Concepts / Feature Maps and Filters

Feature Maps and Filters

Imagine an input feature map laid out as a spatial field.

  • Programming
Interactive lab

Try it: Convolution

How a convolution layer slides a small kernel over an image, multiplying and summing at each position to build a feature map.

How it works

  1. Place the 3×3 kernel over the top-left 3×3 window of the input.
  2. Multiply each input value by the kernel weight on top of it and add the nine products — that sum is one output cell.
  3. Slide the window by the stride and repeat until every position is covered.
  4. Zero padding adds a border so edge pixels are covered too; output size = ⌊(n + 2p − k) / s⌋ + 1.

Default run (11 steps): 5×5 input, 3×3 kernel, stride 1. Output is ⌊(5 + 2×0 − 3) / 1⌋ + 1 = 3 per side. … Done: the kernel visited all 9 positions and produced a 3×3 feature map.

Simplified: One 5×5 single-channel input and one 3×3 kernel. As in deep-learning libraries, the kernel is not flipped (strictly, cross-correlation).

Educational simulation

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From Whole Images to Local Patches

A convolution layer does not treat an image as one enormous, undivided object. Instead, it examines small local regions called patches. For an image, each patch is a small two-dimensional window of the input. The layer applies a learned transformation to these local regions and records the resulting responses in an output feature map.

Key point

The central idea is local examination plus reuse: convolution looks at one patch at a time, but uses the same learned transformation at many locations.

Following the Moving Patch

Imagine an input feature map laid out as a spatial field. A convolution operation selects a local patch at one position. It applies the learned transformation to that patch and places the resulting response at the corresponding position in the output. The operation then examines another patch at a different location and repeats the same process. As this continues across the input, the output records where the transformation responds strongly or weakly.

Input feature mapspatial fieldPatch Alocal windowOutput position AresponsePatch Bnext local windowOutput position Bresponseselectmovetransformtransform
Which local patch is examined at each step, and where does the operation continue next?
Worked example

Tracing Two Patch Positions

A convolution layer examines one local patch and then another patch at a different location. What does it reuse, and what changes?

  1. 1
    Select the first patch

    The layer examines a small local region of the input feature map.

  2. 2
    Apply the learned transformation

    The layer applies its learned transformation to that patch and records a response at the corresponding output position.

  3. 3
    Select another patch

    The examined window moves to a different location in the input.

  4. 4
    Reuse the transformation

    The same transformation is applied again rather than being redesigned for the new patch.

Result

The patch location changes, but the learned transformation is reused. The output therefore records responses at multiple spatial positions.

Reading Feature Map Axes

Convolutions operate over three-dimensional tensors called feature maps. Height and width describe spatial position: they locate a response or feature across the vertical and horizontal dimensions. The third axis is depth, also called the channels axis. Depth represents channels rather than another spatial direction.

Feature mapthree-dimensional tensorHeightvertical positionWidthhorizontal positionDepthchannelscontains axiscontains axiscontains axis
What do height, width, and depth contain, and how are they arranged in a feature map?
AxisMeaning in a feature map
HeightSpatial position along one direction
WidthSpatial position along the other direction
DepthChannels containing feature information

The three axes distinguish spatial position from channel depth.

Filters and Response Maps

Definition

A filter encodes a specific aspect of the input data. When a convolution layer uses several filters, each filter produces a channel in the output. That channel is a response map: a two-dimensional grid showing the response of that filter at different locations in the input.

The output feature map keeps three dimensions. Its height and width identify spatial positions, while its depth is chosen by the layer and contains the filter responses. One output channel can therefore be read as a map of where one learned filter finds its preferred aspect of the input.

Input feature maplocal patchesFilterlearned aspectFilter responsesone value per positionResponse mapoutput channelexamines patchesproducesarrange spatially
How does one filter turn responses from input patches into a channel of the output feature map?
Worked example

Interpreting One Output Channel

A convolution layer uses several filters. How should one resulting output channel be interpreted?

  1. 1
    Identify the filter

    Choose one filter that encodes a particular aspect of the input data.

  2. 2
    Read its local responses

    At different input locations, the filter produces responses to the patches it examines.

  3. 3
    Arrange the responses

    Those responses form a two-dimensional grid aligned with spatial positions.

Result

The selected output channel is a response map showing where the chosen filter responds across the input.

