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TransformationMatrix3x4GeneratorSO3.lua
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TransformationMatrix3x4GeneratorSO3.lua
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local TransformationMatrix3x4SO3, parent = torch.class('nn.TransformationMatrix3x4SO3', 'nn.Module')
--[[
TransformMatrixGenerator(useRotation, useScale, useTranslation) :
TransformMatrixGenerator:updateOutput(transformParams)
TransformMatrixGenerator:updateGradInput(transformParams, gradParams)
This module can be used in between the localisation network (that outputs the
parameters of the transformation) and the AffineGridGeneratorBHWD (that expects
an affine transform matrix as input).
The goal is to be able to use only specific transformations or a combination of them.
If no specific transformation is specified, it uses a fully parametrized
linear transformation and thus expects 6 parameters as input. In this case
the module is equivalent to nn.View(2,3):setNumInputDims(2).
Any combination of the 3 transformations (rotation, scale and/or translation)
can be used. The transform parameters must be supplied in the following order:
rotation (1 param), scale (1 param) then translation (2 params).
Example:
AffineTransformMatrixGenerator(true,false,true) expects as input a tensor of
if size (B, 3) containing (rotationAngle, translationX, translationY).
]]
function TransformationMatrix3x4SO3:__init(useRotation, useScale, useTranslation)
parent.__init(self)
-- if no specific transformation, use fully parametrized version
self.fullMode = not(useRotation or useScale or useTranslation)
if not self.fullMode then
self.useRotation = useRotation
self.useScale = useScale
self.useTranslation = useTranslation
end
self.threshold = 1e-12
end
function TransformationMatrix3x4SO3:check(input)
if self.fullMode then
assert(input:size(2)==7, 'Expected 7 parameters, got ' .. input:size(2))
else
local numberParameters = 0
if self.useRotation then
numberParameters = numberParameters + 3
end
if self.useScale then
numberParameters = numberParameters + 1
end
if self.useTranslation then
numberParameters = numberParameters + 3
end
assert(input:size(2)==numberParameters, 'Expected '..numberParameters..
' parameters, got ' .. input:size(2))
end
end
local function addOuterDim(t)
local sizes = t:size()
local newsizes = torch.LongStorage(sizes:size()+1)
newsizes[1]=1
for i=1,sizes:size() do
newsizes[i+1]=sizes[i]
end
return t:view(newsizes)
end
local function dR_by_dvi(transparams, RotMats, which_vi, threshold)
local omega_x = transparams:select(2,1)
local omega_y = transparams:select(2,2)
local omega_z = transparams:select(2,3)
local omega_skew = torch.Tensor(RotMats:size()):typeAs(transparams)
omega_skew:zero()
omega_skew:select(3,1):select(2,2):copy(omega_z)
omega_skew:select(3,1):select(2,3):copy(-omega_y)
omega_skew:select(3,2):select(2,1):copy(-omega_z)
omega_skew:select(3,2):select(2,3):copy(omega_x)
omega_skew:select(3,3):select(2,1):copy(omega_y)
omega_skew:select(3,3):select(2,2):copy(-omega_x)
local Id_minus_R_ei = torch.Tensor(RotMats:size(1),RotMats:size(2),1):zero():typeAs(transparams)
Id_minus_R_ei:select(2,which_vi):add(1)
local I = torch.Tensor(RotMats:size(1), RotMats:size(2), RotMats:size(3)):zero():typeAs(transparams)
assert(RotMats:size(2) == 3)
assert(RotMats:size(3) == 3)
I:select(2,1):select(2,1):add(1)
I:select(2,2):select(2,2):add(1)
