Images of the Russian Empire:Colorizing the Prokudin-Gorskii photo collection

 1UC Berkeley

# Overview

Sergei Mikhailovich Prokudin-Gorskii (1863-1944) traveled across the Russian Empire and took many colored images. His collections were purchased by the Library of Congress. Each colored image is preserved in the form of three unicolor glass negatives, each representing a color channel. Modern techniques enable us to restore the color from such a collection.

# Methods

Our method consists of two steps. Image alignment and Color Restoration. In an image alignemet phase, we try to align the three channels together. This is non trival since many images have a large offset between channels. We consider image alignment as finding solution of the following optimization problem $$\mathrm{argmin}_{x,y} \; \mathcal{L}(P_{+x,+y},Q)$$ where $$P,Q$$ are images of dimension $$h \times w$$, and $$P_{+x,+y}$$ is the image $$P$$ shifted by vector $$(x,y )$$. We consider two losses, the SSD loss and NCC loss defined by $$SSD(P,Q)= ||P - Q || ^2$$ $$NCC(P,Q)= - \frac{Cov(P,Q)}{\sqrt{Var(P) Var(Q)}}$$ A naive solution is to iterate through a the spcae $$[-15,+15]^2$$, however this approcah failed to cater to the cases where the image has a larger offset in number of pixels due to high resolution. To address this issue, we implement a image pyramid search where we down scale the image by a factor of two until we reach a resolution no greater than 128. We then performs exhaustive search on each level. When images at a particular level becomes larger than $$512 \times 512$$, we perform a center crop for loss calculation to spped up the computation.

In our implementation, we use blue channel as the base image and try to align red and blue channel with it. We found that while NCC loss tends to have better results, it is marginally slower in runtime.

# Bells & Whistle (Enhancement)

#### Conv Filters For Feature Extraction

While the baseline method can already achieve a satisfactory results, it fails when the saturation of color is so huge that the brightness have a huge variance across different channels. (See emir.jpg below) To address this issue, we take the average of the absolute values of gradients across two directions and use the response map in lieu of the raw rgb info as the input of our loss function. In practice, we get such gradients by applying two 3x3 Conv filters on the image. In the Visualization below, we show that while the brighnetness can be drastically different in two channels, the response map reamin a high correlation. Hence, the optimal point on the loss surface will better reflect the ground truth offset.
 Brightness R Brightness B Response Map R Response Map B

#### Auto-Cropping

We implement auto-cropping to further refine the output image. We observe that the borders have low variance across one direction (i.e. they are uniform vertical and horizontal strips). Additonal, they cannot contain orthogonal information (vertical stripes cannot have horizontal edges). Based on these observations, we make the following assumption.

1.96% of the edges are in the actual image.

2.97% of the information (variance) are in the actual image.

For each image, we calculate these two metrics alongside one direction and perfom corresbounding crops from the two sides. An visualization is shown below. We perform auto-cropping on both axis.

 Distribution of Edges alongside X-Axis Distribution of Variance alongside X-Axis

#### Ablation

As shown in the visualization below, our refinements brings visible improvements to image quality.
 Baseline + Filter + AutoCrop

# Results and Visualization

We report the results of our algorithm as folloows

BaselineAutoCrop + Filter
melons.jpg
R[-179, -13] G[-83, -10]R[-180, -13] G[-83, -10]
three_generations.jpg
R[-105, -14] G[-49, -15]R[-108, -13] G[-50, -17]
train.jpg
R[-86, -32] G[-42, -6]R[-86, -32] G[-42, -6]
cathedral.jpg
R[-12, -3] G[-5, -2]R[-12, -3] G[-5, -2]
church.jpg
R[-58, 4] G[-24, -4]R[-58, 4] G[-24, -4]
onion_church.jpg
R[-108, -37] G[-50, -26]R[-108, -37] G[-49, -26]
harvesters.jpg
R[-124, -15] G[-59, -18]R[-123, -15] G[-59, -18]
sculpture.jpg
R[-140, 27] G[-33, 11]R[-140, 27] G[-33, 11]
R[-112, -9] G[-52, -7]R[-114, -11] G[-53, -7]
icon.jpg
R[-90, -23] G[-41, -18]R[-90, -23] G[-41, -18]
self_portrait.jpg
R[-175, -37] G[-77, -29]R[-175, -37] G[-77, -29]
tobolsk.jpg
R[-6, -3] G[-3, -3]R[-6, -3] G[-3, -3]
emir.jpg
R[-86, 316] G[-48, -24]R[-107, -41] G[-49, -23]
monastery.jpg
R[-3, -2] G[3, -2]R[-3, -2] G[3, -2]