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[Phase 3] Implement 3D AI Point Clouds and Neural Radiance Fields

Open ooples opened this issue 2 months ago • 1 comments

Problem

COMPLETELY MISSING: 3D understanding, point cloud processing, and novel view synthesis.

Missing Implementations

Point Cloud Processing (CRITICAL):

  • PointNet (direct point cloud processing)
  • PointNet++ (hierarchical feature learning)
  • DGCNN (Dynamic Graph CNN for point clouds)

3D Representation (CRITICAL):

  • NeRF (Neural Radiance Fields)
  • Instant-NGP (fast NeRF)
  • 3D Gaussian Splatting (new SOTA)

Tasks (HIGH):

  • Point cloud classification
  • Point cloud segmentation
  • 3D object detection
  • Novel view synthesis

Use Cases

  • Autonomous driving (LIDAR)
  • Robotics
  • AR/VR
  • 3D reconstruction

Architecture

  • src/PointCloud/
  • src/NeuralRadianceFields/
  • Integration with existing vision models

Success Criteria

  • ModelNet40, ShapeNet benchmarks
  • Real-time rendering (Gaussian Splatting)
  • PSNR/SSIM metrics for NeRF

ooples avatar Nov 07 '25 03:11 ooples

Issue #399: Junior Developer Implementation Guide

3D AI Models (NeRF, PointNet, MeshCNN)

Table of Contents

  1. Understanding the Problem
  2. 3D Representation Fundamentals
  3. Architecture Overview
  4. Implementation Strategy
  5. Testing Strategy
  6. Step-by-Step Implementation Guide

Understanding the Problem

What Are We Building?

We're implementing support for 3D AI models that can:

  • 3D Object Classification: Recognize objects from 3D shapes (PointNet)
  • 3D Scene Reconstruction: Build 3D scenes from 2D images (NeRF)
  • 3D Shape Analysis: Process mesh structures (MeshCNN)
  • 3D Segmentation: Identify parts of 3D objects
  • Novel View Synthesis: Generate new viewpoints of scenes

Why 3D Models Are Special

3D data requires different representations than 2D images:

  1. Point clouds: Unordered sets of 3D points
  2. Meshes: Vertices, edges, and faces forming surfaces
  3. Voxels: 3D grids (like 3D pixels)
  4. Implicit functions: Neural fields representing surfaces
  5. Permutation invariance: Order of points shouldn't matter

Real-World Use Cases

  • Autonomous driving: Understanding 3D environment from LiDAR
  • Robotics: Grasping and manipulation of objects
  • AR/VR: Creating immersive 3D scenes
  • Medical imaging: CT/MRI scan analysis
  • Architecture: 3D building modeling
  • Gaming: Procedural 3D content generation

3D Representation Fundamentals

Understanding 3D Data Formats

1. Point Clouds

/// <summary>
/// Point cloud: collection of 3D points with optional features.
/// Shape: [num_points, 3+features]
/// </summary>
/// <remarks>
/// For Beginners:
/// A point cloud is a set of 3D points in space:
/// - Each point has (x, y, z) coordinates
/// - Optional: color (R, G, B), normal vector, intensity
/// - Unordered: [point1, point2, point3] same as [point3, point1, point2]
///
/// Example from LiDAR:
/// - Car scanner shoots laser rays
/// - Each ray returns a 3D point
/// - 10,000+ points per scan
/// - Points form the shape of objects
///
/// Challenges:
/// - Irregular: not a grid like images
/// - Unordered: permutation invariance required
/// - Sparse: empty space between points
/// </remarks>
public class PointCloud<T>
{
    // Shape: [num_points, channels]
    // channels: 3 for XYZ, 6 for XYZ+RGB, more for normals/features
    public Tensor<T> Points { get; set; } = new Tensor<T>(new[] { 0, 3 });

    public int NumPoints { get; set; }       // Total points
    public int Channels { get; set; }        // 3=XYZ, 6=XYZ+RGB, etc.
    public bool HasColor { get; set; }       // RGB available?
    public bool HasNormals { get; set; }     // Surface normals available?

    // Bounding box
    public (T minX, T maxX, T minY, T maxY, T minZ, T maxZ) Bounds { get; set; }

    /// <summary>
    /// Get XYZ coordinates only (first 3 channels).
    /// </summary>
    public Tensor<T> GetCoordinates()
    {
        var coords = new Tensor<T>(new[] { NumPoints, 3 });
        for (int i = 0; i < NumPoints; i++)
        {
            coords[i, 0] = Points[i, 0];  // X
            coords[i, 1] = Points[i, 1];  // Y
            coords[i, 2] = Points[i, 2];  // Z
        }
        return coords;
    }

    /// <summary>
    /// Get RGB colors (channels 3-5 if present).
    /// </summary>
    public Tensor<T>? GetColors()
    {
        if (!HasColor || Channels < 6)
            return null;

        var colors = new Tensor<T>(new[] { NumPoints, 3 });
        for (int i = 0; i < NumPoints; i++)
        {
            colors[i, 0] = Points[i, 3];  // R
            colors[i, 1] = Points[i, 4];  // G
            colors[i, 2] = Points[i, 5];  // B
        }
        return colors;
    }
}

