Advanced Perception (LiDAR, Liquid Neural Networks, Vision Transformers) - CSU083 | Shoolini University

Advanced Perception (LiDAR, Liquid Neural Networks, Vision Transformers)

1. Prerequisites

To understand advanced perception techniques like LiDAR, Liquid Neural Networks, and Vision Transformers, the following foundational concepts are required:

1.1 Mathematics & Linear Algebra

1.2 Machine Learning & Deep Learning

1.3 Computer Vision & Image Processing

1.4 Robotics & Autonomous Systems

1.5 Data Structures & Algorithms

2. Core Concepts of Advanced Perception

2.1 LiDAR (Light Detection and Ranging)

LiDAR is a remote sensing technology that uses laser pulses to measure distances and create 3D maps.

2.2 Liquid Neural Networks (LNNs)

Liquid Neural Networks are biologically inspired neural networks where neuron dynamics continuously evolve over time.

2.3 Vision Transformers (ViTs)

Vision Transformers apply Transformer architectures to images instead of sequential text.

3. Why Do These Algorithms Exist?

3.1 Autonomous Vehicles

3.2 Robotics & Industrial Automation

3.3 Medical Imaging & Healthcare

4. When Should You Use It?

4.1 When High-Precision Depth Perception is Required

Use LiDAR when depth estimation and 3D mapping are necessary, such as in autonomous driving.

4.2 When Handling Complex Time-Series Data

Use Liquid Neural Networks for adaptive learning in unpredictable environments, such as financial markets and autonomous systems.

4.3 When Handling Large-Scale Image Processing Tasks

Use Vision Transformers when CNNs struggle with long-range dependencies in images, such as high-resolution medical scans and satellite imagery.

5. How Do They Compare to Alternatives?

5.1 LiDAR vs. Cameras vs. Radar

Technology Strengths Weaknesses
LiDAR Highly accurate depth perception, robust in low-light conditions. Expensive, struggles in adverse weather.
Cameras Rich color and texture information, cost-effective. Poor depth estimation, bad performance in low-light.
Radar Works in all weather conditions, long-range sensing. Lower resolution compared to LiDAR.

5.2 Liquid Neural Networks vs. Traditional Neural Networks

Model Strengths Weaknesses
Liquid Neural Networks Highly adaptive, excels in real-time decision-making. Computationally expensive to train.
Traditional Neural Networks Well-optimized for static datasets. Struggles with dynamic, time-varying data.

5.3 Vision Transformers vs. Convolutional Neural Networks

Model Strengths Weaknesses
Vision Transformers Better long-range dependency capture, state-of-the-art accuracy. Computationally intensive, requires large datasets.
CNNs Efficient on small datasets, well-established. Struggles with long-range dependencies.

6. Basic Implementation

6.1 LiDAR Point Cloud Processing (Python + Open3D)

The following Python implementation reads a LiDAR point cloud and visualizes it using Open3D.


import open3d as o3d
import numpy as np

# Load a sample point cloud file
point_cloud = o3d.io.read_point_cloud("sample.pcd")

# Visualize the point cloud
o3d.visualization.draw_geometries([point_cloud])

Dry Run: Given a sample point cloud file sample.pcd:

6.2 Liquid Neural Network for Time-Series Prediction

Below is a basic PyTorch implementation of a Liquid Neural Network.


import torch
import torch.nn as nn
import torch.optim as optim

class LiquidNeuralNetwork(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(LiquidNeuralNetwork, self).__init__()
        self.hidden = nn.Linear(input_size, hidden_size)
        self.output = nn.Linear(hidden_size, output_size)
    
    def forward(self, x):
        x = torch.tanh(self.hidden(x))  # Non-linear dynamics
        return self.output(x)

# Sample Data
input_tensor = torch.tensor([[0.5]], dtype=torch.float32)
model = LiquidNeuralNetwork(1, 5, 1)
output = model(input_tensor)

print(output)  # Output prediction

Dry Run: Given an input of 0.5:

