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. What does the Fourier transform (Lesson 15) fail to tell you, that wavelets and Gabor filters are designed to capture?
Sine wave basis functions extend across the whole image, so the Fourier transform loses spatial localization; wavelets and Gabor filters use spatially localized oscillations instead.
. In the Haar wavelet transform, what do the approximation (a_k) and detail (d_k) coefficients represent?
a_k is the (scaled) sum of a sample pair, i.e. a local average; d_k is the (scaled) difference, i.e. a local detail.
. In a one-level 2D wavelet decomposition of an image, what does the LH subband respond to?
LH means low-pass along rows, high-pass along columns, which makes it sensitive to horizontal edges.
. What does a Gabor filter's response tell you when the filter is tuned to one orientation and applied to bars drawn at several different orientations?
The response matrix in the lesson is diagonal-dominant: each filter's peak response lands on the bar matching its own tuned orientation, demonstrating orientation selectivity.