I:select(2,3):select(2,3):add(1)
Id_minus_R_ei = torch.bmm(torch.add(I,-RotMats), Id_minus_R_ei)
--Id_minus_R_ei:select(2,1):add(1):add(-RotMats:select(2,1,1):select(2,1))
--Id_minus_R_ei:select(2,2):add(RotMats:select(3,1,1):select(2,2,1))
--Id_minus_R_ei:select(2,3):add(RotMats:select(3,1,1):select(2,3))
--- cross product
local v_cross_Id_minus_R_ei = torch.bmm(omega_skew,Id_minus_R_ei)
local cross_x = v_cross_Id_minus_R_ei:select(2,1)
local cross_y = v_cross_Id_minus_R_ei:select(2,2)
local cross_z = v_cross_Id_minus_R_ei:select(2,3)
local vcross = torch.Tensor(RotMats:size()):typeAs(transparams)
vcross:zero()
vcross:select(3,1):select(2,2):copy(cross_z)
vcross:select(3,1):select(2,3):copy(-cross_y)
vcross:select(3,2):select(2,1):copy(-cross_z)
vcross:select(3,2):select(2,3):copy(cross_x)
vcross:select(3,3):select(2,1):copy(cross_y)
vcross:select(3,3):select(2,2):copy(-cross_x)
local omega_mag = torch.pow(omega_x,2) + torch.pow(omega_y,2) + torch.pow(omega_z,2)
local omega_selected = transparams:select(2,which_vi)
for b = 1, omega_skew:size(1) do
if omega_mag[b] > threshold then
local v_i = omega_selected[b]
--omega_skew[b] = torch.cdiv(torch.mm(torch.Tensor(omega_skew:size(2),omega_skew:size(3)):fill(v_i),omega_skew[b]) + vcross[b], torch.Tensor(omega_skew:size(2),omega_skew:size(3)):fill(omega_mag[b]))
--omega_skew[b] = torch.cdiv(omega_skew[b]:mul(v_i) + vcross[b], torch.Tensor(omega_skew:size(2),omega_skew:size(3)):fill(omega_mag[b]))
omega_skew[b] = omega_skew[b]:mul(v_i) + vcross[b]
omega_skew[b]:div(omega_mag[b])
else
local e_i = torch.Tensor(3,1):typeAs(transparams):zero()
e_i:select(1,which_vi):fill(1)
local eMat = torch.Tensor(3,3):typeAs(transparams):zero()
--[[
[a]x = ( 0 -a3 a2
a3 0 -a1
-a2 a1 0 )
--]]
eMat[1][2] = -e_i[3]
eMat[1][3] = e_i[2]
eMat[2][1] = e_i[3]
eMat[2][3] = -e_i[1]
eMat[3][1] = -e_i[2]
eMat[3][2] = e_i[1]
omega_skew[b] = eMat
end
end
return torch.bmm(omega_skew, RotMats)
--[[
from http://arxiv.org/pdf/1312.0788.pdf
--]]
--- v_i [v]x + [v x (Id - R)e_i]x
---------------------------- R
--- ||v||^{2}
end
function TransformationMatrix3x4SO3:updateOutput(_tranformParams)
local transformParams = _tranformParams
--[[if _tranformParams:nDimension()==1 then
transformParams = addOuterDim(_tranformParams)
else
transformParams = _tranformParams
end]]--
--self:check(transformParams)
local batchSize = transformParams:size(1)
if self.fullMode then
self.output = transformParams:view(batchSize, 3, 4)
else
local completeTransformation = torch.zeros(batchSize,4,4):typeAs(transformParams)
completeTransformation:select(3,1):select(2,1):add(1)
completeTransformation:select(3,2):select(2,2):add(1)
completeTransformation:select(3,3):select(2,3):add(1)
completeTransformation:select(3,4):select(2,4):add(1)
local transformationBuffer = torch.Tensor(batchSize,4,4):typeAs(transformParams)
local paramIndex = 1
if self.useRotation then
--local alphas = transformParams:select(2, paramIndex)
local omega_x = transformParams:select(2,paramIndex)
local omega_y = transformParams:select(2,paramIndex+1)
local omega_z = transformParams:select(2,paramIndex+2)
paramIndex = paramIndex + 3
local omega_skew = torch.Tensor(batchSize,4,4):typeAs(transformParams)
omega_skew:zero()
omega_skew:select(3,1):select(2,2):copy(omega_z)
omega_skew:select(3,1):select(2,3):copy(-omega_y)
omega_skew:select(3,2):select(2,1):copy(-omega_z)
omega_skew:select(3,2):select(2,3):copy(omega_x)
