This is a question about pattern recognition and feature extraction.
I am familiar with Hough transforms, the Fast Radial Transform and variants (e.g., GFRS), but these highlight circles, spheres, etc.
I need an image filter that will highlight the centroid of a series of spokes radiating from it, such as the center of a asterix or the spokes of a bicycle wheel (even if the round wheel is obscured. Does such a filter exist?
The Hough Transform extended to orthogonal ellipses uses this model, accumulating on $\theta$ for all $\{x, y\}$ with parameter matrix
\begin{Bmatrix} c_x & c_y \\ r_x & r_y \end{Bmatrix}
where
$$1 = \dfrac {(x - c_x) \, \cos \theta} {r_x} + \dfrac {(y - c_y) \, \sin \theta} {r_y}$$
The question is looking to detect the normal lines, so any of the several algorithms for the above model can be modified to accumulate on $r$ for all $\{x, y\}$ with parameter matrix
\begin{Bmatrix} c_x & c_y \\ r_x & r_y \end{Bmatrix}
where
$$0 = \dfrac {x - c_x} {r_x} + \dfrac {y - c_y} {r_y}$$
Lines that intersect $(c_x, c_y)$ don't rely on $r_x$ or $r_y$. However, it may be useful to recognize that, if radially equally spaced, viewing the lines from a position other than one that projects into the plane of the lines at $(c_x, c_y)$ will present a line density that is a function of $\arctan (r_x, r_y)$.
First step would be getting the object out of the scene. This bit is not trivial in your case, however, there are many methods to choose from. I suggest reading about watershed threshold algorithm.
Second part is easier. Once you have a single segmented object at hand, perform noise removal. Next step is to extract the contours. Find the center of gravity, transform coordinates to polar and represent these contours as a function which has the x axis as degrees and y axis as distance from the center. Take the Fourier transform of this function. If the shape is symmetrical, there will be few non-zero entries, and a large spike in the spectrum.