2. Triangle Meshes

/// <summary>
/// Triangle mesh: vertices connected by triangular faces.
/// Common format: .obj, .stl, .ply files.
/// </summary>
/// <remarks>
/// For Beginners:
/// A mesh represents a 3D surface using:
/// - Vertices: 3D points (corners)
/// - Faces: Triangles connecting 3 vertices
/// - Edges: Lines between vertices
///
/// Example cube:
/// - 8 vertices (corners)
/// - 12 triangles (2 per face × 6 faces)
/// - 18 edges
///
/// Why triangles?
/// - Simplest polygon (always planar)
/// - Easy to render
/// - Standard in computer graphics
/// </remarks>
public class TriangleMesh<T>
{
    // Vertices: [num_vertices, 3] for XYZ coordinates
    public Tensor<T> Vertices { get; set; } = new Tensor<T>(new[] { 0, 3 });

    // Faces: [num_faces, 3] with vertex indices
    // Each face is [v1_idx, v2_idx, v3_idx]
    public Tensor<int> Faces { get; set; } = new Tensor<int>(new[] { 0, 3 });

    // Edges: [num_edges, 2] with vertex indices (derived from faces)
    public Tensor<int> Edges { get; set; } = new Tensor<int>(new[] { 0, 2 });

    // Optional: per-vertex normals (for smooth shading)
    public Tensor<T>? VertexNormals { get; set; }

    // Optional: per-vertex colors
    public Tensor<T>? VertexColors { get; set; }

    public int NumVertices => Vertices.Shape[0];
    public int NumFaces => Faces.Shape[0];
    public int NumEdges => Edges.Shape[0];

    /// <summary>
    /// Compute edges from faces (each triangle has 3 edges).
    /// </summary>
    public void ComputeEdges()
    {
        var edgeSet = new HashSet<(int, int)>();

        for (int f = 0; f < NumFaces; f++)
        {
            int v0 = Faces[f, 0];
            int v1 = Faces[f, 1];
            int v2 = Faces[f, 2];

            // Add edges (ensure v_min < v_max for uniqueness)
            AddEdge(edgeSet, v0, v1);
            AddEdge(edgeSet, v1, v2);
            AddEdge(edgeSet, v2, v0);
        }

        Edges = new Tensor<int>(new[] { edgeSet.Count, 2 });
        int idx = 0;
        foreach (var (v0, v1) in edgeSet)
        {
            Edges[idx, 0] = v0;
            Edges[idx, 1] = v1;
            idx++;
        }
    }

    private void AddEdge(HashSet<(int, int)> edges, int v0, int v1)
    {
        if (v0 > v1)
            (v0, v1) = (v1, v0);  // Ensure v0 < v1
        edges.Add((v0, v1));
    }

    /// <summary>
    /// Compute vertex normals (average of adjacent face normals).
    /// </summary>
    public void ComputeVertexNormals()
    {
        VertexNormals = new Tensor<T>(new[] { NumVertices, 3 });

        // Initialize to zero
        for (int v = 0; v < NumVertices; v++)
        {
            for (int d = 0; d < 3; d++)
            {
                VertexNormals[v, d] = (T)(object)0.0;
            }
        }

        // Accumulate face normals
        for (int f = 0; f < NumFaces; f++)
        {
            int v0 = Faces[f, 0];
            int v1 = Faces[f, 1];
            int v2 = Faces[f, 2];

            // Get vertices
            var p0 = GetVertex(v0);
            var p1 = GetVertex(v1);
            var p2 = GetVertex(v2);

            // Compute face normal: (p1-p0) × (p2-p0)
            var normal = CrossProduct(
                Subtract(p1, p0),
                Subtract(p2, p0));

            // Add to vertex normals
            for (int d = 0; d < 3; d++)
            {
                dynamic n = VertexNormals[v0, d];
                VertexNormals[v0, d] = (T)(object)(n + normal[d]);

                n = VertexNormals[v1, d];
                VertexNormals[v1, d] = (T)(object)(n + normal[d]);

                n = VertexNormals[v2, d];
                VertexNormals[v2, d] = (T)(object)(n + normal[d]);
            }
        }

        // Normalize
        for (int v = 0; v < NumVertices; v++)
        {
            double norm = 0;
            for (int d = 0; d < 3; d++)
            {
                double val = Convert.ToDouble(VertexNormals[v, d]);
                norm += val * val;
            }
            norm = Math.Sqrt(norm);

            if (norm > 1e-10)
            {
                for (int d = 0; d < 3; d++)
                {
                    double val = Convert.ToDouble(VertexNormals[v, d]);
                    VertexNormals[v, d] = (T)(object)(val / norm);
                }
            }
        }
    }

    private T[] GetVertex(int idx)
    {
        return new[]
        {
            Vertices[idx, 0],
            Vertices[idx, 1],
            Vertices[idx, 2]
        };
    }

    private T[] Subtract(T[] a, T[] b)
    {
        return new[]
        {
            (T)(object)(Convert.ToDouble(a[0]) - Convert.ToDouble(b[0])),
            (T)(object)(Convert.ToDouble(a[1]) - Convert.ToDouble(b[1])),
            (T)(object)(Convert.ToDouble(a[2]) - Convert.ToDouble(b[2]))
        };
    }

    private T[] CrossProduct(T[] a, T[] b)
    {
        double ax = Convert.ToDouble(a[0]);
        double ay = Convert.ToDouble(a[1]);
        double az = Convert.ToDouble(a[2]);
        double bx = Convert.ToDouble(b[0]);
        double by = Convert.ToDouble(b[1]);
        double bz = Convert.ToDouble(b[2]);

        return new[]
        {
            (T)(object)(ay * bz - az * by),
            (T)(object)(az * bx - ax * bz),
            (T)(object)(ax * by - ay * bx)
        };
    }
}

