It is a pure geometry problem that can be solved in the Python console

The problem:

Find the midpoint of a segment x1,y1,x2,y2 is easy

x = (x1 + x2)/2
y = (y1 + y2)/2

so in the Python console

def mid(pt1, pt2):
   x = (pt1.x() + pt2.x())/2
   y = (pt1.y() + pt2.y())/2
   return QgsPoint(x,y)

def pair(list):
   '''Iterate over pairs in a list '''
    for i in range(1, len(list)):
        yield list[i-1], list[i]

def create_geometry(point,pr):
    # create geometry record 
    seg = QgsFeature()
    seg.setGeometry(QgsGeometry.fromPoint(point))
    pr.addFeatures( [seg] )

# memory layer
pt_layer = QgsVectorLayer("Point", "midpoint", "memory")
pr = pt_layer.dataProvider()

for elem in mylayer.selectedFeatures():
    line = elem.geometry()
    for seg_start, seg_end in pair(line.asPolyline()):
       line_start = QgsPoint(seg_start)
       line_end = QgsPoint(seg_end)
       # midpoint 
       midpt= mid(line_start, line_end)
       # add midpoint point to layer
       create_geometry(midpt,pr)
       pt_layer.updateExtents()

QgsMapLayerRegistry.instance().addMapLayers([pt_layer])

Result

It is a pure geometry problem that can be solved in the Python console

The problem:

Find the midpoint of a segment x1,y1,x2,y2 is easy

x = (x1 + x2)/2
y = (y1 + y2)/2

so in the Python console

def mid(pt1, pt2):
    x = (pt1.x() + pt2.x())/2
    y = (pt1.y() + pt2.y())/2
    return QgsPoint(x,y)

def pair(list):
    '''Iterate over pairs in a list '''
    for i in range(1, len(list)):
        yield list[i-1], list[i]

def create_geometry(point, pr):
    # create geometry record 
    seg = QgsFeature()
    seg.setGeometry(QgsGeometry.fromPoint(point))
    pr.addFeatures( [seg] )

# memory layer
pt_layer = QgsVectorLayer("Point", "midpoint", "memory")
pr = pt_layer.dataProvider()

for elem in mylayer.selectedFeatures():
    line = elem.geometry()
    for seg_start, seg_end in pair(line.asPolyline()):
        line_start = QgsPoint(seg_start)
        line_end = QgsPoint(seg_end)
        # midpoint 
        midpt = mid(line_start, line_end)
        # add midpoint point to layer
        create_geometry(midpt,pr)
        pt_layer.updateExtents()

QgsMapLayerRegistry.instance().addMapLayers([pt_layer])

Result