Image-like Reshaping

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Problem Statement

Reshape flat data into image-like 3D arrays and back.

Background

Images are typically 3D arrays: (height, width, channels)

Grayscale: (H, W, 1)
RGB: (H, W, 3)

Flattening and reshaping is common in deep learning:

Flatten for fully-connected layers
Reshape for convolutional layers

Your Task

Write a function image_reshape(flat_data, height, width, channels) that:

Reshapes flat data to image shape (H, W, C)
Also returns channel-first format (C, H, W)
Returns flattened form

Output Format

Return a dictionary with:

"image": Shape (H, W, C) as list
"channels_first": Shape (C, H, W) as list
"flat": Flattened as list
"shape": Original image shape as list

Example

Input

data = [0..11], height = 2, width = 2, channels = 3

Output

Image shape [2, 2, 3], channels_first shape [3, 2, 2]

Reasoning

Inputs: flat_data is the 12 numbers $0, 1, \dots, 11$ in one line; height $=2$ , width $=2$ , channels $=3$ ; $2 \times 2 \times 3 = 12$ slots, one per number.
Image layout $(H, W, C)$ : channel varies fastest, then column, then row. The value at row $h$ , column $w$ , channel $c$ is $6h + 3w + c$ . Pixel $(0,0)$ holds [0, 1, 2], pixel $(0,1)$ holds [3, 4, 5], and the second row holds [6, 7, 8] and [9, 10, 11].
Channels first $(C, H, W)$ : each channel becomes its own $2 \times 2$ plane: entry $(c, h, w)$ equals image entry $(h, w, c)$ . Channel 0 collects $0, 3, 6, 9$ → [[0, 3], [6, 9]]; channel 1 is [[1, 4], [7, 10]]; channel 2 is [[2, 5], [8, 11]]. Shape [3, 2, 2].
flat and shape: reading the image back in the same order returns $0$ through $11$ unchanged; shape is [2, 2, 3].
Notice channels-first is not the 12 numbers re-cut in order into a $3 \times 2 \times 2$ block; each value keeps its pixel and channel.

Constraints

len(flat_data) == height * width * channels
Use np.transpose for axis reordering

More from NumPy Foundations

Solve Linear Systemmedium Matrix Operationseasy Dot Producteasy Array Stackingeasy Array Reshapingeasy

Concept primer

Background Knowledge

NumPy arrays are multidimensional structures for efficient numerical computation, enabling vectorized operations without explicit loops for speed and simplicity. In image processing, data is often represented as 3D arrays with shape (height, width, channels)—where height (H) and width (W) define spatial dimensions, and channels (C) capture color (e.g., 3 for RGB) or other features (e.g., 1 for grayscale). Flattening converts this to 1D for tasks like feeding into neural networks, while reshaping reconstructs the structure, preserving total elements: $H \times W \times C$ must match the flat array length.

Channel ordering matters: "channels-last" (H, W, C) is common in image libraries like Pillow/OpenCV, while "channels-first" (C, H, W) suits frameworks like PyTorch for convolutional operations. Understanding np.reshape() and np.transpose() is key—the former changes shape without data copying (if compatible), the latter swaps axes (e.g., via (2,0,1) for HWC to CHW).

Algorithm/Approach

Use NumPy's reshaping paradigm:

Validate flat data length equals $H \times W \times C$ .
Reshape to channels-last (H, W, C).
Transpose to channels-first (C, H, W).
Flatten back to 1D.
Package as dictionary with shapes and data as lists.

This leverages NumPy's strided views for zero-copy operations, ensuring efficiency.

Step-by-Step Strategy

Input validation: Check len(flat_data) == height * width * channels; raise error if not.
Reshape to image: image = flat_data.reshape((height, width, channels)).
Channels-first: channels_first = np.transpose(image, (2, 0, 1)).
Flatten: flat = image.flatten() (or flat_data.copy() since identical).
Capture shapes: image_shape = [height, width, channels], etc.
Return dict: {"image": image.tolist(), "channels_first": channels_first.tolist(), "flat": flat.tolist(), "shape": image_shape}.

Test with sample: np.arange(12).reshape(2,2,3) yields [[[0,1,2],[3,4,5]], [[6,7,8],[9,10,11]]].

Common Pitfalls

Shape mismatch: Forgetting to verify flat_data.size == HWC causes ValueError.
Data type: Ensure flat_data is NumPy array; tolist() fails on non-numeric.
Transpose axes: Wrong order (e.g., (0,1,2) does nothing); use (2,0,1) for HWC → CHW.
Copy vs. view: reshape() creates views (good), but tolist() materializes lists (fine for output).
Integer inputs: height, width, channels must be int; floats truncate unexpectedly.

Time & Space Complexity

Time: $O(N)$ where $N = H \times W \times C$ —reshape/transpose are $O(1)$ metadata ops + $O(N)$ for tolist()/flatten.
Space: $O(N)$ extra for lists (views are $O(1)$ , but output copies data); in-place possible but dict requires it. Efficient for typical image sizes (e.g., $224^2 \times 3 \approx 150k$ ).

solution.py

Python 3.13

Test results