3. Voxel Grids

/// <summary>
/// Voxel grid: 3D grid of occupied/empty cells (like 3D pixels).
/// Shape: [depth, height, width] or [depth, height, width, channels]
/// </summary>
/// <remarks>
/// For Beginners:
/// Voxels are 3D pixels:
/// - Grid divides space into small cubes
/// - Each cube (voxel) is either filled or empty
/// - Like Minecraft blocks
///
/// Example: 32×32×32 voxel grid
/// - 32,768 voxels total
/// - Each voxel: 1 = occupied, 0 = empty
/// - Forms a 3D shape
///
/// Pros:
/// - Regular structure (easy to process with 3D CNNs)
/// - Simple representation
///
/// Cons:
/// - Memory intensive (32³ = 32,768 voxels)
/// - Fixed resolution
/// - Sparse (most voxels are empty)
/// </remarks>
public class VoxelGrid<T>
{
    // Shape: [depth, height, width] for binary occupancy
    // Or: [depth, height, width, channels] for features
    public Tensor<T> Grid { get; set; } = new Tensor<T>(new[] { 32, 32, 32 });

    public int Depth { get; set; }
    public int Height { get; set; }
    public int Width { get; set; }
    public int Channels { get; set; }  // 1 for binary, >1 for features

    // Real-world bounding box
    public (double minX, double maxX) BoundsX { get; set; }
    public (double minY, double maxY) BoundsY { get; set; }
    public (double minZ, double maxZ) BoundsZ { get; set; }

    public double VoxelSize { get; set; }  // Size of each voxel in world units

    /// <summary>
    /// Check if a voxel at (d, h, w) is occupied.
    /// </summary>
    public bool IsOccupied(int d, int h, int w)
    {
        if (d < 0 || d >= Depth || h < 0 || h >= Height || w < 0 || w >= Width)
            return false;

        double val = Convert.ToDouble(Grid[d, h, w]);
        return val > 0.5;
    }

    /// <summary>
    /// Convert 3D world coordinates to voxel indices.
    /// </summary>
    public (int d, int h, int w) WorldToVoxel(double x, double y, double z)
    {
        int d = (int)((z - BoundsZ.minZ) / VoxelSize);
        int h = (int)((y - BoundsY.minY) / VoxelSize);
        int w = (int)((x - BoundsX.minX) / VoxelSize);

        return (d, h, w);
    }

    /// <summary>
    /// Convert voxel indices to 3D world coordinates (center of voxel).
    /// </summary>
    public (double x, double y, double z) VoxelToWorld(int d, int h, int w)
    {
        double x = BoundsX.minX + (w + 0.5) * VoxelSize;
        double y = BoundsY.minY + (h + 0.5) * VoxelSize;
        double z = BoundsZ.minZ + (d + 0.5) * VoxelSize;

        return (x, y, z);
    }
}

4. Neural Radiance Fields (Implicit Representation)

/// <summary>
/// Neural Radiance Field (NeRF): implicit 3D representation.
/// Maps (x, y, z, theta, phi) → (r, g, b, density).
/// </summary>
/// <remarks>
/// For Beginners:
/// NeRF represents 3D scenes as a continuous function:
/// - Input: 3D position (x, y, z) + viewing direction (theta, phi)
/// - Output: Color (RGB) + density (opacity)
///
/// Instead of storing voxels or meshes, NeRF uses a neural network:
/// - Network learns the function
/// - Can query any point in 3D space
/// - Infinitely high resolution (continuous)
///
/// How it works:
/// 1. For each pixel in an image:
/// 2. Cast a ray through the pixel
/// 3. Sample points along the ray
/// 4. Query NeRF network at each point
/// 5. Composite colors/densities → pixel color
///
/// Applications:
/// - Novel view synthesis (new camera angles)
/// - 3D reconstruction from images
/// - Virtual tours
/// </remarks>
public class NeuralRadianceField<T>
{
    // Position encoding network
    private readonly PositionalEncoder<T> _posEncoder;

    // Direction encoding network
    private readonly PositionalEncoder<T> _dirEncoder;

    // MLP for density and features
    private readonly MultilayerPerceptron<T> _densityMLP;

    // MLP for RGB color
    private readonly MultilayerPerceptron<T> _colorMLP;

    public NeuralRadianceField(
        int posEncodingLevels = 10,
        int dirEncodingLevels = 4,
        int hiddenSize = 256,
        int numLayers = 8)
    {
        Guard.Positive(hiddenSize, nameof(hiddenSize));
        Guard.Positive(numLayers, nameof(numLayers));

        // Positional encoding for XYZ (higher frequency = finer details)
        _posEncoder = new PositionalEncoder<T>(
            inputDim: 3,  // XYZ
            numFrequencies: posEncodingLevels);

        // Positional encoding for viewing direction (lower frequency)
        _dirEncoder = new PositionalEncoder<T>(
            inputDim: 3,  // Direction vector
            numFrequencies: dirEncodingLevels);

        int posEncodedDim = 3 * 2 * posEncodingLevels;  // sin+cos for each frequency
        int dirEncodedDim = 3 * 2 * dirEncodingLevels;

        // MLP: encoded_pos → density + features
        _densityMLP = new MultilayerPerceptron<T>(
            inputSize: posEncodedDim,
            hiddenSizes: Enumerable.Repeat(hiddenSize, numLayers).ToArray(),
            outputSize: hiddenSize + 1,  // +1 for density
            activation: "relu");

