THE GARDEN

Filtering, noise, and frequency analysis

Updated 11 Oct 2026

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  Spatial filters and edges

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    Convolution -> combines a pixel neighborhood using kernel weights.

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      generally, kernel dimensions is odd x odd. there's a 2x2 kernel for edge detection / more complex stuff

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      Types

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        ignoring outer element of the matrix (only valid ones)

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        Same -> add 1 zero padding, convolute the vlaid ones

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        Full -> add 2 zero paddings, convolute the valid ones

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      Frequency types

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        low freq -> part of img where pixels in img have similarity with neighboring pixels

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        high freq -> part of img where img have low similarity with its neighboring pixels

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    Padding -> supplies values beyond the image boundary.

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      common choices: zero, reflection, replication.

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      padding choice changes boundary behavior.

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    Mean / Gaussian filters -> smooth noise; may blur edges.

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    Median filter -> useful for salt-and-pepper noise.

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    Sharpening -> emphasizes local differences.

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    Sobel -> estimates directional gradients.

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    Canny -> smooths -> detects gradients -> suppresses non-maxima -> links thresholded edges.

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      an edge response is not automatically an object boundary.

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    convolution illustration: slide a small kernel over a pixel neighborhood and show the weighted-sum output; include Sobel edge response if space permits.

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  Frequency domain

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    DFT -> represents an image as spatial frequencies.

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    Low frequencies -> slowly changing image structure.

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    High frequencies -> fine detail and rapid changes.

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    Centered magnitude spectrum -> shows frequency strength.

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    Frequency masks -> apply a mask, then invert the transform.

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    Low-pass -> removes high frequencies.

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      for smoothing, reducing noise (?)

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      $\sum_i \sum_j g(i, j)= 1$, where $g(i, j) > 0$

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      e.g. $g = \begin{pmatrix} \frac{1}{9}&\frac{1}{9}&\frac{1}{9} \\ \frac{1}{9}&\frac{1}{9}& \frac{1}{9} \\ \frac{1}{9}& \frac{1}{9} &\frac{1}{9} \end{pmatrix}$

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    High-pass -> removes low frequencies.

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      untuk something idk

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      $\sum_i \sum_j g(i, j) = 0$, $g(i, j) \in \mathbb{R}$ (?)

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      e.g.: $g = \begin{pmatrix} 0 &{-1}& 0 \\ {-1}& 4 &{-1} \\ 0& {-1}& 0 \end{pmatrix}$

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    Band-pass -> retains a selected range.

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      meloloskan data di frekuensi tertentu

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      unutk penajaman bagian tepi objek (?)

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      $\sum_i \sum_j g(i, j) \neq 0$ , $g(i, j) \in \mathbb{R}$ (?)

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      e.g.: $g = \begin{pmatrix} 0 &{-1}& 0 \\ {-1}& 5 &{-1} \\ 0& {-1}& 0 \end{pmatrix}$

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    false color terjadi pada hiseq saja. filtering tiddak harus intensitas saja kaya hiseq

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    Notch filter -> targets selected frequency peaks.

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    Periodic interference -> often appears as paired off-center peaks.

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    Sharp frequency cutoff -> can cause ringing.

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    centered spectrum illustration: label low/high frequencies, paired periodic-noise peaks, and low-pass/high-pass/notch masks.

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