Hypercolumns for Object Segmentation and Fine-grained Localization Hypercolumns for Object Segmentation and Fine-grained Localization
Paper summary So the hypervector is just a big vector created from a network: `"We concatenate features from some or all of the feature maps in the network into one long vector for every location which we call the hypercolumn at that location. As an example, using pool2 (256 channels), conv4 (384 channels) and fc7 (4096 channels) from the architecture of [28] would lead to a 4736 dimensional vector."` So how exactly do we construct the vector? ![](https://i.imgur.com/hDvHRwT.png) Each activation map results in a single element of the resulting hypervector. The corresponding pixel location in each activation map is used as if the activation maps were all scaled to the size of the original image. The paper shows the below formula for the calculation. Here $\mathbf{f}_i$ is the value of the pixel in the scaled space and each $\mathbf{F}_{k}$ are points in the activation map. $\alpha_{ik}$ scales the known values to produce the midway points. $$\mathbf{f}_i = \sum_k \alpha_{ik} \mathbf{F}_{k}$$ Then the fully connected layers are simply appended to complete the vector. So this gives us a representation for each pixel but is it a good one? The later layers will have the input pixel in their receptive field. After the first few layers it is expected that the spatial constraint is not strong.
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Hypercolumns for Object Segmentation and Fine-grained Localization
Bharath Hariharan and Pablo Arbeláez and Ross Girshick and Jitendra Malik
arXiv e-Print archive - 2014 via arXiv
Keywords: cs.CV

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