        // MLP: features + encoded_dir → RGB
        _colorMLP = new MultilayerPerceptron<T>(
            inputSize: hiddenSize + dirEncodedDim,
            hiddenSizes: new[] { hiddenSize / 2 },
            outputSize: 3,  // RGB
            activation: "relu");
    }

    /// <summary>
    /// Query the radiance field at a 3D point with viewing direction.
    /// </summary>
    /// <param name="position">3D position (x, y, z).</param>
    /// <param name="direction">Viewing direction (normalized).</param>
    /// <returns>RGB color and density.</returns>
    public (Tensor<T> rgb, T density) Query(Tensor<T> position, Tensor<T> direction)
    {
        Guard.NotNull(position, nameof(position));
        Guard.NotNull(direction, nameof(direction));

        // position: [batch, 3]
        // direction: [batch, 3]

        // Step 1: Positional encoding
        var encodedPos = _posEncoder.Forward(position);
        var encodedDir = _dirEncoder.Forward(direction);

        // Step 2: Predict density and features from position
        var densityAndFeatures = _densityMLP.Forward(encodedPos);

        // Split: last channel is density, rest are features
        int batchSize = densityAndFeatures.Shape[0];
        int featureDim = densityAndFeatures.Shape[1] - 1;

        var features = new Tensor<T>(new[] { batchSize, featureDim });
        var density = new Tensor<T>(new[] { batchSize });

        for (int b = 0; b < batchSize; b++)
        {
            density[b] = densityAndFeatures[b, featureDim];  // Last channel

            for (int d = 0; d < featureDim; d++)
            {
                features[b, d] = densityAndFeatures[b, d];
            }
        }

        // Apply activation to density (ensure non-negative)
        density = ReLU(density);

        // Step 3: Predict RGB from features and viewing direction
        var combined = Concatenate(features, encodedDir);
        var rgb = _colorMLP.Forward(combined);

        // Apply sigmoid to RGB (ensure [0, 1] range)
        rgb = Sigmoid(rgb);

        return (rgb, density[0]);  // Simplified - return first batch item
    }

    private Tensor<T> ReLU(Tensor<T> x)
    {
        var result = x.Clone();
        for (int i = 0; i < x.Size; i++)
        {
            double val = Convert.ToDouble(x.Data[i]);
            result.Data[i] = (T)(object)Math.Max(0, val);
        }
        return result;
    }

    private Tensor<T> Sigmoid(Tensor<T> x)
    {
        var result = x.Clone();
        for (int i = 0; i < x.Size; i++)
        {
            double val = Convert.ToDouble(x.Data[i]);
            result.Data[i] = (T)(object)(1.0 / (1.0 + Math.Exp(-val)));
        }
        return result;
    }

    private Tensor<T> Concatenate(Tensor<T> a, Tensor<T> b)
    {
        // Concatenate along last dimension
        int batch = a.Shape[0];
        int dimA = a.Shape[1];
        int dimB = b.Shape[1];

        var result = new Tensor<T>(new[] { batch, dimA + dimB });

        for (int i = 0; i < batch; i++)
        {
            for (int j = 0; j < dimA; j++)
            {
                result[i, j] = a[i, j];
            }
            for (int j = 0; j < dimB; j++)
            {
                result[i, dimA + j] = b[i, j];
            }
        }

        return result;
    }
}

/// <summary>
/// Positional encoding: map continuous values to high-frequency features.
/// Used in NeRF to help network represent high-frequency details.
/// </summary>
public class PositionalEncoder<T>
{
    private readonly int _inputDim;
    private readonly int _numFrequencies;

    public PositionalEncoder(int inputDim, int numFrequencies)
    {
        Guard.Positive(inputDim, nameof(inputDim));
        Guard.Positive(numFrequencies, nameof(numFrequencies));

        _inputDim = inputDim;
        _numFrequencies = numFrequencies;
    }

    public Tensor<T> Forward(Tensor<T> x)
    {
        // x: [batch, input_dim]
        // Output: [batch, input_dim * 2 * num_frequencies]

        int batch = x.Shape[0];
        int outputDim = _inputDim * 2 * _numFrequencies;

        var encoded = new Tensor<T>(new[] { batch, outputDim });

        for (int b = 0; b < batch; b++)
        {
            int idx = 0;
            for (int d = 0; d < _inputDim; d++)
            {
                double val = Convert.ToDouble(x[b, d]);

                for (int freq = 0; freq < _numFrequencies; freq++)
                {
                    double frequency = Math.Pow(2, freq) * Math.PI;

                    // sin(2^freq * pi * x)
                    encoded[b, idx++] = (T)(object)Math.Sin(frequency * val);

                    // cos(2^freq * pi * x)
                    encoded[b, idx++] = (T)(object)Math.Cos(frequency * val);
                }
            }
        }

        return encoded;
    }
}

Architecture Overview

Model Taxonomy

3D AI Models
├── Point Cloud Models (Unordered points)
│   ├── PointNet (Permutation-invariant classification)
│   ├── PointNet++ (Hierarchical feature learning)
│   ├── DGCNN (Dynamic Graph CNN)
│   └── Point Transformer
│
├── Mesh Models (Vertices + faces)
│   ├── MeshCNN (Convolutions on edges)
│   ├── MeshNet (Face-based features)
│   └── SpiralNet (Spiral convolutions)
│
├── Voxel Models (3D grids)
│   ├── 3D CNN (Standard convolutions)
│   ├── VoxNet (Voxel-based classification)
│   └── OctNet (Hierarchical octrees)
│
└── Implicit Models (Neural fields)
    ├── NeRF (Neural Radiance Fields)
    ├── DeepSDF (Signed Distance Functions)
    └── Occupancy Networks

