (usize, usize),
) -> NdimageResult<Vec<f64>> {
    let (y, x) = position;
    let mut sequence = Vec::new();

    for frame in temporal_memory {
        if y < frame.shape()[0] && x < frame.shape()[1] {
            // Extract all temporal features for this pixel and combine them
            let mut pixel_features = Vec::new();
            for feature_idx in 0..frame.shape()[2] {
                pixel_features.push(frame[(y, x, feature_idx)]);
            }

            // Combine features into a single temporal value (weighted average)
            let combined_value = pixel_features
                .iter()
                .enumerate()
                .map(|(i, &val)| val * (i as f64 + 1.0) / pixel_features.len() as f64)
                .sum::<f64>();

            sequence.push(combined_value);
        }
    }

    // If sequence is too short, pad with zeros
    while sequence.len() < 8 {
        sequence.push(0.0);
    }

    Ok(sequence)
}

/// Detects causal relationships in temporal sequences
///
/// Implements multiple causality detection algorithms:
/// 1. Granger causality using cross-correlation analysis
/// 2. Transfer entropy approximation using variance-based entropy
///
/// # Arguments
/// * `temporal_sequence` - Temporal sequence of feature values
/// * `pixel_id` - Unique identifier for the source pixel
/// * `config` - Configuration parameters for causality analysis
///
/// # Returns
/// Vector of detected causal relationships with confidence scores
#[allow(dead_code)]
fn detect_causal_relationships(
    temporal_sequence: &[f64],
    pixel_id: usize,
    config: &AdvancedConfig,
) -> NdimageResult<Vec<CausalRelation>> {
    let mut causal_relations = Vec::new();

    if temporal_sequence.len() < config.causal_depth {
        return Ok(causal_relations);
    }

    // Granger causality-inspired analysis
    for delay in 1..config.causal_depth.min(temporal_sequence.len() / 2) {
        let mut cause_values = Vec::new();
        let mut effect_values = Vec::new();

        for i in delay..temporal_sequence.len() {
            cause_values.push(temporal_sequence[i - delay]);
            effect_values.push(temporal_sequence[i]);
        }

        if cause_values.len() < 3 {
            continue;
        }

        // Calculate correlation coefficient
        let cause_mean = cause_values.iter().sum::<f64>() / cause_values.len() as f64;
        let effect_mean = effect_values.iter().sum::<f64>() / effect_values.len() as f64;

        let numerator: f64 = cause_values
            .iter()
            .zip(effect_values.iter())
            .map(|(&c, &e)| (c - cause_mean) * (e - effect_mean))
            .sum();

        let cause_var: f64 = cause_values.iter().map(|&c| (c - cause_mean).powi(2)).sum();

        let effect_var: f64 = effect_values
            .iter()
            .map(|&e| (e - effect_mean).powi(2))
            .sum();

        let denominator = (cause_var * effect_var).sqrt();

        if denominator > 1e-10 {
            let correlation = numerator / denominator;
            let causal_strength = correlation.abs();

            // Threshold for significant causal relationship
            if causal_strength > 0.3 {
                // Calculate confidence based on sample size and strength
                let confidence =
                    (causal_strength * (cause_values.len() as f64).ln() / 10.0).min(1.0);

                // Determine target pixel (simplified for demonstration)
                let target_id = if correlation > 0.0 {
                    pixel_id + delay // Positive influence on neighboring pixel
                } else {
                    if pixel_id >= delay {
                        pixel_id - delay
                    } else {
                        pixel_id
                    } // Negative influence
                };

                causal_relations.push(CausalRelation {
                    source: pixel_id,
                    target: target_id,
                    strength: causal_strength,
                    delay,
                    confidence,
                });
            }
        }
    }

    // Transfer entropy-based causality detection
    for window_size in 2..=(config.causal_depth / 2).min(temporal_sequence.len() / 4) {
        if temporal_sequence.len() < window_size * 2 {
            continue;
        }

        // Simplified transfer entropy calculation
        let mut entropy_source = 0.0;
        let mut entropy_target = 0.0;
        let mut mutual_entropy = 0.0;

        for i in window_size..temporal_sequence.len() - window_size {
            let source_window = &temporal_sequence[i - window_size..i];
            let target_window = &temporal_sequence[i..i + window_size];

            // Simplified entropy calculation using variance
            let source_var = calculate_window_variance(source_window);
            let target_var = calculate_window_variance(target_window);

            entropy_source += source_var;
            entropy_target += target_var;

            // Cross-correlation as proxy for mutual information
            let cross_corr = source_window
                .iter()
                .zip(target_window.iter())
                .map(|(&s, &t)| s * t)
                .sum::<f64>()
                / window_size as f64;

            mutual_entropy += cross_corr.abs();
        }

        let n_windows = (temporal_sequence.len() - window_size * 2) as f64;
        if n_windows > 0.0 {
            entropy_source /= n_windows;
            entropy_target /= n_windows;
            mutual_entropy /= n_windows;

            // Transfer entropy approximation
            let transfer_entropy = mutual_entropy / (entropy_source + entropy_target + 1e-10);

            if transfer_entropy > 0.2 {
                let confidence = (transfer_entropy * n_windows.ln() / 5.0).min(1.0);

                causal_relations.push(CausalRelation {
                    source: pixel_id,
                    target: pixel_id + window_size, // Simplified target determination
                    strength: transfer_entropy,
                    delay: window_size,
                    confidence,
                });
            }
        }
    }

    // Sort by strength and keep only the strongest relationships
    causal_relations.sort_by(|a, b| {
        b.strength
            .partial_cmp(&a.strength)
            .unwrap_or(Ordering::Equal)
    });
    causal_relations.truncate(config.causal_depth / 2);