omega_skew:select(3,3):select(2,1):copy(omega_y)
omega_skew:select(3,3):select(2,2):copy(-omega_x)
omega_skew_sqr = torch.bmm(omega_skew,omega_skew)
local theta_sqr = torch.pow(omega_x,2) + torch.pow(omega_y,2) + torch.pow(omega_z,2)
local theta = torch.pow(theta_sqr,0.5)
local sin_theta = torch.sin(theta)
local sin_theta_div_theta = torch.cdiv(sin_theta,theta)
local one_minus_cos_theta = torch.ones(theta:size()):typeAs(transformParams) - torch.cos(theta)
--local one_minus_cos_theta = torch.add(torch.ones(theta:size()), -torch.cos(theta) )
local one_minus_cos_div_theta_sqr = torch.cdiv(one_minus_cos_theta,theta_sqr)
local sin_theta_div_theta_tensor = torch.ones(omega_skew:size()):typeAs(transformParams)
local one_minus_cos_div_theta_sqr_tensor = torch.ones(omega_skew:size()):typeAs(transformParams)
for b = 1, batchSize do
if theta_sqr[b] > self.threshold then
sin_theta_div_theta_tensor[b] = sin_theta_div_theta_tensor[b]:fill(sin_theta_div_theta[b])
one_minus_cos_div_theta_sqr_tensor[b] = one_minus_cos_div_theta_sqr_tensor[b]:fill(one_minus_cos_div_theta_sqr[b])
else
sin_theta_div_theta_tensor[b] = sin_theta_div_theta_tensor[b]:fill(1)
one_minus_cos_div_theta_sqr_tensor[b] = one_minus_cos_div_theta_sqr_tensor[b]:fill(0)
end
end
--- need to add boundary conditions i.e. when the size of the rot vector is very small ~ = 0
completeTransformation = completeTransformation + torch.cmul(sin_theta_div_theta_tensor,omega_skew) + torch.cmul(one_minus_cos_div_theta_sqr_tensor, omega_skew_sqr)
-- print (completeTransformation)
-- transformationBuffer:zero()
-- transformationBuffer:select(3,3):select(2,3):add(1)
-- local cosines = torch.cos(alphas)
-- local sinuses = torch.sin(alphas)
-- transformationBuffer:select(3,1):select(2,1):copy(cosines)
-- transformationBuffer:select(3,2):select(2,2):copy(cosines)
-- transformationBuffer:select(3,1):select(2,2):copy(sinuses)
-- transformationBuffer:select(3,2):select(2,1):copy(-sinuses)
-- completeTransformation = torch.bmm(completeTransformation, transformationBuffer)
end
self.rotationOutput = completeTransformation:narrow(2,1,3):narrow(3,1,3):clone()
if self.useScale then
-- local scaleFactors = transformParams:select(2,paramIndex)
paramIndex = paramIndex + 1
transformationBuffer:zero()
transformationBuffer:select(3,1):select(2,1):copy(scaleFactors)
transformationBuffer:select(3,2):select(2,2):copy(scaleFactors)
transformationBuffer:select(3,3):select(2,3):add(1)
completeTransformation = torch.bmm(completeTransformation, transformationBuffer)
end
self.scaleOutput = completeTransformation:narrow(2,1,3):narrow(3,1,3):clone()
-- print ( self.scaleOutput )
if self.useTranslation then
local txs = transformParams:select(2,paramIndex)
local tys = transformParams:select(2,paramIndex+1)
local tzs = transformParams:select(2,paramIndex+2)
transformationBuffer:zero()
transformationBuffer:select(3,1):select(2,1):add(1)
transformationBuffer:select(3,2):select(2,2):add(1)
transformationBuffer:select(3,3):select(2,3):add(1)
transformationBuffer:select(3,4):select(2,4):add(1)
transformationBuffer:select(3,4):select(2,1):copy(txs)
transformationBuffer:select(3,4):select(2,2):copy(tys)
transformationBuffer:select(3,4):select(2,3):copy(tzs)
-- print (transformationBuffer)
completeTransformation = torch.bmm(completeTransformation, transformationBuffer)
-- print (completeTransformation)
end
self.output=completeTransformation:narrow(2,1,3)
