In image processing and computer vision, the technique that localizes an object and analyzes it across a series of progressively coarser, redundant layers is called:

Introduction / Context:
Multiscale analysis is central to image processing. By repeatedly smoothing and subsampling an image, algorithms create a stack of lower-resolution versions. Objects can be detected or tracked consistently across scales, improving robustness to size changes and noise. The commonly used construction is the Gaussian pyramid, from which other pyramids (like Laplacian) are derived.

Given Data / Assumptions:

• Goal: localize and analyze objects at multiple resolutions.
• Layers are redundant (coarser levels summarize finer details).
• Gaussian smoothing precedes subsampling to avoid aliasing.

Concept / Approach:
A Gaussian pyramid is built by convolving the image with a Gaussian kernel and downsampling iteratively. This yields a hierarchy used for scale-space analysis, feature detection, and coarse-to-fine search. The Laplacian pyramid (differences between levels) is often computed from the Gaussian stack for compression or blending.

Step-by-Step Solution:

Verification / Alternative check:
Standard texts present Gaussian pyramids for coarse-to-fine optical flow, image registration, and object detection; this matches the description of redundant multiresolution layers.

Why Other Options Are Wrong:

Common Pitfalls:
Skipping pre-subsampling smoothing causes aliasing; confusing Gaussian and Laplacian pyramids—the latter is derived from the former.

Final Answer:
Gaussian pyramid