6.3 Vision Transformer (ViT) for Image Classification

A basic Vision Transformer (ViT) model using Hugging Face Transformers.


from transformers import ViTForImageClassification, ViTFeatureExtractor
from PIL import Image
import torch

# Load a pre-trained Vision Transformer model
model = ViTForImageClassification.from_pretrained("google/vit-base-patch16-224")
feature_extractor = ViTFeatureExtractor.from_pretrained("google/vit-base-patch16-224")

# Load and preprocess an image
image = Image.open("sample_image.jpg").convert("RGB")
inputs = feature_extractor(images=image, return_tensors="pt")

# Perform inference
with torch.no_grad():
    outputs = model(**inputs)

# Print the predicted label
predicted_class = outputs.logits.argmax(-1).item()
print(f"Predicted class: {predicted_class}")

Dry Run: Given an image sample_image.jpg:

8. Time & Space Complexity Analysis

8.1 LiDAR Point Cloud Processing Complexity

Space Complexity

8.2 Liquid Neural Networks Complexity

Space Complexity

8.3 Vision Transformers Complexity

Space Complexity

9. How Space Consumption Changes with Input Size

9.1 LiDAR Space Growth

9.2 Liquid Neural Networks Space Growth

9.3 Vision Transformers Space Growth

10. Trade-offs in Advanced Perception

10.1 LiDAR vs. Camera vs. Radar

Method Pros Cons
LiDAR High accuracy, great for 3D mapping. Expensive, weather-sensitive.
Camera Color and texture information. Poor depth perception, fails in low light.
Radar Works in all weather conditions. Lower resolution compared to LiDAR.

10.2 Liquid Neural Networks vs. Standard RNNs

Model Pros Cons
Liquid Neural Networks Adaptive, memory-efficient for dynamic inputs. Slower training, needs specialized tuning.
Recurrent Neural Networks (RNNs) Well-established, optimized for sequential data. Struggles with long-term dependencies.

10.3 Vision Transformers vs. Convolutional Neural Networks

Model Pros Cons
Vision Transformers Better long-range dependency capture, scalable. Computationally expensive.
CNNs Efficient on small datasets, low-cost. Struggles with global context.

11. Optimizations & Variants

11.1 LiDAR Optimizations

Common Optimizations
Variants

11.2 Liquid Neural Networks Optimizations

Common Optimizations
Variants

11.3 Vision Transformers (ViTs) Optimizations

Common Optimizations
Variants

12. Iterative vs. Recursive Implementations

12.1 LiDAR Point Cloud Processing

Iterative Implementation (Efficient)

import open3d as o3d

# Load and process LiDAR data iteratively
def process_lidar(file):
    point_cloud = o3d.io.read_point_cloud(file)
    downsampled = point_cloud.voxel_down_sample(voxel_size=0.05)  # Iterative downsampling
    return downsampled

processed = process_lidar("sample.pcd")
o3d.visualization.draw_geometries([processed])
Recursive Implementation (Inefficient for Large Data)

def recursive_downsample(point_cloud, depth):
    if depth == 0:
        return point_cloud
    return recursive_downsample(point_cloud.voxel_down_sample(0.05), depth - 1)

point_cloud = o3d.io.read_point_cloud("sample.pcd")
processed = recursive_downsample(point_cloud, 3)
o3d.visualization.draw_geometries([processed])
Efficiency Comparison

12.2 Liquid Neural Networks

Iterative Implementation

import torch
import torch.nn as nn

class LiquidNN(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(LiquidNN, self).__init__()
        self.hidden = nn.Linear(input_size, hidden_size)
        self.output = nn.Linear(hidden_size, output_size)

    def forward(self, x):
        for _ in range(5):  # Iterative updates
            x = torch.tanh(self.hidden(x))
        return self.output(x)

model = LiquidNN(1, 5, 1)
output = model(torch.tensor([[0.5]]))
print(output)
Recursive Implementation

def recursive_forward(model, x, depth):
    if depth == 0:
        return model.output(x)
    x = torch.tanh(model.hidden(x))
    return recursive_forward(model, x, depth - 1)

output = recursive_forward(model, torch.tensor([[0.5]]), 5)
print(output)
Efficiency Comparison