PointNet Architecture

/// <summary>
/// PointNet: Deep learning on point sets for 3D classification and segmentation.
/// Key innovation: Permutation invariance via max pooling.
/// </summary>
/// <remarks>
/// For Beginners:
/// PointNet processes unordered point clouds directly:
///
/// Problem: Point order shouldn't matter
/// - [p1, p2, p3] should give same result as [p3, p1, p2]
///
/// Solution: Symmetric function (max pooling)
/// 1. Transform each point independently (shared MLP)
/// 2. Pool features across all points (max pooling)
/// 3. Global feature is permutation-invariant
///
/// Architecture:
/// Input: [batch, num_points, 3] (XYZ coordinates)
/// → Input Transform (learn optimal rotation)
/// → Shared MLP: [3] → [64] → [64]
/// → Feature Transform (align features)
/// → Shared MLP: [64] → [128] → [1024]
/// → Max Pool: [batch, num_points, 1024] → [batch, 1024]
/// → Classification MLP: [1024] → [512] → [256] → [num_classes]
///
/// Why it works:
/// - max(f(p1), f(p2), ..., f(pN)) is same for any order
/// - Each point processed independently (shared weights)
/// - Global context from max pooling
/// </remarks>
public class PointNetModel<T> : IPointCloudModel<T>
{
    private readonly PointNetConfig _config;
    private readonly TransformNet<T> _inputTransform;
    private readonly SharedMLP<T> _mlp1;
    private readonly TransformNet<T> _featureTransform;
    private readonly SharedMLP<T> _mlp2;
    private readonly MaxPooling<T> _globalPooling;
    private readonly MultilayerPerceptron<T> _classificationHead;

    public PointNetModel(PointNetConfig config)
    {
        Guard.NotNull(config, nameof(config));

        _config = config;

        // Input transform: learn 3×3 rotation matrix
        _inputTransform = new TransformNet<T>(
            inputDim: 3,
            outputDim: 3);

        // First MLP: 3 → 64 → 64
        _mlp1 = new SharedMLP<T>(
            inputSize: 3,
            hiddenSizes: new[] { 64, 64 },
            activation: "relu");

        // Feature transform: learn 64×64 transformation
        _featureTransform = new TransformNet<T>(
            inputDim: 64,
            outputDim: 64);

        // Second MLP: 64 → 128 → 1024
        _mlp2 = new SharedMLP<T>(
            inputSize: 64,
            hiddenSizes: new[] { 128, 1024 },
            activation: "relu");

        // Max pooling over points
        _globalPooling = new MaxPooling<T>(axis: 1);  // Pool over num_points

        // Classification head: 1024 → 512 → 256 → num_classes
        _classificationHead = new MultilayerPerceptron<T>(
            inputSize: 1024,
            hiddenSizes: new[] { 512, 256 },
            outputSize: config.NumClasses,
            activation: "relu");
    }

    public PointCloudOutput<T> Forward(PointCloud<T> pointCloud)
    {
        Guard.NotNull(pointCloud, nameof(pointCloud));

        // Get coordinates: [batch, num_points, 3]
        var points = pointCloud.Points;

        // Step 1: Input transform (align input)
        var transformMatrix = _inputTransform.Forward(points);
        var transformedPoints = ApplyTransform(points, transformMatrix);

        // Step 2: First MLP (point-wise features)
        var features1 = _mlp1.Forward(transformedPoints);
        // features1: [batch, num_points, 64]

        // Step 3: Feature transform (align features)
        var featureMatrix = _featureTransform.Forward(features1);
        var transformedFeatures = ApplyTransform(features1, featureMatrix);

        // Step 4: Second MLP (higher-level features)
        var features2 = _mlp2.Forward(transformedFeatures);
        // features2: [batch, num_points, 1024]

        // Step 5: Global max pooling (permutation-invariant)
        var globalFeatures = _globalPooling.Forward(features2);
        // globalFeatures: [batch, 1024]

        // Step 6: Classification
        var logits = _classificationHead.Forward(globalFeatures);

        return new PointCloudOutput<T>
        {
            Logits = logits,
            GlobalFeatures = globalFeatures,
            PointFeatures = features2
        };
    }

    private Tensor<T> ApplyTransform(Tensor<T> points, Tensor<T> matrix)
    {
        // points: [batch, num_points, dim]
        // matrix: [batch, dim, dim]
        // result: [batch, num_points, dim]

        int batch = points.Shape[0];
        int numPoints = points.Shape[1];
        int dim = points.Shape[2];

        var result = new Tensor<T>(points.Shape);

        for (int b = 0; b < batch; b++)
        {
            for (int p = 0; p < numPoints; p++)
            {
                for (int i = 0; i < dim; i++)
                {
                    dynamic sum = (T)(object)0.0;
                    for (int j = 0; j < dim; j++)
                    {
                        sum += points[b, p, j] * matrix[b, i, j];
                    }
                    result[b, p, i] = (T)(object)sum;
                }
            }
        }

        return result;
    }
}

public class PointNetConfig
{
    public int NumClasses { get; set; } = 40;  // ModelNet40
    public bool UseFeatureTransform { get; set; } = true;
}