--print(self.output)
end
if _tranformParams:nDimension()==1 then
self.output = self.output:select(1,1)
end
return self.output
end
function TransformationMatrix3x4SO3:updateGradInput(_tranformParams, _gradParams)
local transformParams, gradParams
if _tranformParams:nDimension()==1 then
transformParams = addOuterDim(_tranformParams)
gradParams = addOuterDim(_gradParams):clone()
else
transformParams = _tranformParams
gradParams = _gradParams:clone()
end
local batchSize = transformParams:size(1)
if self.fullMode then
self.gradInput = gradParams:view(batchSize, 6)
else
local paramIndex = transformParams:size(2)
self.gradInput:resizeAs(transformParams)
if self.useTranslation then
local gradInputTranslationParams = self.gradInput:narrow(2,paramIndex-2,3)
local tParams = torch.Tensor(batchSize, 1, 3):typeAs(transformParams)
tParams:select(3,1):copy(transformParams:select(2,paramIndex-2))
tParams:select(3,2):copy(transformParams:select(2,paramIndex-1))
tParams:select(3,3):copy(transformParams:select(2,paramIndex))
paramIndex = paramIndex-3
local selectedOutput = self.scaleOutput
local selectedGradParams = gradParams:narrow(3,1,4):narrow(3,4,1):transpose(2,3)
gradInputTranslationParams:copy(torch.bmm(selectedGradParams, selectedOutput))
local gradientCorrection = torch.bmm(selectedGradParams:transpose(2,3), tParams)
gradParams:narrow(3,1,3):narrow(3,1,3):add(1,gradientCorrection)
end
if self.useScale then
local gradInputScaleparams = self.gradInput:narrow(2,paramIndex,1)
local sParams = transformParams:select(2,paramIndex)
paramIndex = paramIndex-1
local selectedOutput = self.rotationOutput
local selectedGradParams = gradParams:narrow(2,1,2):narrow(3,1,2)
gradInputScaleparams:copy(torch.cmul(selectedOutput, selectedGradParams):sum(2):sum(3))
gradParams:select(3,1):select(2,1):cmul(sParams)
gradParams:select(3,2):select(2,1):cmul(sParams)
gradParams:select(3,1):select(2,2):cmul(sParams)
gradParams:select(3,2):select(2,2):cmul(sParams)
end
if self.useRotation then
--local rParams = transformParams:select(2,paramIndex)
local rotationDerivative = torch.zeros(batchSize, 3, 3):typeAs(transformParams)
local gradInputRotationParams = self.gradInput:narrow(2,1,1)
--torch.sin(rotationDerivative:select(3,1):select(2,1),-rParams)
--torch.sin(rotationDerivative:select(3,2):select(2,2),-rParams)
--torch.cos(rotationDerivative:select(3,1):select(2,2),rParams)
--torch.cos(rotationDerivative:select(3,2):select(2,1),rParams):mul(-1)
rotationDerivative = dR_by_dvi(transformParams,self.rotationOutput,1, self.threshold)
local selectedGradParams = gradParams:narrow(2,1,3):narrow(3,1,3)
gradInputRotationParams:copy(torch.cmul(rotationDerivative,selectedGradParams):sum(2):sum(3))
rotationDerivative = dR_by_dvi(transformParams,self.rotationOutput,2, self.threshold)
--local selectedGradParams = gradParams:narrow(2,1,3):narrow(3,1,3)
gradInputRotationParams = self.gradInput:narrow(2,2,1)
gradInputRotationParams:copy(torch.cmul(rotationDerivative,selectedGradParams):sum(2):sum(3))
rotationDerivative = dR_by_dvi(transformParams,self.rotationOutput,3, self.threshold)
--local selectedGradParams = gradParams:narrow(2,1,3):narrow(3,1,3)
gradInputRotationParams = self.gradInput:narrow(2,3,1)
gradInputRotationParams:copy(torch.cmul(rotationDerivative,selectedGradParams):sum(2):sum(3))
end
end
if _tranformParams:nDimension()==1 then
self.gradInput = self.gradInput:select(1,1)
end
return self.gradInput
end