Remove small objects -- Liver image segmentation

Question

I need to make a liver image segmentation starting from a matrix of Hounsfield units (input-image) and a mask approximation of the liver (input-mask).

After some processing, I ended up with this representation of the liver. The main problem now is how to remove those small objects and keep only the liver in the image. I will explain what I did to obtain this image:

1) Hounsfield thresholding + Normalization - After this step, the image looks like this

def slice_window(img, level, window):
    low  = level - window / 2
    high = level + window / 2
    return img.clip(low, high)

# `hu_mat` is the input image
hu_mat_slice = slice_window(hu_mat, 100, 50)

def translate_ranges(img, from_range_low, from_range_high, to_range_low, to_range_high):
    return np.interp(img,
                    (from_range_low, from_range_high),
                    (to_range_low, to_range_high))

hu_mat_norm = translate_ranges(hu_mat_slice, hu_mat_slice.min(), hu_mat_slice.max(), 0, 1)

2) ROI (Convex Hull) + Binarizing - After this step, the image looks like this

I tried to isolate the liver as much as I could by using the initial mask approximation. I generated the Convex Hull and kept only the points inside the convex hull.

def in_hull(hull, points, x):
    hull_path = Path(points[hull.vertices])
    # radius=25: "expands" the polygon; this ensures me the liver will not end up cutted
    return hull_path.contains_point(x, radius=25)

hu_mat_hull = np.zeros((len(hu_mat_norm), len(hu_mat_norm[0])))
for i in range(len(hu_mat_norm)):
    for j in range(len(hu_mat_norm[0])):
        if not in_hull(hull, points, (i, j)):
            hu_mat_hull[i][j] = 0
        else:
            hu_mat_hull[i][j] = hu_mat_norm[i][j]

threshold_confidence = 0.5
hu_mat_binary = np.array([[0 if el < threshold_confidence else 1 for el in row] for row in hu_mat_hull])

3) Remove small objects

For this part, I tried to use the some morphology for removing the small objects from the image:

from skimage import morphology
hu_mat_bool = np.array(hu_mat_binary, bool)
rem_small = morphology.remove_small_objects(hu_mat_bool, min_size=1000).astype(int)

I used different values for the min_size parameter, but this is the best resulted image. Actually, it removes something, but very little. Those small objects which are close to the liver are ignored.

I've also tried to find contours in the image and keep only the largest one:

from skimage import measure
contours = measure.find_contours(hu_mat_orig_hull, 0.95)

The found contours are present here. I tried to make a dilation starting from the small contours, but didn't succeed to remove the small objects from the image.

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What else should I try in order to remove those small objects and generate a mask similar to this?