【Advanced】Image Retrieval in MATLAB: Using Feature Hashing for Image Retrieval

# 1. Overview of Image Retrieval

Image retrieval refers to the use of computer technology to quickly and accurately find images similar to a query image or image features from an image database based on the user's input. It is widely used in computer vision, multimedia, e-commerce, and other fields. Image retrieval techniques are mainly divided into pixel-based, feature-based, and semantic-based methods. Among them, feature-based methods have received widespread attention due to their efficiency and robustness.

# 2. Application of Feature Hashing in Image Retrieval

### 2.1 Concept and Principle of Feature Hashing

#### 2.1.1 Construction of Hash Functions

A hash function is a function that maps data of arbitrary length to a fixed-length output. In image retrieval, ***mon hash functions include:

***Linear Hash Function:** Adds each element in the feature vector and then takes the modulus of the result.
***Perceptual Hash Function (pHash):** Reduces the image to a smaller size, then applies the Discrete Cosine Transform (DCT), and finally hashes the DCT coefficients.
***Locality-Sensitive Hash Function (LSH):** Projects the feature vector onto multiple random hyperplanes and hashes based on the projection results.

#### 2.1.2 Establishment and Query of Hash Tables

A hash table is an array containing hash buckets, each storing features with the same hash value. When querying an image, map the image feature to the hash table and check the corresponding hash bucket. If similar hash values are present in the hash bucket, it is considered that the query image is similar to the stored image.

### 2.2 Advantages and Limitations of Feature Hashing in Image Retrieval

**Advantages:**

***Fast Retrieval:** Hash table queries are very fast, allowing for real-time retrieval of a large number of images.
***Low Memory Consumption:** Hash tables only store hash values, not complete feature vectors, thus consuming less memory.
***Robustness:** Hash functions can tolerate noise and distortion in images.

**Limitations:**

***Hash Collisions:** Different feature vectors may have the same hash value, leading to hash collisions.
***Accuracy:** Hash table queries can only provide approximate results and may not retrieve completely similar images.
***Feature Selection:** The performance of hash functions depends on the selected features, and different features may lead to different retrieval results.

**Code Block:**

import numpy as np

def linear_hash(feature_vector):
     """
     Constructs a linear hash function

     Parameters:
         feature_vector: Image feature vector

     Returns:
         Hash value
     """
     hash_value = np.sum(feature_vector) % 1000
     return hash_value

**Code Logic Analysis:**

This code block implements a linear hash function, summing each element in the feature vector and then taking the modulus to obtain the hash value.

**Parameter Description:**

* `feature_vector`: Image feature vector, a numpy array.

**Table:**

| Hash Function | Pros | Cons |
|---|---|---|
| Linear Hash | Simple construction, fast speed |