CRTP with Derived templated class failed to compile with error "has already been initialized"

Question

EDIT: As suggested, I reformat all the question to be much shorter and straight to the point, if you want all the code, check the edit.

Im trying to explicitly instantiate a CRTP template in a .cpp for 2 reasons,

1. Enable only specific types of Pixel (mostly arithmetic)
2. Speed up compilation time using a .cpp

But by using the following, I have problem with the explicit instantiation at the end of the .cpp, here the code:

Pixel.h

#include <cstdio>               // std::size_t
#include <initializer_list>     // std::initializer_list

template<typename T, std::size_t N, template<typename> class Derived>
struct Pixel
{
    // Friend the derived class to allow it to use current ctor.
    friend Derived<T>;

public:

    T ch[N];

    void print() const;

    // Ctor are protected to avoid instantiation of Pixel object
    // but they are needed to create the array object at the end.
protected:
    Pixel();
    Pixel(T val);
    Pixel(const std::initializer_list<T>& list);
};



template<typename T>
struct PixRGB : public Pixel<T, 3, PixRGB>
{
    // Create an alias for an easy accessor over the base class.
    using Base = Pixel<T, 3, PixRGB>;

    PixRGB();
    PixRGB(T val);
    PixRGB(const std::initializer_list<T>& list);
};

Pixel.cpp

#include "Pixel.h"    

#include <algorithm>    // std::copy
#include <iostream>     // std::cout
#include <string>       // std::to_string

template<typename T, std::size_t N, template<typename> class Derived>
Pixel<T, N, Derived>::Pixel() {}    

template<typename T, std::size_t N, template<typename> class Derived>
Pixel<T, N, Derived>::Pixel(T val) { for (int i = 0; i < N; i++) ch[i] = val; }    

template<typename T, std::size_t N, template<typename> class Derived>
Pixel<T, N, Derived>::Pixel(const std::initializer_list<T> & list)
{ std::copy(list.begin(), list.end(), std::begin(ch)); }    

template<typename T, std::size_t N, template<typename> class Derived>
void Pixel<T, N, Derived>::print() const {
    for (int i = 0; i < N; i++)
        std::cout << std::to_string(ch[i]) << " ";
}

// PixRGB
template<typename T> 
PixRGB<T>::PixRGB() : Base() {}

template<typename T> 
PixRGB<T>::PixRGB(T val) : Base(val) {}

template<typename T> 
PixRGB<T>::PixRGB(const std::initializer_list<T> & list) : Pixel<T, 3, PixRGB>(list) {}    

// Explicit instantiation
template struct PixRGB<float>;
template struct Pixel<float, 3, PixRGB>;

Main.cpp

#include <iostream>    
#include "Pixel.h"

int main()
{
    std::cout << "Sizeof PixRGB<float> : " << sizeof(PixRGB<float>) << std::endl;

    PixRGB<float> a = { 1.0f, 2.0f, 3.0f };
    a.print();

    return 0;   
}

The compilation error

Pixel.cpp(42): error C2614: 'PixRGB<float>': illegal member initialization: 'Pixel<float,3,PixRGB<float> >' is not a base or member
Pixel.cpp(42): note: while compiling class template member function 'PixRGB<float>::PixRGB(const std::initializer_list<T> &)'
        with
        [
            T=float
        ]
Pixel.cpp(45): note: see reference to class template instantiation 'PixRGB<float>' being compiled
Pixel.cpp(41): error C2437: 'Base': has already been initialized
Pixel.cpp(41): note: while compiling class template member function 'PixRGB<float>::PixRGB(T)'
        with
        [
            T=float
        ]
Pixel.cpp(40): error C2437: 'Base': has already been initialized
Pixel.cpp(40): note: while compiling class template member function 'PixRGB<float>::PixRGB(void)'

Note that I tried to change Base(list) to Pixel<T,3,PixRGB>(list) for testing purpose, and the error message change (as shown above), if I put back Base(list), the error is similar to other two ctors.

The above compile/execute well if I change the template of Pixel to be:

template<typename T, std::size_t N, class Derived>

But I need to know typename such as Derived to support function as this one:

template<typename T2>
Derived<T2> convert() const;