TransformNet (T-Net)

/// <summary>
/// T-Net: Learns transformation matrix to align inputs/features.
/// Ensures invariance to geometric transformations.
/// </summary>
public class TransformNet<T>
{
    private readonly int _inputDim;
    private readonly int _outputDim;
    private readonly SharedMLP<T> _mlp;
    private readonly MaxPooling<T> _pooling;
    private readonly MultilayerPerceptron<T> _fcLayers;

    public TransformNet(int inputDim, int outputDim)
    {
        Guard.Positive(inputDim, nameof(inputDim));
        Guard.Positive(outputDim, nameof(outputDim));

        _inputDim = inputDim;
        _outputDim = outputDim;

        // Shared MLP for point-wise features
        _mlp = new SharedMLP<T>(
            inputSize: inputDim,
            hiddenSizes: new[] { 64, 128, 1024 },
            activation: "relu");

        // Max pooling over points
        _pooling = new MaxPooling<T>(axis: 1);

        // FC layers to predict transformation matrix
        _fcLayers = new MultilayerPerceptron<T>(
            inputSize: 1024,
            hiddenSizes: new[] { 512, 256 },
            outputSize: outputDim * outputDim,
            activation: "relu");
    }

    public Tensor<T> Forward(Tensor<T> points)
    {
        // points: [batch, num_points, input_dim]

        // Extract features
        var features = _mlp.Forward(points);
        // features: [batch, num_points, 1024]

        // Global pooling
        var globalFeatures = _pooling.Forward(features);
        // globalFeatures: [batch, 1024]

        // Predict transformation matrix
        var matrixFlat = _fcLayers.Forward(globalFeatures);
        // matrixFlat: [batch, output_dim * output_dim]

        // Reshape to matrix and add identity
        int batch = matrixFlat.Shape[0];
        var matrix = new Tensor<T>(new[] { batch, _outputDim, _outputDim });

        for (int b = 0; b < batch; b++)
        {
            for (int i = 0; i < _outputDim; i++)
            {
                for (int j = 0; j < _outputDim; j++)
                {
                    int idx = i * _outputDim + j;
                    double val = Convert.ToDouble(matrixFlat[b, idx]);

                    // Add identity matrix (helps training stability)
                    if (i == j)
                        val += 1.0;

                    matrix[b, i, j] = (T)(object)val;
                }
            }
        }

        return matrix;
    }
}

MeshCNN Architecture

/// <summary>
/// MeshCNN: Convolutional neural network for triangle meshes.
/// Operates on edges (unique to each mesh architecture).
/// </summary>
/// <remarks>
/// For Beginners:
/// MeshCNN processes meshes using edge-based convolutions:
///
/// Key idea: Edges are the fundamental unit
/// - Each edge connects two triangles
/// - Edge features: dihedral angle, edge length, etc.
/// - Convolution: aggregate features from neighboring edges
///
/// Edge pooling (like max pooling for images):
/// - Collapse edges to reduce mesh complexity
/// - Similar to image downsampling
/// - Maintains mesh connectivity
///
/// Architecture:
/// Input: Mesh with N edges
/// → Edge feature extraction (5 features per edge)
/// → Mesh Conv blocks (learn edge features)
/// → Edge pooling (reduce from N to N/2 edges)
/// → More conv blocks
/// → Global pooling
/// → Classification
///
/// Applications:
/// - 3D shape classification
/// - Mesh segmentation (label each face)
/// - Shape correspondence
/// </remarks>
public class MeshCNNModel<T> : IMeshModel<T>
{
    private readonly MeshCNNConfig _config;
    private readonly EdgeFeatureExtractor<T> _featureExtractor;
    private readonly List<MeshConvBlock<T>> _convBlocks;
    private readonly List<EdgePooling<T>> _poolingLayers;
    private readonly GlobalPooling<T> _globalPooling;
    private readonly MultilayerPerceptron<T> _classifier;

    public MeshCNNModel(MeshCNNConfig config)
    {
        Guard.NotNull(config, nameof(config));

        _config = config;

        // Extract initial edge features
        _featureExtractor = new EdgeFeatureExtractor<T>();

        // Convolution and pooling blocks
        _convBlocks = new List<MeshConvBlock<T>>();
        _poolingLayers = new List<EdgePooling<T>>();

        int currentChannels = 5;  // Initial edge features
        foreach (int channels in config.ConvChannels)
        {
            _convBlocks.Add(new MeshConvBlock<T>(
                inChannels: currentChannels,
                outChannels: channels));

            _poolingLayers.Add(new EdgePooling<T>(
                targetReduction: 0.5));  // Reduce by 50%

            currentChannels = channels;
        }

        // Global pooling over all edges
        _globalPooling = new GlobalPooling<T>();

        // Classification head
        _classifier = new MultilayerPerceptron<T>(
            inputSize: currentChannels,
            hiddenSizes: new[] { 256, 128 },
            outputSize: config.NumClasses,
            activation: "relu");
    }

    public MeshOutput<T> Forward(TriangleMesh<T> mesh)
    {
        Guard.NotNull(mesh, nameof(mesh));

        // Step 1: Extract edge features
        var edgeFeatures = _featureExtractor.Extract(mesh);
        // edgeFeatures: [num_edges, 5]

        var currentMesh = mesh;
        var currentFeatures = edgeFeatures;

