probability distribution for regression / expanding classification (softmax layer) to allow 3

[Philipp H]

I have a working network for pixel-wise image segmentation, i.e. two images as input one as data one as label (ground_truth). Therefore, I am using a `SoftmaxWithLoss` layer as shown below:

    layer {

      name: "conv"

      type: "Convolution"

      bottom: "bottom"

      top: "conv"

      convolution_param {

    num_output: 256 # <-- "256 classes"

        ...

      }

    }

    layer {

      name: "loss"

      type: "SoftmaxWithLoss"

      bottom: "data"

      bottom: "label"

      top: "loss"

    }

My input image values range from [0-255], that is why I have 256 classes.

Now I want to transform this segmentation / classification task to a regression task. I assumed the only things I have to change is the `loss layer` and the `num_output` in the `convolution layer` like this:

    layer {

      name: "conv"

      type: "Convolution"

      bottom: "bottom"

      top: "conv"

      convolution_param {

        num_output: 1 # <-- "regression"

        ...

      }

    }

    layer {

      name: "loss"

      type: "EuclideanLoss"

      bottom: "data"

      bottom: "label"

      top: "loss"

    }

My regression task does not produce satisfying results at all.

I think the problem for the regression task compared to the classification task is that for the classification task I have good a distribution over all depth values --> `num_output = 256` --> In the end I have a result of `256 x 128 x x128` that means one probability for each `depth class`. For the regression task my output is `num_output = 1` which only returns `one depth value` per pixel rather than `256` for the classification task.

 

1. Classification:

Does anyone know how to adjust the `softmax layer` in order to produce results like: `256 x a_number_greater_1 x width x depth` rather than `256 x width x depth`. 

or 

2. Regression:

Is there any other approach to achieve results as a distribution of probabilities like the `softmax layer` does?