Reusing One Transformation

The transformation is not redesigned for every patch. It is reused across the input, allowing the same learned pattern to be sought in multiple places. This reuse is what lets one filter create a response map instead of learning a separate transformation for every spatial position.

Patch oneinput locationSame filterreused transformationResponse oneoutput positionPatch twoinput locationResponse twooutput positionPatch threeinput locationResponse threeoutput positionapplyapplyapplyproduceproduceproduce
How does the same filter transformation move across patches while producing one output value per position?

What do you think happens?

A learned pattern appears in a different local region of an input. Does the convolution layer need an entirely new learned pattern for that new location?

  • Yes, because each location is a separate problem

  • No, because the same local transformation is reused

Reveal answer
Answer:

No, because the same local transformation is reused.

Reusing the transformation lets the network search for the learned pattern at multiple locations.

Location and Pattern Hierarchies

Convolution layers learn translation-invariant patterns. If a network learns a pattern in one part of a picture, it can recognize that pattern elsewhere because the same local transformation is applied at different locations. The pattern does not have to be learned as an entirely new pattern for every position.

Input patternone locationResponse mapone response locationInput patternanother locationResponse mapanother response locationsame transformationsame transformation
What changes in the response map when a learned pattern shifts to another location in the input?

Convolutional networks also learn spatial hierarchies of patterns. An early convolution layer can learn small local patterns such as edges. A later layer can learn larger patterns made from features learned earlier. Further layers can continue combining these features into increasingly complex and abstract visual concepts. The important progression is from small and local to larger and more abstract.

Local patternsedgesLarger patternscombined earlier featuresAbstract conceptsincreasing complexityprovide building blockscombine into
How do local responses become increasingly larger and more abstract patterns across layers?

Common Misunderstandings

  • Common mistake

    Thinking convolution examines the entire image as one undivided pattern.

    What it looks like

    Treating a convolution layer as though it learns one global relationship involving every pixel at once.

    Why it fails

    Convolution examines small local regions or patches of the input.

    Do this instead

    Track the operation from one local patch to another and focus on how responses are recorded across positions.

  • Common mistake

    Assuming a new transformation is learned for every spatial location.

    What it looks like

    Describing the filter used in one corner as different from the filter used elsewhere solely because the patch location changed.

    Why it fails

    The same learned transformation is reused across patches.

    Do this instead

    Separate the changing patch location from the reused filter transformation.

  • Common mistake

    Treating depth as another spatial direction.

    What it looks like

    Reading the depth axis as though it described a third physical position in the image.

    Why it fails

    Height and width describe spatial position; depth represents channels.

    Do this instead

    Interpret depth as the channel axis.

  • Common mistake

    Assuming output channels are still specifically RGB color channels.

    What it looks like

    Interpreting every output channel as red, green, or blue.

    Why it fails

    Output channels represent filters and the responses produced by those filters.

    Do this instead

    Read an output channel as a response map for one filter.

Check Your Understanding

MEDIUM

Describe the path from an input feature map to one output response map. Your explanation should mention a local patch, a filter, reuse across locations, spatial position, and output channels.

Hints
  • Start with what the convolution layer selects from the input.
  • Explain what remains the same as the selected patch changes.
  • Finish by describing what one output channel represents.
EASY

A pattern moves from one location in an input picture to another. Explain why a convolutional network can seek the same learned pattern at the new location without learning it as an entirely new pattern.

Hints
  • Focus on whether the transformation is tied to one location.
  • Use the term translation-invariant pattern in your explanation.

Key Takeaways

  1. 1
    Convolution examines small local patches instead of treating the entire image as one undivided pattern.
  2. 2
    The same learned transformation is reused across different patches, producing responses at different spatial positions.
  3. 3
    Height and width describe spatial position, while depth represents channels.
  4. 4
    Each filter can produce an output channel that acts as a two-dimensional response map.
  5. 5
    Convolutional networks recognize patterns across locations and build increasingly complex concepts from small local features.

At a glance

  • A convolution operation extracts and examines local patches of an input feature map.
  • One learned transformation is reused across patches, allowing the same pattern to be recognized at multiple locations.
  • Feature maps have height, width, and depth axes; depth represents channels.
  • A filter produces a response map, which becomes a channel in the output feature map.
  • Convolutional networks progress from small local patterns to larger and more abstract spatial concepts.

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