Image Registration by Direct Optimization

Image Registration
In this tutorial we are going to learn how to perform the task of image alignment by optimizing the similarity transformation between two images in order to create a photo with wide in-focus area from set of narrow-focused images.

Dmytro Mishkin


September 6, 2021

Open in google colab

The images are courtesy of Dennis Sakva

!pip install kornia
!pip install kornia-rs
import io

import requests

def download_data(url: str, filename: str = "") -> str:
    filename = url.split("/")[-1] if len(filename) == 0 else filename
    # Download
    bytesio = io.BytesIO(requests.get(url).content)
    # Save file
    with open(filename, "wb") as outfile:

    return filename


Import needed libraries

import os
from copy import deepcopy
from typing import List

import imageio
import kornia as K
import kornia.geometry as KG
import matplotlib.pyplot as plt
import numpy as np
import torch
import torch.nn.functional as F
from tqdm import tqdm

def get_data_directory(base):
    path = os.path.join("../", base)
    if os.path.isdir(os.path.join(path, "data")):
        return os.path.join(path, "data/")
    return get_data_directory(path)

Images preview

Let’s check our images. There are almost 100 of them, so we will show only each 10th

fnames = os.listdir("bee")
fnames = [f"bee/{x}" for x in sorted(fnames) if x.endswith("JPG")]
fig, axis = plt.subplots(2, 5, figsize=(12, 4), sharex="all", sharey="all", frameon=False)
for i, fname in enumerate(fnames):
    if i % 10 != 0:
    j = i // 10
    img =,
    axis[j // 5][j % 5].imshow(K.tensor_to_image(img), aspect="auto")
plt.subplots_adjust(wspace=0.05, hspace=0.05)

So the focus goes from back to the front, so we have to match and merge them in the same order.

Image registration

We will need ImageRegistrator object to do the matching. Because the photos are takes so that only slight rotation, shift and scale change is possible, we will use similarity mode, which does exactly this.

use_cuda: bool = torch.cuda.is_available()
device = torch.device("cuda" if use_cuda else "cpu")
registrator = KG.ImageRegistrator("similarity", loss_fn=F.mse_loss, lr=8e-4, pyramid_levels=3, num_iterations=500).to(device)

We will register images sequentially with ImageRegistrator.

models = []
for i, fname in tqdm(enumerate(fnames)):
    if i == 0:
    prev_img =[i - 1],, device=device)[None, ...]
    curr_img =,, device=device)[None, ...]
    model = registrator.register(prev_img, curr_img)

Let’s take the final (the most close-focused) image as the reference - this means that we have to convert our image transforms from (between i and i+1) mode into (between i and last). We can do it by matrix multiplication.

models_to_final = [torch.eye(3, device=device)[None]]
for m in models[::-1]:
    models_to_final.append(m @ models_to_final[-1])
models_to_final = models_to_final[::-1]

Let’s check what do we got.

fig, axis = plt.subplots(2, 5, figsize=(12, 4), sharex="all", sharey="all", frameon=False)
for i, fname in enumerate(fnames):
    if i % 10 != 0:
    timg =,, device=device)[None, ...]
    j = i // 10
    timg_dst = KG.homography_warp(timg, models_to_final[i], timg.shape[-2:])
    axis[j // 5][j % 5].imshow(K.tensor_to_image(timg_dst * 255.0).astype(np.uint8), aspect="auto")
plt.subplots_adjust(wspace=0.05, hspace=0.05)

Finally we will merge the image sequence into single image. The idea is to detect the image parts, which are in focus from the current image and blend them into the final images. To get the sharp image part we can use kornia.filters.laplacian. Then we reproject image1 into image2, and merge them using mask we created.

def merge_sharp1_into2(timg1, timg2, trans1to2, verbose=False):
    curr_img = timg2.clone()
    warped = KG.homography_warp(timg1, torch.inverse(trans1to2), timg.shape[-2:])
    mask1 = K.filters.laplacian(K.color.rgb_to_grayscale(timg1), 7).abs()
    mask1_norm = (mask1 - mask1.min()) / (mask1.max() - mask1.min())
    mask1_blur = K.filters.gaussian_blur2d(mask1_norm, (9, 9), (1.6, 1.6))
    mask1_blur = mask1_blur / mask1_blur.max()
    warped_mask = KG.homography_warp(mask1_blur.float(), torch.inverse(models_to_final[i]), timg1.shape[-2:])
    curr_img = warped_mask * warped + (1 - warped_mask) * curr_img
    if verbose:
        fig, axis = plt.subplots(1, 4, figsize=(15, 6), sharex="all", sharey="all", frameon=False)
        axis[1].set_title("Sharp mask on img1")
        axis[3].set_title("Blended image")
    return curr_img

timg1 =[50],, device=device)[None, ...]
timg2 =[-1],, device=device)[None, ...]
out = merge_sharp1_into2(timg1, timg2, models_to_final[50], True)

The blending does not look really good, but that is because we are trying to merge non-consequtive images with very different focus. Let’s try to apply it sequentially and see, what happens.

We will also create a video of our sharpening process.

base_img =[-1],, device=device)[None, ...]
curr_img = deepcopy(base_img)

    video_writer = imageio.get_writer("sharpening.avi", fps=8)
    video_writer.append_data((K.tensor_to_image(curr_img) * 255.0).astype(np.uint8))
    video_ok = True
    video_ok = False

with torch.no_grad():
    for i, fname in tqdm(enumerate(fnames)):
        timg =,, device=device)[None, ...]
        curr_img = merge_sharp1_into2(,, models_to_final[i].to(device))
        if video_ok:
            video_writer.append_data((K.tensor_to_image(curr_img) * 255.0).astype(np.uint8))
if video_ok:
plt.title("Final result")
Text(0.5, 1.0, 'Final result')

Now we can play the video of our sharpening. The code is ugly to allow running from Google Colab (as shown here)

from base64 import b64encode

from IPython.display import HTML

if video_ok:
    mp4 = open("sharpening.avi", "rb").read()
    mp4 = open(get_data_directory("") + "sharpening.mp4", "rb").read()
data_url = "data:video/mp4;base64," + b64encode(mp4).decode()

<video width=400 controls>
      <source src="{data_url}" type="video/mp4">

Result looks quite nice and more detailed, although a bit soft. You can try yourself different blending parameters yourself (e.g. blur kernel size) in order to improve the final result.