How can I create unique path alias for image styles? image_style_url returns the public url of an image in the files/styles folder. Is it possible to create alias to that? What I want is the following:

Call image_style_url from the image style and the uri, which gives me typical public url /sites/default/files/style/[style_name]/path/to/image/[image_file_name]. I want to serve simple url like /image/[randomized_number] to the user that will internally alias to the aforementioned public url. This is similar to asking what pathauto module does for /node/[nid], but for image styles.

Note that I do not want custom url to individual images per se, but rather a way to programmatically create unique unpredictable url aliases for image styles.
Is a little difficult because image_style_url() uses internally image_style_path() who creates the path /sites/default/files/style/[style_name]/path/to/...
Maybe you can use File (Field) Paths module:

The File (Field) Paths module extends the default functionality of Drupal's core Upload module, the FileField module and many other File Upload modules by adding the ability to use node tokens in destination paths and filenames.
In simple terms, File (Field) Paths allows you to automatically sort and rename your uploaded files using token based replacement patterns to maintain a nice clean filesystem.

If you only want to change the path alias you can use hook_node_insert() or hook_insert()
/**
 * Implements hook_insert().
 */
function mymodule_node_insert($node) {
    // Set the URL alias
    if (empty($node-&gt;path['alias'])) {
        $node-&gt;path['alias'] = 'image/' . my_random_function();
    }
}