        // Step 2: Apply conv and pooling blocks
        for (int i = 0; i < _convBlocks.Count; i++)
        {
            // Convolution
            currentFeatures = _convBlocks[i].Forward(
                currentMesh,
                currentFeatures);

            // Pooling (reduces mesh complexity)
            (currentMesh, currentFeatures) = _poolingLayers[i].Forward(
                currentMesh,
                currentFeatures);
        }

        // Step 3: Global pooling
        var globalFeatures = _globalPooling.Forward(currentFeatures);
        // globalFeatures: [1, channels]

        // Step 4: Classification
        var logits = _classifier.Forward(globalFeatures);

        return new MeshOutput<T>
        {
            Logits = logits,
            GlobalFeatures = globalFeatures,
            EdgeFeatures = currentFeatures
        };
    }
}

public class MeshCNNConfig
{
    public int[] ConvChannels { get; set; } = new[] { 32, 64, 128, 256 };
    public int NumClasses { get; set; } = 30;  // SHREC dataset
}

EdgeFeatureExtractor

/// <summary>
/// Extracts geometric features from mesh edges.
/// Features: dihedral angle, edge length, edge ratios, etc.
/// </summary>
public class EdgeFeatureExtractor<T>
{
    public Tensor<T> Extract(TriangleMesh<T> mesh)
    {
        Guard.NotNull(mesh, nameof(mesh));

        if (mesh.Edges.Shape[0] == 0)
        {
            mesh.ComputeEdges();
        }

        int numEdges = mesh.NumEdges;

        // 5 features per edge:
        // 1. Dihedral angle (angle between adjacent faces)
        // 2. Edge length
        // 3. Edge length ratio to adjacent edges
        // 4-5. Additional geometric features
        var features = new Tensor<T>(new[] { numEdges, 5 });

        for (int e = 0; e < numEdges; e++)
        {
            int v0 = mesh.Edges[e, 0];
            int v1 = mesh.Edges[e, 1];

            // Feature 1: Dihedral angle
            double dihedralAngle = ComputeDihedralAngle(mesh, v0, v1);
            features[e, 0] = (T)(object)dihedralAngle;

            // Feature 2: Edge length
            double edgeLength = ComputeEdgeLength(mesh, v0, v1);
            features[e, 1] = (T)(object)edgeLength;

            // Features 3-5: Additional geometric properties
            // (Simplified - real implementation would compute more features)
            features[e, 2] = (T)(object)1.0;
            features[e, 3] = (T)(object)1.0;
            features[e, 4] = (T)(object)1.0;
        }

        return features;
    }

    private double ComputeDihedralAngle(TriangleMesh<T> mesh, int v0, int v1)
    {
        // Find two faces sharing this edge
        // Compute normal vectors of both faces
        // Dihedral angle = angle between normals

        // Simplified - real implementation would find adjacent faces
        return Math.PI / 4;  // Placeholder
    }

    private double ComputeEdgeLength(TriangleMesh<T> mesh, int v0, int v1)
    {
        double dx = Convert.ToDouble(mesh.Vertices[v0, 0]) -
                    Convert.ToDouble(mesh.Vertices[v1, 0]);
        double dy = Convert.ToDouble(mesh.Vertices[v0, 1]) -
                    Convert.ToDouble(mesh.Vertices[v1, 1]);
        double dz = Convert.ToDouble(mesh.Vertices[v0, 2]) -
                    Convert.ToDouble(mesh.Vertices[v1, 2]);

        return Math.Sqrt(dx * dx + dy * dy + dz * dz);
    }
}

Implementation Strategy

Project Structure

src/
├── ThreeD/
│   ├── IPointCloudModel.cs
│   ├── IMeshModel.cs
│   ├── PointCloud.cs
│   ├── TriangleMesh.cs
│   ├── VoxelGrid.cs
│   └── Preprocessing/
│       ├── PointCloudNormalizer.cs
│       ├── MeshSimplifier.cs
│       └── VoxelConverter.cs
│
├── ThreeD/Models/
│   ├── PointNet/
│   │   ├── PointNetModel.cs
│   │   ├── PointNetConfig.cs
│   │   ├── TransformNet.cs
│   │   ├── SharedMLP.cs
│   │   └── PointNetProcessor.cs
│   │
│   ├── MeshCNN/
│   │   ├── MeshCNNModel.cs
│   │   ├── MeshCNNConfig.cs
│   │   ├── MeshConvBlock.cs
│   │   ├── EdgePooling.cs
│   │   └── EdgeFeatureExtractor.cs
│   │
│   └── NeRF/
│       ├── NeRFModel.cs
│       ├── NeRFConfig.cs
│       ├── VolumeRenderer.cs
│       ├── RayCaster.cs
│       └── PositionalEncoder.cs
│
└── ThreeD/Utils/
    ├── PointCloudIO.cs (Load/save .ply, .pcd)
    ├── MeshIO.cs (Load/save .obj, .stl)
    ├── GeometricUtils.cs
    └── Visualization.cs

Testing Strategy

Unit Tests

namespace AiDotNetTests.ThreeD;

public class PointCloudTests
{
    [Fact]
    public void PointCloud_GetCoordinates_ReturnsXYZ()
    {
        // Arrange
        var pointCloud = CreateTestPointCloud(numPoints: 100);

        // Act
        var coords = pointCloud.GetCoordinates();

        // Assert
        Assert.NotNull(coords);
        Assert.Equal(100, coords.Shape[0]);
        Assert.Equal(3, coords.Shape[1]);  // XYZ
    }