12.3 Vision Transformers

Iterative Implementation (Efficient)

from transformers import ViTForImageClassification, ViTFeatureExtractor
from PIL import Image
import torch

model = ViTForImageClassification.from_pretrained("google/vit-base-patch16-224")
feature_extractor = ViTFeatureExtractor.from_pretrained("google/vit-base-patch16-224")

image = Image.open("sample_image.jpg").convert("RGB")
inputs = feature_extractor(images=image, return_tensors="pt")

with torch.no_grad():
    for _ in range(3):  # Iterative forward passes
        outputs = model(**inputs)

print(outputs.logits.argmax(-1).item())
Recursive Implementation (Inefficient)

def recursive_forward(model, inputs, depth):
    if depth == 0:
        return model(**inputs)
    return recursive_forward(model, inputs, depth - 1)

output = recursive_forward(model, inputs, 3)
print(output.logits.argmax(-1).item())
Efficiency Comparison

13. Edge Cases & Failure Handling

13.1 Common Pitfalls and Edge Cases

LiDAR (Light Detection and Ranging)
Liquid Neural Networks
Vision Transformers (ViTs)

14. Test Cases to Verify Correctness

14.1 LiDAR Testing

Test Case 1: Noisy Data Handling

import open3d as o3d
import numpy as np

# Create synthetic noisy point cloud
def test_noise_removal():
    noisy_points = np.random.rand(1000, 3) * 100  # Random noise
    pcd = o3d.geometry.PointCloud()
    pcd.points = o3d.utility.Vector3dVector(noisy_points)

    # Apply statistical outlier removal
    filtered_pcd, _ = pcd.remove_statistical_outlier(nb_neighbors=20, std_ratio=2.0)

    assert len(filtered_pcd.points) < len(pcd.points), "Noise filtering failed"

test_noise_removal()

14.2 Liquid Neural Networks Testing

Test Case 2: Gradient Stability

import torch

# Model with liquid neurons
class LiquidNN(torch.nn.Module):
    def __init__(self):
        super().__init__()
        self.hidden = torch.nn.Linear(1, 10)
        self.output = torch.nn.Linear(10, 1)

    def forward(self, x):
        return self.output(torch.tanh(self.hidden(x)))

# Test stability of gradients
def test_gradient_stability():
    model = LiquidNN()
    input_tensor = torch.tensor([[0.5]], dtype=torch.float32, requires_grad=True)
    
    output = model(input_tensor)
    output.backward()
    
    assert torch.all(input_tensor.grad.abs() < 10), "Unstable gradient detected"

test_gradient_stability()

14.3 Vision Transformer Testing

Test Case 3: Small Input Handling

from transformers import ViTForImageClassification, ViTFeatureExtractor
from PIL import Image
import torch

# Load model
model = ViTForImageClassification.from_pretrained("google/vit-base-patch16-224")
feature_extractor = ViTFeatureExtractor.from_pretrained("google/vit-base-patch16-224")

# Create tiny image
def test_small_image():
    img = Image.new("RGB", (10, 10), (255, 255, 255))  # Very small image
    inputs = feature_extractor(images=img, return_tensors="pt")

    try:
        outputs = model(**inputs)
    except Exception as e:
        assert "size mismatch" in str(e), "Small image handling failed"

test_small_image()

15. Real-World Failure Scenarios

15.1 LiDAR Failures

15.2 Liquid Neural Network Failures

15.3 Vision Transformer Failures

16. Real-World Applications & Industry Use Cases

16.1 LiDAR Applications

16.2 Liquid Neural Network Applications

16.3 Vision Transformer Applications

17. Open-Source Implementations

17.1 LiDAR Open-Source Libraries

17.2 Liquid Neural Network Open-Source Implementations

17.3 Vision Transformer Open-Source Implementations

18. Practical Project: Object Detection using LiDAR & Vision Transformers

18.1 Project Overview

This project integrates LiDAR with a Vision Transformer to detect objects in an outdoor environment, such as pedestrians and vehicles.