    Ok(causal_relations)
}

/// Calculates the overall causal influence on a pixel
///
/// Computes the aggregate causal influence on a pixel based on all detected
/// causal relationships in the graph. Takes into account both direct and
/// indirect causal pathways.
///
/// # Arguments
/// * `relationships` - Direct causal relationships for the pixel
/// * `causal_graph` - Complete causal relationship graph
/// * `config` - Configuration parameters for influence calculation
///
/// # Returns
/// Normalized causal influence score (0.0 to 1.0)
#[allow(dead_code)]
fn calculate_causal_influence(
    relationships: &[CausalRelation],
    causal_graph: &BTreeMap<usize, Vec<CausalRelation>>,
    _config: &AdvancedConfig,
) -> NdimageResult<f64> {
    if relationships.is_empty() {
        return Ok(0.0);
    }

    // Calculate direct influence
    let direct_influence: f64 = relationships
        .iter()
        .map(|rel| rel.strength * rel.confidence)
        .sum();

    // Calculate indirect influence through the causal graph
    let mut indirect_influence = 0.0;
    for relation in relationships {
        if let Some(target_relations) = causal_graph.get(&relation.target) {
            for target_rel in target_relations {
                // Weight indirect influence by distance and confidence
                let distance_weight = 1.0 / (relation.delay as f64 + 1.0);
                indirect_influence +=
                    target_rel.strength * target_rel.confidence * distance_weight * 0.5;
            }
        }
    }

    // Combine direct and indirect influences
    let total_influence = direct_influence + indirect_influence;

    // Normalize to [0, 1] range using a sigmoid-like function
    let normalized_influence = total_influence / (1.0 + total_influence);

    Ok(normalized_influence)
}

/// Calculates variance of values in a temporal window
///
/// Computes the statistical variance of a window of temporal values,
/// used as a proxy for entropy in causality analysis.
///
/// # Arguments
/// * `window` - Slice of temporal values
///
/// # Returns
/// Variance of the window values
#[allow(dead_code)]
fn calculate_window_variance(window: &[f64]) -> f64 {
    if window.is_empty() {
        return 0.0;
    }

    let mean = window.iter().sum::<f64>() / window.len() as f64;
    let variance = window.iter().map(|&x| (x - mean).powi(2)).sum::<f64>() / window.len() as f64;

    variance
}

/// Analyzes temporal causality patterns across multiple scales
///
/// Performs multi-scale temporal analysis to detect causal patterns
/// at different temporal resolutions.
///
/// # Arguments
/// * `temporal_memory` - Complete temporal memory buffer
/// * `config` - Configuration parameters
///
/// # Returns
/// Multi-scale causality analysis results
#[allow(dead_code)]
pub fn analyze_multiscale_temporal_causality(
    temporal_memory: &VecDeque<Array3<f64>>,
    config: &AdvancedConfig,
) -> NdimageResult<Vec<Array2<f64>>> {
    let mut scales_results = Vec::new();

    if temporal_memory.is_empty() {
        return Ok(scales_results);
    }

    let (height, width, _) = temporal_memory[0].dim();

    // Analyze at different temporal scales
    for scale in 1..=3 {
        let mut scale_result = Array2::zeros((height, width));
        let step_size = scale * 2;

        // Sample temporal memory at different scales
        let mut scaled_memory = VecDeque::new();
        for (i, frame) in temporal_memory.iter().enumerate() {
            if i % step_size == 0 {
                scaled_memory.push_back(frame.clone());
            }
        }

        if scaled_memory.len() >= config.causal_depth / scale {
            for y in 0..height {
                for x in 0..width {
                    // Extract temporal sequence at this scale
                    if let Ok(temporal_sequence) =
                        extract_pixel_temporal_sequence(&scaled_memory, (y, x))
                    {
                        let pixel_id = y * width + x;

                        // Detect causal relationships at this scale
                        if let Ok(relationships) =
                            detect_causal_relationships(&temporal_sequence, pixel_id, config)
                        {
                            let causal_strength: f64 = relationships
                                .iter()
                                .map(|rel| rel.strength * rel.confidence)
                                .sum();

                            scale_result[(y, x)] = causal_strength / (scale as f64);
                        }
                    }
                }
            }
        }

        scales_results.push(scale_result);
    }

    Ok(scales_results)
}

#[cfg(test)]
mod tests {
    use super::*;
    use scirs2_core::ndarray::Array2;

    #[test]
    fn test_calculate_window_variance() {
        let window = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let variance = calculate_window_variance(&window);
        assert!(variance > 0.0);

        // Test empty window
        let empty_window = vec![];
        let zero_variance = calculate_window_variance(&empty_window);
        assert_eq!(zero_variance, 0.0);
    }

    #[test]
    fn test_image_to_temporal_representation() {
        let image = Array2::<f64>::zeros((10, 10));
        let result = image_to_temporal_representation(&image.view());
        assert!(result.is_ok());

        let temporal_features = result.unwrap();
        assert_eq!(temporal_features.dim(), (10, 10, 4));
    }

    #[test]
    fn test_extract_pixel_temporal_sequence() {
        let mut temporal_memory = VecDeque::new();
        let frame1 = Array3::<f64>::zeros((5, 5, 4));
        let frame2 = Array3::<f64>::ones((5, 5, 4));

        temporal_memory.push_back(frame1);
        temporal_memory.push_back(frame2);

        let result = extract_pixel_temporal_sequence(&temporal_memory, (2, 2));
        assert!(result.is_ok());

        let sequence = result.unwrap();
        assert!(!sequence.is_empty());
    }
}