[Tex/LaTex] Advices on drawing a complex figure using tikz

Question

I'm working on wedding invitations and there's a logo that identifies the braid and the broom. Originally this was taken from the internet in a low resolution and quality that ruins up the overall aspect of the invitation. I'd like to draw this complex figure using Tikz, which I show below:

As you can see, the quality of the picture isn't very high and is going to look worse when it gets printed out.

There are a couple of open flanks on which I'd need some advice, to say:

Contour of the heart:

I'd like the heart to look just like the one located on the lower right corner of the following image: http://1.bp.blogspot.com/-BDWeR0RCqfU/Tec8AcrN6MI/AAAAAAAAFDw/CsikMUj4PYI/s1600/HeartCurves_801.gif
That means plotting a parametric equation. So far, I've been trying to plot the equation, but I don't find a way to plot such a function. Here is the code I've tried

 \documentclass[10pt,final]{article}
 \usepackage[utf8]{inputenc}
\usepackage[paperwidth=21cm, paperheight=10.5cm, top=4mm, left=8mm, right=8mm, bottom=4mm]{geometry}
\usepackage{fontspec}
\usepackage[german]{babel}
\usepackage{tikz}
\usepackage{graphicx}
\begin{document}
\begin{tikzpicture}[domain=0:4]
      \draw[->] (-3,0) -- (4.2,0) node[right] {$x$};
      \draw[->] (0,-3) -- (0,4.2) node[above] {$y$};
      \draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9);
       \draw[scale=0.5,domain=-3:3,smooth,variable=\x,red]  plot ({2*cos(\x r)*cos(\x r)*cos(\x r)},{\x});
    \end{tikzpicture}
\end{document} 

The question here is how to plot the parametric function.

Branches:

I've wondering how to produce the lines representing the branches within the heart. I was considering to produce the lines using the classical control points, but I guess there must be better ways to produce them. Also, another problem that I see is to define the branches within the contour of the heart.

Leaves:

For the leaves I have a simple solution that uses the control points.

\documentclass[10pt,final]{article}
 \usepackage[utf8]{inputenc}
\usepackage[paperwidth=21cm, paperheight=10.5cm, top=4mm, left=8mm, right=8mm, bottom=4mm]{geometry}
\usepackage{fontspec}
\usepackage[german]{babel}
\usepackage{tikz}
\usepackage{graphicx}
\begin{document}
\begin{tikzpicture}[domain=0:4]
\fill [green](0,0) .. controls (1,1)   and (2,0.5).. (3,0);
\fill [green] (0,0) .. controls (1,-1)  and (2,-0.5).. (3,0);
\draw [green](-0.5,0)--(0,0);

    \end{tikzpicture}
\end{document} 

I could use the @Qrrbrbirlbel's answer (Use a custom shape as a "building block") as a base to define the leave as shapes, but the problem that arises here is to place the leaves at specific point of the branches at specific angles.

Answer 1

How to convert image to tikz using inkscape

1. Open inkscape and import the image

2. Select the image and use Trace Bitmap...

3. For the image you posted I selected the following configuration:

4. The resulting vectorised version of your image:

If the lines are not smooth enough or too smooth, these parameters can be adjusted in the trace options.

At this point I would simply save the vector image as .pdf and use it with \includegraphics.

5. To convert the image to tikz, there exists and extension. [Be careful, the resulting file size may be huge]