Light Field Refocusing Shift

mediumPROLight FieldsLight FieldCV: Image-Based Rendering

Compute the pixel shift for refocusing in a light field.

Light fields enable digital refocusing - changing the focal plane after capture. To focus at depth $d$ instead of the original $d_0$ , we shift each subaperture image by:

$shift = (s - s_0) \cdot \frac{d_0 - d}{d}$

where:

$s$ is the subaperture position
$s_0$ is the central subaperture
$d_0$ is the original focal distance
$d$ is the target focal distance

Objects at depth $d$ will be in focus (zero parallax), while objects at other depths are blurred.

If the target focal distance $d$ is 0, return 0.0 instead of dividing by zero. Round the result to 4 decimal places.

Example

Input

refocus_shift(2, 0, 10, 5)

Output

2.0

Reasoning

Inputs: s = 2 is the subaperture's position, s_center = 0 is the central subaperture, d_original = 10 is the depth the capture was focused at, and d_target = 5 is the new, closer depth we want sharp.
Baseline offset: $s - s_0 = 2 - 0 = 2$ . This view's distance from the centre sets how strongly it must move; the centre view itself never moves.
Depth factor: $\frac{d_0 - d}{d} = \frac{10 - 5}{5} = 1$ . Halving the focal distance makes the factor exactly 1.
Shift: $2 \cdot 1 = 2$ , already exact at 4 decimal places, so the result is 2.0 pixels.
Notice: the sign carries meaning. Refocusing farther (say $d = 20$ ) gives $\frac{10 - 20}{20} = -0.5$ and a shift of $-1$ , the opposite direction. When $d = d_0$ the factor is 0 and nothing moves, since the focal plane is unchanged.

Constraints

s: subaperture position
s_center: center subaperture position
d_original: original focal distance
d_target: target focal distance
Return shift in pixels, rounded to 4 decimal places

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Concept primerPREVIEW

To refocus a light field at a new depth, you compute a per-view shift proportional to the subaperture offset $(s - s_0)$ and the relative depth change $\frac{d_0 - d}{d}$ , then apply that shift when aligning/warping views before averaging.

1. Background Knowledge

A light field represents all rays in space parameterized by position and direction, often as a grid of subaperture images (views) taken from slightly different camera positions. Each subaperture image corresponds to a different point on the camera aperture; together they encode parallax: nearby objects shift more between views than distant ones.

Digital refocusing with a light field works by re-aligning these subaperture images so that rays from a chosen depth $d$ line up. If you shift each view by a depth-dependent amount and then average, objects at depth $d$ exhibit zero parallax (they align exactly) and become sharp, while other depths misalign and blur. The given formula

shift = (s - s_0) \cdot \frac{d_0 - d}{d}

encodes how much each subaperture $s$ should be shifted relative to the central one $s_0$ to change focus from the original depth $d_0$ to a new depth $d$ .

2. Algorithm / General Approach

At a high level, the pattern is:

Compute a scalar refocus factor from $d_0$ and $d$ : $\alpha = \frac{d_0 - d}{d}$ .
For each subaperture index $s$ , compute its relative offset from the center: $\Delta s = s - s_0$ .
Multiply to get the shift: $shift = \Delta s \cdot \alpha$ .
Use this shift (possibly in x and y) to warp or sample the subaperture image when constructing the refocused image.

The coding task usually boils down to implementing the math for shift (possibly returning a float or vector), not the entire rendering pipeline.

3. Step-by-Step Strategy

Assume you are given $s, s_0, d_0, d$ (often as scalars or small vectors):

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solution.py

Python 3.13

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