18.2 Implementation Steps

  1. Capture 3D point cloud data using LiDAR.
  2. Use Open3D to preprocess the point cloud (filter noise and segment objects).
  3. Capture a 2D image of the same scene.
  4. Use a Vision Transformer (ViT) to classify objects in the 2D image.
  5. Fuse both modalities to improve object detection.

18.3 Code Implementation

Step 1: Load & Preprocess LiDAR Data

import open3d as o3d
import numpy as np

# Load LiDAR point cloud
point_cloud = o3d.io.read_point_cloud("sample.pcd")

# Downsample to reduce noise
downsampled_pcd = point_cloud.voxel_down_sample(voxel_size=0.05)

# Segment objects
plane_model, inliers = downsampled_pcd.segment_plane(distance_threshold=0.02, ransac_n=3, num_iterations=1000)
segmented_objects = downsampled_pcd.select_by_index(inliers, invert=True)

# Visualize results
o3d.visualization.draw_geometries([segmented_objects])
Step 2: Classify Objects using Vision Transformers

from transformers import ViTFeatureExtractor, ViTForImageClassification
from PIL import Image
import torch

# Load pre-trained Vision Transformer
model = ViTForImageClassification.from_pretrained("google/vit-base-patch16-224")
feature_extractor = ViTFeatureExtractor.from_pretrained("google/vit-base-patch16-224")

# Load image
image = Image.open("scene.jpg").convert("RGB")

# Preprocess image
inputs = feature_extractor(images=image, return_tensors="pt")

# Predict objects
with torch.no_grad():
    outputs = model(**inputs)
predicted_class = outputs.logits.argmax(-1).item()

print(f"Detected object class: {predicted_class}")
Step 3: Fusion of LiDAR & Vision Transformer Data

def fuse_data(lidar_objects, image_objects):
    fusion_dict = {}
    for i, obj in enumerate(lidar_objects):
        fusion_dict[f"LiDAR_Object_{i}"] = image_objects
    return fusion_dict

# Example fusion
lidar_objects = ["Vehicle", "Pedestrian"]
image_objects = ["Person", "Car"]

fusion_result = fuse_data(lidar_objects, image_objects)
print(fusion_result)

18.4 Expected Output

18.5 Future Enhancements

19. Competitive Programming & System Design Integration

19.1 Competitive Programming with Advanced Perception

19.2 System Design Integration

Use Case: Autonomous Vehicle Perception Stack
Scalability Considerations

20. Assignments

20.1 Solve At Least 10 Problems Using These Algorithms

Problem Set:
  1. LiDAR Data Filtering: Remove noise from a point cloud dataset.
  2. 3D Object Segmentation: Implement RANSAC-based plane segmentation.
  3. Path Planning: Use A* search to navigate through a LiDAR-mapped environment.
  4. Time-Series Forecasting: Train a Liquid Neural Network to predict stock market trends.
  5. Sensor Fusion: Integrate LiDAR and camera data for improved detection.
  6. Image Classification with ViT: Train a Vision Transformer to classify images.
  7. Object Detection Pipeline: Combine CNNs and ViTs for robust perception.
  8. Real-Time AI Inference: Optimize a Liquid Neural Network for edge deployment.
  9. Multi-Modal Learning: Build a model that fuses LiDAR, images, and radar.
  10. Efficient Processing: Optimize a LiDAR-based system for real-time applications.

20.2 Use in a System Design Problem

Scenario: Smart City Surveillance System

20.3 Implement Under Time Constraints