    [Fact]
    public void PointNet_ProcessPointCloud_ReturnsLogits()
    {
        // Arrange
        var config = new PointNetConfig { NumClasses = 40 };
        var model = new PointNetModel<double>(config);

        var pointCloud = CreateTestPointCloud(numPoints: 1024);

        // Act
        var output = model.Forward(pointCloud);

        // Assert
        Assert.NotNull(output.Logits);
        Assert.Equal(40, output.Logits.Shape[1]);  // 40 classes
    }

    private PointCloud<double> CreateTestPointCloud(int numPoints)
    {
        var points = new Tensor<double>(new[] { numPoints, 3 });

        // Generate random points
        var random = new Random();
        for (int i = 0; i < numPoints; i++)
        {
            points[i, 0] = random.NextDouble();  // X
            points[i, 1] = random.NextDouble();  // Y
            points[i, 2] = random.NextDouble();  // Z
        }

        return new PointCloud<double>
        {
            Points = points,
            NumPoints = numPoints,
            Channels = 3
        };
    }
}

Step-by-Step Implementation Guide

Phase 1: Core 3D Infrastructure (8 hours)

AC 1.1: 3D Data Structures

Files:

  • src/ThreeD/PointCloud.cs
  • src/ThreeD/TriangleMesh.cs
  • src/ThreeD/VoxelGrid.cs

AC 1.2: Preprocessing

Files:

  • src/ThreeD/Preprocessing/PointCloudNormalizer.cs
  • src/ThreeD/Preprocessing/MeshSimplifier.cs

Tests: tests/ThreeD/PreprocessingTests.cs

Phase 2: PointNet Implementation (12 hours)

AC 2.1: Transform Networks

File: src/ThreeD/Models/PointNet/TransformNet.cs

AC 2.2: Shared MLP

File: src/ThreeD/Models/PointNet/SharedMLP.cs

AC 2.3: Complete PointNet

File: src/ThreeD/Models/PointNet/PointNetModel.cs

Tests: tests/ThreeD/Models/PointNet/PointNetTests.cs

Phase 3: MeshCNN Implementation (14 hours)

AC 3.1: Edge Features

File: src/ThreeD/Models/MeshCNN/EdgeFeatureExtractor.cs

AC 3.2: Mesh Convolutions

File: src/ThreeD/Models/MeshCNN/MeshConvBlock.cs

AC 3.3: Edge Pooling

File: src/ThreeD/Models/MeshCNN/EdgePooling.cs

AC 3.4: Complete MeshCNN

File: src/ThreeD/Models/MeshCNN/MeshCNNModel.cs

Tests: tests/ThreeD/Models/MeshCNN/MeshCNNTests.cs

Phase 4: NeRF Implementation (16 hours)

AC 4.1: Positional Encoding

File: src/ThreeD/Models/NeRF/PositionalEncoder.cs

AC 4.2: Volume Rendering

File: src/ThreeD/Models/NeRF/VolumeRenderer.cs

AC 4.3: Ray Casting

File: src/ThreeD/Models/NeRF/RayCaster.cs

AC 4.4: Complete NeRF

File: src/ThreeD/Models/NeRF/NeRFModel.cs

Tests: tests/ThreeD/Models/NeRF/NeRFTests.cs

Phase 5: Documentation (4 hours)

AC 5.1: XML Documentation

Complete API documentation.

AC 5.2: Usage Examples

Create examples for 3D classification, mesh processing, novel view synthesis.

Checklist Summary

Phase 1: Core Infrastructure (8 hours)

  • [ ] Implement PointCloud, TriangleMesh, VoxelGrid
  • [ ] Implement preprocessing utilities
  • [ ] Write unit tests
  • [ ] Test with real 3D data files

Phase 2: PointNet (12 hours)

  • [ ] Implement TransformNet
  • [ ] Implement SharedMLP
  • [ ] Create PointNetModel
  • [ ] Write integration tests
  • [ ] Test on ModelNet40

Phase 3: MeshCNN (14 hours)

  • [ ] Implement edge feature extraction
  • [ ] Implement mesh convolutions
  • [ ] Implement edge pooling
  • [ ] Create MeshCNNModel
  • [ ] Write integration tests
  • [ ] Test on SHREC dataset

Phase 4: NeRF (16 hours)

  • [ ] Implement positional encoding
  • [ ] Implement volume rendering
  • [ ] Implement ray casting
  • [ ] Create NeRFModel
  • [ ] Write integration tests
  • [ ] Test novel view synthesis

Phase 5: Documentation (4 hours)

  • [ ] Add XML documentation
  • [ ] Create usage examples
  • [ ] Write performance benchmarks

Total Estimated Time: 54 hours

Success Criteria

  1. PointNet: Achieves >85% accuracy on ModelNet40
  2. MeshCNN: Segments meshes accurately
  3. NeRF: Renders novel views with high quality
  4. Tests: 80%+ coverage
  5. Performance: Real-time or near real-time
  6. Documentation: Complete XML docs and examples

Common Pitfalls

Pitfall 1: Ignoring Permutation Invariance

Problem: Point order affects results. Solution: Use symmetric functions (max pooling).

Pitfall 2: Memory Issues with Large Meshes

Problem: Millions of vertices. Solution: Mesh simplification, edge pooling.

Pitfall 3: Slow NeRF Rendering

Problem: Querying network for every ray sample. Solution: Hierarchical sampling, caching.

Resources

ooples avatar Nov 07 '25 04:11 ooples